CUET General Test

118 General Test for CUET Difference Series Characteristics of Series Increasing Series Decreasing Series Difference between successive 5 9 13 17 48 40 32 24 numbers is same. +4 +4 +4 –8 –8 –8 Difference between successive 10 19 37 64 27 18 11 6 numbers is in Arithmetic Progression (AP). +9 +18 +27 –9 –7 –5 9, 18 and 27 are in AP. –9, –7 and –5 are in AP. Difference between successive 11 17 29 47 154 119 91 70 numbers is multiple of a par- +6 +12 +18 –35 –28 –21 ticular number. 6, 12 and 18 are multiples of 6. –35, – 28 and – 21 are multiples of 7. Difference between successive 7 32 68 117 40 15 –1 –10 numbers is a perfect square. +52 +62 +72 –(5)2 –(4)2 –(3)2 Difference between successive 10 21 34 51 70 50 37 20 1 numbers is prime number. +11 +13 +17 +19 –13 –17 –19 11, 13, 17, 19 are prime numbers. –13, –17, –19 are prime numbers. Difference between successive 36 12 24 48 36 30 27 number is in GP (Geometric +12 Progression). +3 +6 –12 –6 –3 3, 6, 12 are in GP. – 12, – 6 and – 3 are in GP. Ratio Series Characteristics of Series Increasing Series Decreasing Series Ratio between each subsequent number is same. 2 10 50 250 1250 3125 625 125 25 5 Ratio between each subsequent ×5 ×5 ×5 ×5 ÷5 ÷5 ÷5 ÷5 number is in Arithmetic Progression (AP). 1 5 40 440 660 60 7.5 1.5 Ratio between each subsequent ×5 ×8 ×11 ÷11 ÷8 ÷5 number is a perfect square number. 3 12 192 6912 44100 900 36 4 Ratio between each subsequent number is the multiple of a ×22 ×42 ×62 ÷72 ÷52 ÷32 particular number. 5 10 40 320 108 18 6 3 Ratio between each subsequent number is a prime number. ×2 ×4 ×8 ÷6 ÷3 ÷3 3 6 18 90 150 30 10 3 ×2 ×3 ×5 ÷5 ÷3 ÷2

Arithmetic 119 Ratio between each subsequent 13 18 216 729 27 3 1 number is in Geometric ×12 Progression (GP). ×3 ×6 ÷27 ÷9 ÷3 3, 6, 12 are in GP. 27, 9, 3 are in GP. Alternating Series In an alternating series, the successive terms increase and decrease alternately. This series is formed by performing two different kinds of operations alternately on successive terms. For example, 5 48 10 48 15 12 20... +5 +5 +5 ÷ (1)2 ÷ (2)2 Here, Ist, IIIrd, Vth and VIIth terms form a series having difference between subsequent terms by same number i.e., 5. Here, IInd, IVth and VIth terms form a different series having ratio between subsequent terms as the square of a number. Illustrative Examples 1. Look at this series: 3, 4, 7, 8, 11, 12, ... . What 3. Find out the wrong term in the given series. number should come next? 143, 156, 169, 182, 221, 232, 274 Sol. This alternating addition series begins with 3; Sol. There are two series. then 1 is added to give 4; then 3 is added to give 7; then 1 is added and so on. First is 143, 169, 221, 247 Hence the required number is 15. as 143 + 26 = 169 2. Find the next term in the series: C4x, F9U, 116R, 169 + 52 = 221 ........... . 221 + 26 = 247 Sol. Since, the series follows the following patterns: Second is 156, 182, 234 1st letter: C +3 F +3 I +3 L as 156 + 26 = 184 Number: 4(22) 9(32) 16(42) 25 (52) 182 + 52 = 234 3rd letter: X –3 U –3 R –3 O Thus complete series is 143, 156, 169, 182, 221, 234, 247. Hence the required answer is L25O. EXERCISE Directions (Q. No. 1–20) : Look at the series in the 3. V, VIII, XI, XIV, —, XX, ... following questions and fill in the blanks. (A) IX (B) XXIII 1. F2, —, D8, C16, B32, ... (C) XV (D) XVII (A) A16 (B) G4 4. 70, 71, 76, —, 81, 86, 70, 91, ... (C) E4 (D) E3 (A) 70 (B) 71 2. 664, 332, 340, 170, —, 89, ... (C) 80 (D) 96 (A) 85 (B) 97 5. 8, 43, 11, 41, —, 39, 17, ... (C) 109 (D) 178 (A) 8 (B) 14 (C) 43 (D) 44

120 General Test for CUET 6. VI, 10, V, 11, —, 12, III, ... Directions (Q. Nos. 21-30). Find the wrong term in each (A) II (B) IV of the following series. (C) IX (D) 14 21. 14, 28, 112, 672, 5374, 53760 7. (1/9), (1/3), 1, —, 9, ... (A) 112 (B) 672 (A) (2/3) (B) 3 (C) 5374 (D) 28 (C) 6 (D) 27 22. 6, 10, 27, 104, 505, 3084, 21581 8. 93, 73, 93, 63, 93, —, 93, 43, ... (A) 3084 (B) 27 (A) 33 (B) 53 (C) 21581 (D) 505 (C) 73 (D) 93 23. 2, 4, 8, 30, 105, 420, 1890 9. 15, —, 27, 27, 39, 39, ... (A) 4 (B) 8 (A) 51 (B) 39 (C) 30 (D) 105 (C) 23 (D) 15 24. 16, 19, 21, 30, 46, 71, 107 10. 72, 76, 73, 77, 74, —, 75, ... (A) 19 (B) 21 (A) 70 (B) 71 (C) 71 (D) 107 (C) 75 (D) 78 25. 48, 24, 72, 34, 108, 54 11. J14, L16, —, P20, R22, ... (A) 54 (B) 34 (A) S24 (B) N18 (C) 108 (D) 72 (C) M18 (D) T24 26. 25, 80, 245, 735, 2225 12. XXIV, XX, —, XII, VIII, ... (A) 80 (B) 245 (A) XXII (B) XIII (C) 735 (D) 2225 (C) XVI (D) IV 27. 25, 52, 65, 56, 95, 105 13. U32, V29, —, X23, Y20, ... (A) 52 (B) 56 (A) W26 (B) W17 (C) 95 (D) 105 (C) Z17 (D) Z26 28. 81, 9, 144, 14, 225, 15, 324, 18 14. 2, 1, (1/2), (1/4), — (A) 81 (B) 225 (A) (1/3) (B) (1/8) (C) 14 (D) 18 (C) (2/8) (D) (1/16) 29. 4, 7, 12, 13, 16 15. 7, 10, 8, 11, 9, 12, — (A) 7 (B) 12 (A) 7 (B) 10 (C) 13 (D) 16 (C) 12 (D) 13 30. 6, 11, 18, 27, 36 16. 58, 52, 46, 40, 34, — (A) 11 (B) 18 (A) 26 (B) 28 (C) 27 (D) 36 (C) 30 (D) 32 31. Mr Rohit Roy has booked a flat with a builder. The builder promised to hand over the flat in 17. 31, 29, 24, 22, 17, — the Month of June 2012. But he was able to hand over the flat only in December, 2013. Mr Rohit (A) 15 (B) 14 noticed that in contract letter there was a clause for penalty, that read as—In case of default the (C) 13 (D) 12 builder is liable to pay a penalty of ` 20,000 for the first month, ` 25,000 for the second month, 18. 1.5, 2.3, 3.1, 3.9, — ` 30,000 for the third month and so on. Mr Roy took legal help and charged the builder with (A) 4.2 (B) 4.4 due penalty. How much money would Mr Roy receive? (C) 4.7 (D) 5.1 19. 201, 202, 204, 207, — (A) 205 (B) 208 (C) 210 (D) 211 20. 544, 509, 474, 439, — (A) ` 20,000 (B) ` 50,000 (A) 404 (B) 414 (C) ` 1,20,000 (D) ` 1,65,000 (C) 420 (D) 445

Arithmetic 121 32. The second day of trade fair drew double the km to reach his destination. How much money crowd that was there on the first day. Third day did he pay for bus ticket? saw the number of visitors triple as on the first dayand so, on. If on second day the number of (A) ` 18 (B) ` 20 visitors was 20,000. How many people visited the fair during first four days? (C) ` 30 (D) ` 36 (A) 40,000 (B) 80,000 35. In a competitive exam, scoring pattern is as follows: (C) 1,00,000 (D) 1,20,000 • 5 marks for each correct answer 33. Mrs Shama wanted a group discussion among • (– 2) marks for each incorrect answer the students of her class. She divided the students in groups of 4. From each group one • 0 marks for each unaswered question student was sent out. However, one student from a group kept sitting. The teacher allocated Four friends, namely Sumit, Pushpa, Gurmeet last student of each group an identification and Danny appeared in the exam. There were number as given below. 60 questions in booklet. Two days later, they downloaded the correct answers from internet 6, 9, 15, 21, 24, 28 and tallied their answers, as shown in the table. Which friend will score the least? What was the number of the student who missed Correct Incorrect Unanswered going out? Sumit 35 20 5 (A) 21 (B) 24 (C) 28 (D) 30 Pushpa 32 8 20 34. State bus service has recently revised its fare as Gurmeet 34 6 20 following : For first 5 km — ` 2 per km Danny 40 5 15 Next 10 km — ` 1.5 per km (A) Sumit (B) Pushpa (C) Gurmeet (D) Danny Up to next 40 km — ` 1 per km In addition to the distance cost, a fixed charge of ` 2 is added to each ticket. Mr Puri travelled 18 ANSWERS 1. (C) 2. (D) 3. (D) 4. (A) 5. (B) 6. (B) 7. (B) 8. (B) 9. (D) 10. (D) 11. (B) 12. (C) 13. (A) 14. (B) 15. (B) 16. (B) 17. (A) 18. (C) 19. (D) 20. (A) 21. (C) 22. (D) 23. (B) 24. (A) 25. (B) 26. (C) 27. (D) 28. (C) 29. (B) 30. (D) 31. (D) 32. (C) 33. (C) 34. (C) 35. (A)

IX.  PROFIT AND LOSS Important Points 1. Cost price. The price at which an article is purchased is called its Cost Price. It is abbreviated as C.P. 2. Selling price. The price at which an article is sold is called its selling price. It is abbreviated as S.P. 3. Profit. If S.P. > C.P., then the seller is said to have a profit (Gain) and Profit = S.P. – C.P. 4. Loss. If C.P. > S.P., then the seller is said to have a loss and Loss = C.P. –S.P. 5. Profit and Loss are always calculated on Cost Price and are usually expressed as a percentage. Illustrative Examples 1. A businessman purchased a car for ` 8000 and Sol. Cost of 34 kg of tea @ ` 22.50 per kg sold it for ` 11000. What was his gain per cent? = 34 × 22.50 = ` 765 Sol. C.P. = ` 8000 Cost of 29 kg of tea @ ` 15 per kg S.P. = ` 11000 = 29 × 15 = ` 435 Gain = 11000 – 8000 = ` 3000 Total amount of tea = 34 + 29 = 63 kg  Gain on ` 8000 = ` 3000 Total investment = ` 765 + ` 435 = ` 1200 ∴ Gain on ` 100 = 3000 × 100 =` 37 1 Profit on ` 1200 @ 5% = 1200 × 5 = ` 60 8000 2 100 ∴ Profit = 37 1 % . Hence he should sell 63 kg of tea for 2 ` (1200 + 60) 2. The C.P. of 12 pens is equal to S.P. of 10 pens. = ` 1260 Find gain per cent. 1260 Sol. Let C.P. of 12 pens be ` 100 or he should sell 1 kg of tea for ` 63 i.e. for ` 20. ∴ S.P. of 10 pens = ` 100 5. A bicycle agent allows 20% discount on his marked price and then makes a profit of 20% on ∴ S.P. of 12 pens = 100 × 12 = ` 120 10 his out lay (C.P.). What is the marked price in which he gains ` 40? ∴ Profit on ` 100 = 120 – 100 = ` 20 ∴ Profit = 20%. Sol. Let the marked price of the bicycle be ` 100 3. A dishonest dealer professes to sell his goods at cost price, but he used a weight of 900 gm for a S.P. of the bicycle = 100 – 20 = ` 80 kg. Find his gain per cent. Profit = 20% Sol. Let C.P. of 1 gm = ` 1  If S.P. is ` 120, then C.P. = ` 100 ∴ C.P. of 900 gm = ` 900 ∴ If S.P. is ` 80, then C.P. = 100 × 80 =` 200 S.P. of 900 gm = C.P. of 1 kg = ` 1000 120 3 ∴ Profit of ` 900 = 1000 – 900 = ` 100 Actual gain = 80 – 200 =` 40 3 3 100 1 ∴ Profit of ` 100 = 900 × 100 =` 11 9  If gain is ` 40 , then marked price = ` 100 3 ∴ Profit percent = 11 1 % . ∴ If gain is ` 1, then marked price 9 4. A shopkeeper mixes 34 kg of tea which costs = 100 × 3 =` 300 ` 22.50 per kg with 29 kg of tea which costs 40 40 ` 15 per kg. At what rate he must sell the mixture ∴ If gain is ` 40, then marked price so that he may get a profit of 5% on the total = 300 × 40 = ` 300. investment. 40 145

146 General Test for CUET 6. A man sold his radio at a loss of 5%. He had ∴ Second S.P. of radio = 90 + 90 = ` 112.50 4 purchased it at 10% lesser cost price and sold it at ` 42 more selling price then he would have Difference in two S.P. = ` 112.50 – 95 had a gain of 1 of the C.P. Find the C.P. of the = ` 17.50 radio. 4  When difference in ` 17.50, then C.P. Sol. Suppose C.P. of radio = ` 100 = ` 100 ∴ When difference in ` 42, then C.P. First S.P. = 100 – 5 = ` 95 Second C.P. of radio = 100 – 10 = ` 90 100 × 42 17.50 Profit on it = 1 × 90 =` 90 = = ` 240 4 4 ∴ C.P. of radio = ` 240. EXERCISE 1. If C.P. is ` 300 and profit is 15%, find S.P. 9. Oranges were purchased at the rate of 11 oranges for ` 1. How many oranges be sold for (A) ` 345 (B) ` 354 ` 39 in order to get 30% profit? (C) ` 300 (D) ` 400 (A) 230 (B) 320 2. If C.P. is ` 150 and loss 20%, find S.P. (C) 300 (D) 330 (A) ` 100 (B) ` 120 1 3 (C) ` 130 (D) ` 85 10. A man got 25 % loss by selling a horse 3. Find profit percent if C.P. is ` 60 and S.P. is for ` 1000. If he had sold the horse for ` 67.50. ` 1200, find his loss percent. (A) 10% (B) 12 1 % (A) 12.5% (B) 10.5% 2 (C) 10.4% (D) 10% 1 (C) 15% (D) 7 2 % 11. An article was sold at 15% profit. If that article would have been sold at 25% loss, then ` 20 less 4. Find loss percent if C.P. is ` 75 and S.P. is ` 60. would have been got. Find the C.P. of the article. (A) 10% (B) 15% (A) ` 50 (B) ` 40 (C) 20% (D) 25% (C) ` 100 (D) ` 60 5. In selling an article for ` 24, as much percentage loss occurs as is the C.P. Find the C.P. of the 12. Suresh sells his goods at 20% profit to Ramesh. article. Ramesh sells that goods to Mahesh at 25% profit. If Mahesh purchased that goods for ` 210, (A) ` 10 or ` 50 (B) ` 20 or ` 50 for how many rupees did Suresh purchase the goods? (C) ` 30 or ` 50 (D) ` 40 or ` 60 6. Ramesh purchased a goat. He sold it for (A) ` 120 (B) ` 160 ` 31.25 and got as much percent of profit as (C) ` 140 (D) ` 180 much is the C.P. of the goat. Find the C.P. of the 13. A manufacturer sells goods to an agent goat. at a profit of 10%. The agent's whole sale price to a shopkeeper is at a profit of 20% (A) ` 20 (B) ` 25 and the shopkeeper retails his goods at a profit of 25%. Find the manufacturing (C) ` 10 (D) ` 50 cost of goods bought from the shop for ` 41.25. 7. A man purchased 10 quintals of wheat for ` 625 and sold them at 10% profit. Find at what rate did he sell the wheat? (A) ` 68.75/Quintal (B) ` 50/Quintal (A) ` 20 (B) ` 25 (C) ` 80/Quintal (D) ` 100/Quintal (C) ` 30 (D) ` 40 8. A man purchased 11 knives for ` 10 and sold at 14. The S.P. of 120 copies is equal to C.P. of 150 the rate of 10 knives for ` 11. Find profit percent. copies. Find the gain percent. (A) 10% (B) 25% (C) 21% (D) 20%

Arithmetic 147 (A) 25% (B) 20% 23. A tradesman defrauds by means of a false balance to the extent of 10% in buying and to (C) 30% (D) 40% the same extent, in selling goods. What percent does he gain on his outlay by defraud? 15. By selling 150 mangoes, a shopkeeper gets profit equal to S.P. of 30 mangoes. Find his gain (A) 20% (B) 21% percent. (A) 50% (B) 15% (C) 15% (D) 25% (C) 20% (D) 25% 24. A man purchases a horse and a carriage. If he sells the horse at 10% loss and carriage at 20% 16. If a man sold 150 chairs for rupees equal to the profit, he neither gains nor loses. If he sells the C.P. of 120 chairs, find the loss percent. horse at 5% gain and carriage at 5% loss he loses ` 10 in all. Find the cost price of the horse. (A) 20% (B) 15% (C) 30% (D) 10% (A) ` 200 (B) ` 300 17. A bicycle agent allows 25 percent discount on (C) ` 400 (D) ` 500 his marked price and then makes a profit of 20 25. The cost price of 4 chairs and 5 tables is percent on his outlay. What is the marked price ` 330. If the chair are sold at 25% loss and tables on which he gains ` 40? at 25% profit, then the total S.P. of all is ` 372.50. (A) ` 240 (B) ` 350 Find the cost price of a chair. (C) ` 300 (D) ` 320 (A) ` 20 (B) ` 10 18. A tradesman marks his goods at 25% above cost (C) ` 15 (D) ` 25 price. If he allows his customers 10% discount, how much percent profit does he make? 26. A man sells two cows @ ` 1995 each. He gets 15% profit on one and 15% loss on the other. Find the (A) 10% (B) 12% total loss in percent. (C) 12.5% (D) 7.5% (A) 2 1 % (B) 2 1 % 2 4 19. A shopkeeper makes a profit of 20% even after giving a discount of 10% on the marked price (C) 3 1 % (D) 3 1 % 4 2 of an article,. If the marked price of the article is ` 500, What is the cost of the article? 27. A man purchase 10 cows for ` 37500. He sells 6 cows at 10% loss. 4 cow die. At what rate should (A) ` 400 (B) ` 375 he sell the remaining cows so as to get a profit of 10% on total investment? (C) ` 250 (D) ` 350 20. How much percent more than the cost price (A) ` 1725 per cow (B) ` 2000 per cow should a shopkeeper mark on his goods so that after allowing discount of 12 1 % , he should (C) ` 1500 per cow (D) ` 2250 per cow 2 28. A man purchased 840 oranges. He sells 1 of have a gain of 5% in his outlay? 4 (A) 20% (B) 10% these at 20% loss. At what percent profit should (C) 25% (D) 15% he sell the remaining oranges so as to get a profit of 20% overall? 21. A man bought a merchandise whose price was listed at ` 160. He was given successive (A) 30% (B) 33 1 % 3 discounts of 20% and 10%. Determine the price (C) 35% (D) 40% he paid for the merchandise. (A) ` 110 (B) ` 115.20 29. An item costing ` 200 is being sold at 10% loss. If the price is further reduced by 5%, the selling (C) ` 117.50 (D) ` 137 price will be 22. A dishonest shopkeeper professes to sell pulses (A) ` 170 (B) ` 171 at the cost price but uses a false weight of 950 gm. Find his gain percent. (C) ` 175 (D) ` 179 (A) 5 4 % (B) 5 2 % Hint. S.P. of item = ` 180 19 19 S.P. after 5% further reduction (C) 4 13 % (D) 5 5 % = 180 – 180 × 5 = 171. 19 19 100

148 General Test for CUET 30. A bicycle is sold at 20 percent profit. If it had = ` 120x =` 6x been sold at 20 percent loss, the selling price 100 5 would have been ` 100 less. The cost price of the and S.P. at 20% loss cycle is 80x 4x (A) 200 (B) 250 = ` 100 =` 5 (C) 300 (D) 350 ∴ 6x – 4x = 100 5 5 Hint. Let the C.P. of the cycle be ` x. Then, S.P. at 20% profit ⇒ x = 250. ANSWERS 1. (A) 2. (B) 3. (B) 4. (C) 5. (D) 6. (B) 7. (A) 8. (C) 9. (D) 10. (C) 11. (A) 12. (C) 13. (B) 14. (A) 15. (D) 16. (A) 17. (D) 18. (C) 19. (B) 20. (A) 21. (B) 22. (D) 23. (B) 24. (C) 25. (A) 26. (B) 27. (A) 28. (B) 29. (B) 30. (B)

XII.  TIME AND DISTANCE Important Points 1. Distance = Speed × Time 2. Time = Distance Speed 3. Speed = Distance Time 4. 18 kilometres per hour = 5 metres per second. 5. If two bodies are moving in the same direction, they will cross each other with a speed equal to the difference of their speeds. 6. If two bodies are moving in the opposite direction, then their relative velocity will be equal to the sum of their speeds. 7. If the speed of a body is changed in a certain ratio say 3 : 4 then the time taken by it to travel a given distance is changed into the inverse ratio i.e. 4 : 3. Illustrative Examples 1. A train runs at a speed of 60 kilometres per hour. or 9x + 244 – 4x = 324 Express its speed in metres/second. or 5x = 324 – 244 = 80 Sol. 60 kilometres per hour 80 5 60 × 1000 or x = = 16 kilometres 60 × 60 = Hence the distance travelled on foot = 16 2 metres/second. = 16 km. 3 3. A train 100 metres long meets a man going in 2. A man travelled a distance of 61 kilometres opposite direction at the rate of 5 km/hr and in 9 hours partly on foot at the rate of passes him in 7.2 seconds. At what rate is the 4 kilometres per hour and partly on bicycle at 9 train going? kilometres per hour. Find the distance travelled on foot. Sol.  The distance covered by the train in 7.2 second Sol. Total distance travelled = 61 kilometres = 100 metres = 100 km 1000 Suppose distance travelled on foot = x kilometres = 1 km. ∴ Distance travelled by bicycle = (61 – x) kilometres 10 Total time taken = 9 hours ∴ The distance covered by the train in 3600 seconds Time taken in travelling on foot = x hours = 1 × 3600 km = 50 km. 4 10 × 7.2 Time taken in travelling by bicycle ∴ Speed of train + speed of man = 50 km/hr. = 61 – x hours ∴ Speed of the train = 50 – 5 = 45 km/hr. 9 4. The distance between two cities A and B ∴ x + 61 – x = 9 is 110 m. A motor-cycle rider starts from 4 9 A towards B at 7 a.m. with speed of 10 km/hr. Another motor-cyclist starts from or 9x + 4 (61 – x) = 9 B towards at 8 a.m. with a speed of 25 36 km/hr. Find when will they cross each other? or 9x + 4(61 – x) = 36 × 9 = 324 Sol. Suppose they meet after x hrs from the start of the first rider from A. 158

Arithmetic 159 Then the distance travelled by first rider in x hrs hour. Prove that the train stops on an average per hour 12 minutes. = 20x km Sol.  Time taken by train to cover 50 kms and the distance travelled by second rider in = 60 minutes (x – 1) hrs = 25(x – 1) km ∴ Time taken by train to cover 40 km 20x + 25(x – 1) = 110 = 60 × 40 50 or 45x = 110 + 25 = 135 = 48 minutes or x = 3 hrs. Hence the train stops per hour Hence they will meet each other at 10 a.m. 5. A train without stoppages travels on an average 60 – 48 = 12 minutes. 50 km an hour, and with stoppages 40 km an EXERCISE 1. A train runs at a speed of 45 km per hour. 6. A person has to reach a place 40 km away. Express its speed in metres per second. He walks at the rate of 4 km/hr for the first 16 km and then travels in a rickshaw for the rest (A) 12 1 metres/sec of the journey. However, if he had travelled 3 by rickshaw for the 16 km and covered the remaining distance on foot at 4 km/hr, he would (B) 25 metres/sec have taken an hour longer to complete the journey. Find the speed of the rickshaw. (C) 10 metres/sec (D) 30 metres/sec 2. Express a speed of 22 ft/sec in miles/hr. (A) 10 km/hr (B) 8 km/hr (A) 10 miles/hr (B) 15 miles/hr (C) 12 km/hr (D) 15 km/hr (C) 20 miles/hr (D) 25 miles/hr 7. Ramesh travels 600 km to reach home, partly by train and the rest by car. He takes 8 hrs, if he 3. A student walks from his house at 2 1 km an travels 120 kms. by train and the rest by car. But 2 he would take 20 minutes more, if he were to travel 200 kms by train and the rest by car. Find hour and reaches his school 6 minutes late. The out the ratio of speed of the train with speed of car. next day he increases his speed by one km an hour and reached 6 minutes early. How far is the school from his house? (A) 11 km (B) 9 km (A) 3 : 4 (B) 4 : 3 4 4 (C) 3 : 5 (D) 5 : 3 (C) 5/4 km (D) 7/4 km 8. A person has to make a journey of 72 kms. He 4. A student reaches his school late by 6 minutes if he travels from his house at a rides a cycle at 12 km/hr. After going a certain speed of 5 km/hr. The next day he increases his speed by 1 km/hr and thus reached his school 6 distance, the cycle is punctured and he walks minutes earlier. Find the distance of school from his house. the remaining distance at 4 1 km/hr. Find when 2 the cycle is punctured if the total time for the (A) 5 km (B) 10 km journey is 8 1 hrs. 2 (C) 6 km (D) 8 km (A) 45 kms (B) 54 kms 5. I am to reach a fixed place. If I travel at (C) 36 kms (D) 50 kms a speed of 3 km/hr. I shall reach late by 40 minutes. If I travel at a speed of 4 km/hr. I 9. I travelled one-third of a journey with a speed of shall reach early by 30 minutes. How far am I 10 km per hour, the next one-third with a speed to go? of 9 km per hour, and the rest at a speed of 8 km per hour. If I had travelled half the journey at a (A) 12 km (B) 14 km speed of 10 km per hour and the other half with a speed of 8 km per hour, I would have been a (C) 10 km (D) 15 km minute longer on the way. What distance did I travel?

160 General Test for CUET (A) 18 km (B) 24 km 17. A motorist covers the distance of 60 km from A to B at a speed of 20 km per hour and return (C) 20 km (D) 30 km journey from B to A at a speed of 30 km per hour. Determine the average speed of the motorist for 10. A man rows a kilometre down the stream in 5 the entire journey. minutes and up the stream in 15 minutes. Find the velocity of the stream. (A) 16 km/hr (B) 18 km/hr (A) 3 km/hr (B) 10 km/hr (C) 24 km/hr (D) 30 km/hr (C) 5 km/hr (D) 4 km/hr 18. A train 150 metres long passes a telegraph post in 12 seconds. Find the speed of the train. In 11. A man rows 15 kilometres down the stream in 3 what time will it pass a bridge 250 metres long? hours 45 minutes and 5 kilometres up stream in 2 hours 30 minutes. Find his speed in still water. (A) 40 km/hr, 30 seconds (A) 4 km/hr (B) 2 km/hr (B) 45 km/hr, 32 seconds (C) 3 km/hr (D) 5 km/hr (C) 50 km/hr, 40 seconds 12. A man can row three quarters of a kilometre (D) 60 km/hr, 20 seconds against the current in 11 1 minutes and returns 19. The driver of a car driving at the speed of 4 38 km/hr locates a bus 40 metres ahead of him. After 20 seconds the bus is 60 metres behind. in 7 1 minutes. Find the speed of man in still Find the speed of the bus. 2 water. (A) 25 km/hr (B) 10 km/hr (A) 2 km/hr (B) 3 km/hr (C) 15 km/hr (D) 20 km/hr (C) 4 km/hr (D) 5 km/hr 20. The speed of a motor boat of length 20 metres in water without current is 13. A boat can be rowed 6 km/hr along the current 40 km/hr. If the motor boat, sailing against a and 4 km/hr against the current. Find the speed river current of 3 km/hr crosses a temple on the of the current. bank in 10 seconds, find the length of the temple. (A) 1 km/hr (B) 2 km/hr (C) 3 km/hr (D) 4 km/hr (A) 50 metres (B) 60 metres 14. A monkey ascends a greased pole (C) 80 metres (D) 100 metres 12 metres high. He ascends 3 metres in first minute and slips down 1 metre in the alternate 21. A train 100 metres long meets a man going in minute. In which minute, he reached the top of opposite direction at the rate of 10 km/hr and the pole? passes him in 7.2 seconds. At what rate is the train going on? (A) 9th (B) 10th (A) 20 km/hr (B) 40 km/hr (C) 11th (D) 12th (C) 30 km/hr (D) 50 km/hr 15. A monkey ascends a greased pole 22. A 60 metres long train travelling at 15 metres high ascending 5 metres in 1st minute, 42 km/hr crosses a train 84 metres long travelling and slipping down 2 metres in another minute at 30 km/hr in the same direction. How long will repeating this process, in what time, shall he it take to fully cross it? reach the top? (A) 42.2 seconds (B) 41.2 seconds 3 (A) 9 minutes (B) 8 5 minutes (C) 40.2 seconds (D) 43.2 seconds (C) 10 3 minutes (D) 11 minutes 23. A car covers a distance of 840 km with 5 a constant speed. If its speed were 10 km/hr more, it would have taken 2 hrs less to 16. The average speed of a train including stoppages cover the distance. Find the speed of the car. was 27 km per hour, excluding stoppages, it was 41 km per hour. How many minutes per hour (A) 40 km/hr (B) 60 km/hr did the train stop? (C) 50 km/hr (D) 80 km/hr (A) 20 1 minutes (B) 25 1 minutes 24. A and B each walks 24 km. The sum of their 2 2 speeds is 7 kilometre per hour and the sum of the times taken is 14 hrs. Find their speeds. (C) 24 1 minutes (D) 16 1 minutes 2 2 (A) 4, 3 (B) 5, 2 (C) 1, 6 (D) 3 1 , 3 1 2 2

Arithmetic 161 25. A thief is spotted by a policeman from a distance that of policeman 12 km per hour, how far the of 200 metres. When the policeman starts the thief will have run before he is overtaken? chase, the thief also starts running. Assuming the speed of the thief to be 10 km per hour and (A) 1 km (B) 2 km (C) 3 km (D) 4 km ANSWERS 1. (A) 2. (B) 3. (D) 4. (C) 5. (B) 6. (B) 7. (A) 8. (B) 9. (A) 10. (D) 11. (C) 12. (D) 13. (A) 14. (C) 15. (B) 16. (A) 17. (C) 18. (B) 19. (D) 20. (C) 21. (B) 22. (D) 23. (B) 24. (A) 25. (A)

II.  THEORY OF QUADRATIC EQUATIONS Important points 1. An equation of the form ax2 + bx + c = 0 where a, b and c are constants and a ≠ 0 is called a quadratic equation. 2. It must be kept in mind that a quadratic equation cannot have more than two roots. 3. Suppose α and β are the roots of the quadratic equation ax2 + bx + c = 0, then we have α = – b + b2 – 4ac ...(1) 2a and β = – b – b2 – 4ac ...(2) 2a Clearly, α + β = – b = – coefficient of x ...(3) and a coefficient of x2 αβ = c a = Absolute constant term ...(4) Coefficient of x2 The given quadratic equation is, ax2 + bx + c = 0 or x2 + b x + c = 0 a a or x2 – a– b kx + c = 0 a a From (3) and (4), or x2 – (α + β)x + αβ = 0 ...(5) or (x – α) (x – β) = 0 ...(6) which is showing that α, β are the roots of ax2 + bx + c = 0. Equation (5) can be stated as follows x2 – (Sum of the roots)x + Product of the roots = 0 or x2 – Sx + P = 0 ...(7) where S = sum of the roots P = product of the roots From equation (7), we can very easily form a quadratic equation whose roots are given. 4. Nature of the roots of a quadratic Equation: The roots of the quadratic equation ax2 + bx + c = 0 are α = – b + b2 – 4ac 2a and β = – b – b2 – 4ac . 2a It is quite obvious that the discrimination of the nature of the roots depends upon the value of b2 – 4ac (viz., the expression under the radical sign) which for the same reason is known as the 'Discriminant' of the quadratic. 5. The following results are to be remembered. 1. If b2 – 4ac is +ve then the roots are real and unequal; they are rational if b2 – 4ac is a perfect square, and irrational it is not a perfect square. 192

Algebra 193 2. If b2 – 4ac = 0, then the roots are evidently real, rational and equal, each of them being b/2a. 3. If b2 – 4ac is –ve then the roots are imaginary and unequal. N.B. It should be borne in mind that the constants a, b and c are supposed to be real and rational quantities. Illustrative Examples 1. Examine the nature of the roots of a2 b2 b a 3x2 + 5x + 4 = 0. Given roots are and Sol. Here a=3 a2 + b2 a3 + b3 b a ab b = 5 ∴ S = = c = 4 = (a + b) 3 – 3ab (a + b) So that b2 – 4ac ab = (5)2 – 4.3.4 a– b 3 – 3 c a– b k a a a = 25 – 48 k = c = – 23. a which is a negative quantity. – b3 + 3bc = a3 a2 Hence the roots are imaginary and unequal. c = 3abc – b3 a2c 2. Examine the nature of the roots of the equation a 25x2 + 20x + 4 = 0. a2 b2 Sol. Here a = 25 and P = b . a b = 20 = αβ = c a c = 4 ∴ b2 – 4ac Hence the required equation is = (20)2 – 4 × 25 × 4 x2 – Sx + P = 0 = 400 – 400 = 0 or x2 – 3abc – b3 x + c = 0 a2c a Hence the roots are real, rational and equal. or a2cx2 – (3abc – b3)x + ac2 = 0. 3. Examine the nature of the roots of the quadratic equation 5. Find the condition that the two quadratic equations a1x2 + b1x + c1 = 0 and a2x2 + b2x + c2 = 0 3x2 + 3x – 1 = 0. have both roots common. Sol. Here a=3 b = 3 Sol. Let the common roots of the two equations c = – 1 a1x2 + b1x + c1 = 0 ...(1) and a2x2 + b2x + c2 = 0 ...(2) ∴ b2 – 4ac be α and β = (3)2 – 4 × 3 × (– 1) = 9 + 12 = 21. Then from (1) α + β = – b1 , and αβ = c1 a1 a1 Which is a +ve quantity but not a perfect square. Hence the roots are real, unequal and irrational. and from (2) α + β = – b2 , and αβ = c2 a2 a2 4. If the roots of ax2 + bx + c = 0 are α and β, find the equation whose roots are a2 and b2 . ∴ – b1 = – b2 , and c1 = c2 b a a1 a2 a1 a2 Sol. The roots of ax2 + bx + c = 0 are α and β or a1 = b1 = c1 a2 b2 c2 α + β = – b ...(1) a which are the required condition. and αβ = c ...(2) a

194 General Test for CUET EXERCISE 1. The equation whose roots are 4 and 5 is 9. The quadratic equation, whose roots are 2 and 5 4 – 15, is given by (A) 20x2 – 41x + 20 = 0 (A) x2 – 2x + 15 = 0 (B) x2 + 15x – 2 = 0 (B) 20x2 + 41x + 20 = 0 (C) x2 + 13x – 30 = 0 (D) x2 – 30 = 0 (C) 20x2 + 41x – 20 = 0 (D) 20x2 – 4x – 20 = 0 Hint. S = Sum of the roots = 2 + (– 15) 2. Examine the nature of the roots of the equation = – 13 x2 + 2x + 1 = 0 P = Product of the roots (A) imaginary, unequal = (2) (– 15) (B) real, rational and equal = – 30 ∴ The required equation is (C) real, unequal, rational (D) real, unequal, irrational x2 – Sx + P = 0 3. If 25x2 – px + 9 = 0 has equal roots, find p ⇒ x2 + 13x – 30 = 0 (A) 30 (B) 20 10. If one root of the equation ax2 + bx + c = 0 is the (C) 10 (D) 25 reciprocal of the other, then 4. Find the equation whose roots are the (A) a = b (B) b = c reciprocals of the roots of the equation (C) a = c (D) a = – c ax2 + bx + c = 0 11. The product of the reciprocals of the roots of the (A) bx2 + cx + a = 0 (B) bx2 + ax + c quadratic equation 2x2 + x + 1 = 0 is (C) cx2 + ax + b = 0 (D) bx2 + bx + a = 0 (A) 1 (B) 2 5. Find the condition that one root of ax2 + bx + c = (C) 3 (D) 4 0 is double of the other Hint. Let the roots of the quadratic equation 2x2 + x + 1 = 0 be α and β. Then, (A) 3b2 + 16ac = 0 (B) 2b2 + 9ac = 0 (C) 3b2 = 16ac (D) 2b2 = 9ac 1 2 6. What is the value of m if one root of αβ = 2x2 – 10x + m = 0 is 2 of the other? ∴ Product of the reciprocals of the roots 3 (A) 9 (B) 10 = 1 . 1 = 1 = 1 = 2 a b ab 1 (C) 11 (D) 12 a 2 k 7. If the roots of the equation x2 – bx + c = 0 are 12. If α, β are the roots of the equation x2 + 7x + 12 = 0, then α2 + β2 equals α and β, then the value of 1 + 1 is a3 b3 (A) 14 (B) 19 (A) b3 –c33bc (B) b3 +c33bc (C) 24 (D) 25 Hint.  α, β are the roots of the equation (C) – b3c+3 3bc (D) – b3 +c33bc x2 + 7x + 12 = 0 ∴ α + β = 7 8. If α and β are the roots of the equation and αβ = 12 2x2 – 3x – 5 = 0 Now, α2 + β2 = (α + β)2 – 2αβ find the equation whose roots are (α – β)2 and (α + β)2 = 49 – 24 = 25 (A) 16x2 + 232x + 441 = 0 13. Given the roots of x2 – 2px + 8p – 15 = 0 are equal, (B) 16x2 – 232x – 441 = 0 the value of p is equal to (C) 16x2 – 232x + 441 = 0 (D) 16x2 + 232x – 441 = 0 (A) 3 or 5 (B) 2 or 5 (C) 3 or 4 (D) 2 or 4

Algebra 195 Hint. For equal roots, discriminant = 0 3x2 + (k – 1)x + 9 = 0, then ⇒ (– 2p)2 – 4(8p – 15) = 0 3(3)2 + (k – 1) 3 + 9 = 0 ⇒ 4p2 – 4(8p – 15) = 0 ⇒ p2 – 8p + 15 = 0 ⇒ 27 + (k – 1) 3 + 9 = 0 ⇒ 3(k – 1) + 36 = 0 ⇒ (p – 3) (p – 5) = 0 ⇒ k – 1 + 12 = 0 ⇒ p = 3 or  5 ⇒ k = – 11 14. Roots of the quadratic equation x2 – 5x – 6 = 0 are 17. If the equation x2 – ax + 1 = 0 has two distinct (A) Equal but negative (B) Unequal but of same signs roots, then the value of a is precisely different (C) Unequal but of opposite signs from (A) 1 and – 1 (B) 2 and – 2 (D) Equal but positive (C) 1 and 2 (D) – 1 and – 2 Hint. x2 – 5x – 6 = 0 18. The graph of a quadratic equation is ⇒ x2 + x – 6x – 6 = 0 (A) A circle (B) Any curve ⇒ x(x + 1) – 6(x + 1) = 0 (C) A parabola ⇒ (x + 1)(x – 6) = 0 (D) None of the above ⇒ x = – 1, 6 19. The point or points where a quadratic polynomial cuts x-axis are called 15. The quadratic equation with rational (A) Turning points co-efficients with one root equal to 1 – √2 is (B) Zeros (A) x2 – 2x + 1 = 0 (B) x2 – 2x – 1 = 0 (C) Ordinates (C) x2 – 2x + 2 = 0 (D) x2 – 2x – 2 = 0 16. x = 3 is a solution of the equation (D) None of the above 3x2 + (k – 1)x + 9 = 0 if k has the value 20. The graph of a quadratic function ax2 + bx + c is (A) 13 (B) – 13 concave upwards when (C) 11 (D) – 11 (A) a > 0 (B) a < 0 Hint. If x = 3 is a solution of the equation (C) a = 0 (D) a > 1 ANSWERS 1. (A) 2. (B) 3. (A) 4. (D) 5. (D) 6. (D) 7. (A) 8. (C) 9. (C) 10. (C) 11. (B) 12. (D) 13. (A) 14. (C) 15. (B) 16. (D) 17. (B) 18. (C) 19. (C) 20. (B)

SECTION D LOGICAL AND ANALYTICAL REASONING

8 Verbal and Non-Verbal Reasoning I.  ANALOGY TEST Important Points Analogy test tests your ability to determine relationship existing between pair of words or letters or numbers. In questions based on analogy, you are given a pair of words or letters or numbers having certain relationship. From the alternatives provided, you have to select the choice that set off by a colon or a ratio sign (:) signifying that word A is related to word B. The double colon (::) that separates the given pair stands for in the same way. Words Analogy is concerned with some relationships as given below: 1. Individual and Class (iii) Blacksmith : Anvil (iv) Carpenter : Saw e.g., Whale : Mammal (v) Tailor : Needle (vi) Chef : Knife Whale belongs to the class of Mammal. Some (vii) Soldier : Gun more examples are given below: (viii) Surgeon : Scalpel 5. Study and Topic (i) Rat : Rodent (ii) Ostrich : Bird e.g., Botany : Plants Botany is the study of Plants. (iii) Snake : Reptile (iv) Man : Mammal Some more examples are given below: (i) Oology : Eggs 2. State and Capital (ii) Zoology : Animals (iii) Ornithology : Birds e.g., Uttar Pradesh : Lucknow (iv) Entomology : Insects (v) Seismology : Earthquakes Lucknow is the capital of Uttar Pradesh. (vi) Onomatology : Names 6. Animal and Young One Some more examples are given below: e.g., Cat : Kitten Kitten is the young one of Cat. (i) Rajasthan : Jaipur Some more examples are given below: (i) Hen : Chicken (ii) Goa : Panaji (ii) Lion : Cub (iii) Cow : Calf (iii) Karnataka : Bangaluru (iv) Sheep : Lamb (v) Horse : Pony (iv) Sikkim : Gangtok (vi) Dog : Puppy 3. Word and Antonym e.g., Gentle : Harsh Gentle and Harsh are antonyms of each other. Some more examples are given below: (i) Fresh : Stale (ii) Lend : Borrow (iii) Chaos : Peace (iv) Cruel : Kind (v) Sink : Float (vi) Initial : Final 4. Worker and Tool e.g., Woodcutter : Axe Axe is the tool used by Woodcutter. Some more examples are given below: (i) Sculptor : Chisel (ii) Author : Pen 233

234 General Test for CUET 7. Male and Female 8. Word and Synonym e.g., Horse : Mare e.g., Ban : Prohibition Mare is the female Horse. Ban and Prohibition are synonyms of each other. Some more examples are given below: Some more examples are given below: (i) Stag : Doe (i) Vacant : Empty (ii) Son : Daughter (ii) Substitute : Replace (iii) Lion : Lioness (iii) Brim : Edge (iv) Nephew : Niece (iv) Mend : Repair (v) Dog : Bitch (v) Sedate : Calm (vi) Drone : Bee (vi) House : Home Alphabet Analogy is concerned with facts stated in Coding-Decoding chapter is applied in problem- solving. In Number Analogy it is necessary to know about the prime numbers, square numbers, square roots, cube numbers and cube roots. Following key points are necessary for solving analogy questions: • Analyse the relationship between the question pair. • Look for the pair of words among the answer choices with a similar relationship. • If more than one answer choices seems to fit, re-examine the relationship in the question pair. • Eliminate answers that do not appear to be the best. • Parts of speech must be same in the related words/letters/numbers. EXERCISE 1. Book : Paper :: Table : ? 8. Grapes : Wine :: Wheat : ? (A) Forest (B) Wood (A) Grain (B) Maize (C) Carpenter (D) Wood Cutter (C) Bread (D) Field 2. Ocean : Ship :: Desert : ? 9. Child : Father :: Book : ? (A) Horse (B) Elephant (A) Author (B) Publisher (C) Sledge (D) Camel (C) Editor (D) Library 3. Diving : Water :: Skating : ? 10. Pyorrhea : Teeth :: Trachoma : ? (A) Ice (B) Sky (A) Eye (B) Skin (C) Mountain (D) Space (C) Lungs (D) Ear 4. Brave : Coward :: Praise : ? 11. Gun : Bullet :: Chimney : ? (A) Applaud (B) Scold (A) House (B) Ground (C) Comment (D) Appreciate (C) Roof (D) Smoke 5. Smoke : Pollution :: War : ? 12. Ancient : Modern :: Often : ? (A) Victory (B) Death (A) Commonly (B) Repeatedly (C) Enemy (D) Army (C) New (D) Seldom 6. Newspaper : Editor :: Film : ? 13. Mother : Daughter :: Aunt : ? (A) Actor (B) Director (A) Cousin (B) Brother (C) Audience (D) Producer (C) Sister (D) Niece 7. Cobbler : Shoe :: Carpenter : ? 14. Cow : Calf :: Lioness : ? (A) Furniture (B) Gold (A) Lion (B) Cub (C) Wood (D) Iron (C) Pub (D) Chick

Verbal and Non-Verbal Reasoning 235 15. Feather : Soft :: Diamond : ? 22. House : Windows :: Man : ? (A) Light (B) Hard (A) Eyes (B) Brain (C) Sharp (D) Costly (C) Speech (D) Emotion 16. Cloth : Metre :: Gold : ? 23. Crocodile : Crawl :: Frog : ? (A) Gram (B) Litter (A) Walk (B) Hop (C) Ton (D) Sovereign (C) Jump (D) Creep 17. Doctor : Medicine :: Teacher : ? 24. Fire : Ashes :: Explosion : ? (A) Students (B) Class (A) Flame (B) Death (C) Principal (D) Knowledge (C) Sound (D) Debris 18. Monday : Friday :: April : ? 25. Professor : Lecture :: Doctor : ? (A) August (B) Tuesday (A) Hospital (B) Disease (C) July (D) Saturday (C) Treatment (D) Patient 19. House : Wall :: Wall : ? 26. King : Throne :: Rider : ? (A) Brick (B) Roof (A) Seat (B) Horse (C) Paint (D) Sand (C) Saddle (D) Chair 20. Ankle : Knee :: Wrist : ? 27. Car : Garage :: Aeroplane : ? (A) Hand (B) Foot (A) Port (C) Elbow (D) Finger (B) Waiting Shed 21. Kangaroo : Australia :: Giraffe : ? (C) Airport (A) Africa (B) India (D) Landing Ground (C) France (D) Japan ANSWERS WITH HINTS 1. (B) Book is made of paper and table 9. (A) Father-child relationship is the same is made of wood. ‘Product’ ‘raw- as author-book relationship. material’ relationship is to be used. 10. (A) Pyorrhea is the disease of teeth while 2. (D) Ship is used to travel in ocean while trachoma is the disease of eye. What the camel is used to travel in a desert. is implied is relation between affected 3. (A) Diving is done in water while skating part of the body and the name of the is done on ice. disease. 4. (B) Coward is the antonym of brave and 11. (D) Bullet is discharged by the gun while smoke is discharged through the scold is the antonym of praise. Word- chimney. antonym relationship in to be used. 5. (B) Smoke causes pollution and 12. (D) Ancient is the antonym of modern while seldom is the antonym of war causes death. Cause - effect often. We use the word - antonym relationship is to be used. relationship for finding the answer. 6. (B) Editor is responsible for the subject matter published in the newspaper, 13. (D) Since mother is to daughter and aunt is to niece. (The relationship between while the Director of a film is senior and junior members of the responsible for the content of the film. family is to be used). 7. (A) Shoe is made by the cobbler while furniture is made by the carpenter. 14. (B) Cub is the young one of lioness; Animal and its young-one relationship Worker - produce product relationship is implied. is implied. 8. (C) Wine is prepared from grapes while 15. (B) Feather is known for its softness. Similarly diamond is known for bread is prepared from wheat. Raw its hardness. We have to deal with material and product relationship is opposites for an answer. implied.

236 General Test for CUET 16. (A) Metre is used to measure cloth. 21. (A) As natural habitat of the Kangaroo is Similarly gram is used to measure Australia, similarly the natural habitat gold. of the Giraffe is Africa. 17. (D) As the doctor prescribes medicine for 22. (A) Windows help us to see the outside patient, in the same way the teacher of the house, eyes help us to see the imparts knowledge to students. surroundings. 18. (A) Friday comes three days after 23. (B) Crocodile crawls from one place to Monday; likewise August comes another; frog hops from one place to three months after April. another. 19. (A) As house is constructed with walls, in 24. (D) Fire followed by ashes; similarly an explosion is followed by its debries. the same way the wall is constructed 25. (C) Professor gives lectures to students, with bricks. while the doctor gives treatment to his patients. 20. (C) Similarly placed joints (last two joints) 26. (C) A king sits on a throne while a rider of the leg compared to similarly sits on his saddle. placed joints (last two joints) of the 27. (C) Car–garage relationship the same as hand; ‘C’ is the answer. As ankle is the aeroplane-airport relationship; ‘C’ is the answer. lowest part of the knee, in the same way wrist is the lowest part of elbow.

X.  ANALYTICAL REASONING AND JUMBLING Important Points In this test, you are required to analyse the given information and answer the questions. The given information have to be put in a suitable form so that the answer could be found easily. ILLUSTRATIVE EXAMPLES I. Directions (Q. No. 1 – 4): P, B, C, D, E, F and II. Directions (Q.No. 5 – 8): Study the following G are in one class. They are sitting on three information carefully and answer the questions benches, Ist, IInd and IIIrd, in such a way that given below: there are at least two of them on each bench and there is at least one girl on each bench. C, a girl A, B, C, D, E, F and G are sitting around a circle student, does not sit with P, E and D. A boy F facing at the centre F is second to the left of A sits only with B. P sits with best friend on bench and second to the right of G. E is third to the Ist; G sits on bench Ist. D sits on bench IIIrd. E is right of B and is not an immediate neighbour of brother of C. F. D is third to the right of C. Now answer the questions: 5. Who is second to the right of B? 1. On which bench do three students sit? (A) C (B) G (A) I (B) II (C) E (D) D (C) III (D) I or II 6. Who is to the immediate left of D? 2. How many girl students are there? (A) F (B) E (A) 3 (B) 4 (C) B (D) G (C) 3 or 4 (D) Data inadequate 7. Who is to the immediate right of C? 3. Who sits with C? (A) G (B) E (A) F, B (B) D (C) A (D) Data inadequate (C) E (D) G 8. In which of the following groups is the first person sitting between the second and the third 4. Who is the sister of E? person? (A) B (B) C (A) CAB (B) EGD (C) F (D) D (C) BAC (D) None of these Sol. 1. (B) As per diagram on bench II, three Sol. All informations can be drawn in a circle. students sit. A PG CB Bench I EF C F B Bench II DE GD Bench III 2. (D) Data inadequate. 5. (A) C is second to the right of B. 6. (D) G is to the immediate left of D. 3. (A) F, B sits with C. 7. (B) E is to the immediate right of C. 8. (D) None follows such condition. 4. (B) C is a sister of E. In this type of test questions are based on a set of information containing certain conditions. It is required to form the proper sequence using the information and answer the given questions. 278

Verbal and Non-Verbal Reasoning 279 EXERCISE I . Directions (Q. No. 1 – 5): A, B, C, D, E and F are the 6 8. Name the person who should change places lectures to be given from Monday to Sunday and only one with C such that he gets the third place from the lecture can be given each day. north end. (i) C should not be given on Friday (A) E (B) F (ii) A should be given just after D (C) G (D) D (iii) There should be a gap of two days between B 9. Immediately between which of the following and F pairs of people is D sitting? (iv) Except Saturday, there has to be a rest day on (A) AC (B) AF any one day. F should be delivered just before this rest day. (C) CE (D) CF (v) E should be given on Wednesday and F should 10. Which of the conditions (i) to (v) given above is not be delivered after it. not required to find out the place in which A is sitting? 1. When will lecture D be delivered? (A) (i) (B) (ii) (A) Friday (B) Saturday (C) (iii) (D) All are required (C) Sunday (D) Thursday I II. Directions (Q. No. 11 – 13): Study the following 2. Which is the rest day? information carefully and answer the questions which follow: (A) Sunday (B) Friday (C) Monday (D) None of these A, B, C, D, E and F are sitting in a straight line facing north. 3. How many lectures are given between F and D? (A) None (B) One C sits to the left of F and C does not sit on extreme of the line. (C) Two (D) Three 4. Which will be the last lecture? D is not an immediate neighbour of C. (A) A Only one person sits between D and F. (B) C Neither A nor E sits at the extreme of line. (C) B A is not an immediate neighbour of C. (D) Cannot be determined 11. How many persons sit between A and C? 5. Which of the given statements is not necessary (A) 1 to know the correct order of the lectures? (A) (i) (B) (ii) (B) 2 (C) (v) (D) (i) and (ii) (C) 3 II. Directions (Q. No. 6 – 10): Study the given information (D) Cannot be determined carefully and answer these questions: 12. Left end position is occupied by (i) A, B, C, D, E, F and G are sitting on a wall and all (A) F (B) A of them are facing east. (C) B (D) Either F or D (ii) C is to the immediate right of D 13. If persons are made to sit in an alphabetical (iii) B is at an extreme end and has E as his neighbour. order from left to right, then position of how many persons will not change? (iv) G is between E and F (v) D is sitting third from the south end (A) One (B) Two 6. Who is sitting to the right of E? (C) Three (D) None of these (A) A (B) C IV. Directions (Q. No. 14 – 17): On the basis of the information provided below, answer the following questions: (C) D (D) None of these 7. Which of the following pairs of people are P, Q, R, S, T and U are sitting on a circle facing sitting at the extreme ends? centre at equal distances. (A) AB (B) AE – P is not adjacent to Q and R (C) CB (D) FB – S is not adjacent to R or T

280 General Test for CUET – Q and R are adjacent – C sits third to the left of G. – U is in between R and S. – H sits second to the right of E but E is not an immediate neighbour of C and G. 14. Which of the following is a correct neighbour pair? – Two of them sit between A and D but A, D each are not immediate neighbour of H. (A) P and U (B) S and U (C) Q and P (D) Q and U – B is not an immediate neighbour of A and H. 15. Which of the following is in right sequence? 23. Who is the next person to HCDB (i.e. after B)? (A) P, U, Q (B) U, P, T (A) B (B) C (C) Q, R, U (D) S, P, Q (C) E (D) G 16. If one neighbour of P is S, then who is the other neighbour? 24. Three of the following four are similar in a certain way based on their positions in the (A) Q (B) R seating arrangement. Which of the following does not belong to that group? (C) T (D) U 17. Who is placed vertically opposite to T? (A) DC (B) CH (A) Q (B) R (C) GA (D) BD (C) S (D) U 25. Who represents immediate neighbour of A? V. Directions (Q. No. 18 – 22): Study the following (A) G, E (B) C, B information carefully and answer the questions given below: (C) C, H (D) H, E P, Q, R, S, T, U, V and W sit around a circular 26. F is at what position to A in the above table not necessarily in the same order, facing its arrangement? centre. V is fourth to the right of P, T is second to the right of R, P is second to the right of S. Q is (A) Third to the right second to the right of U. R is not an immediate neighbour of U or S. (B) Immediate left (C) Fifth to the right 18. Which first person of the following pair is sitting (D) Second to the right to the immediate right of the second person? VII. Directions (Q. No. 27 – 29): Read the following (A) TU (B) VU informations to answer the questions based on it: (C) WT (D) QS Seven letters are arranged in a line as follows: 19. Who sits second to the right of W? (i) E and F have one letter between them (A) T (B) V (ii) G is to the right of A (C) U (D) Data inadequate (iii) B is to the immediate left of F 20. Who is third to the left of W? (iv) There is one letter between D and A (A) P (B) S (v) D is not G's neighbour (C) Q (D) Data inadequate (vi) G and F have two letters between them 21. What is U's position with respect to R? 27. Which letter is second to the left of letter A? (A) 4th to the left (B) 5th to the left (A) C (B) B (C) 2nd to the right (D) 3rd to the right (C) D (D) E 22. Who is to the immediate right of T? 28. Which letter will be exactly in the middle of the letters series so obtained? (A) U (B) V (A) D (B) A (C) S (D) Data inadequate (C) E (D) None of the above VI. Directions (Q. No. 23 – 26): Study the following 29. Which pair of the letters is adjacent to the letter information carefully and answer the questions which B? follow: (A) A and C (B) G and E A, B, C, D, E, F, G and H are sitting on a circular table, facing its centre but not necessarily in the (C) E and F (D) C and D same order.

Verbal and Non-Verbal Reasoning 281 ANSWERS WITH HINTS I 1. (A) Friday 2. (D) None of these 3. (C) Two 4. (B) C 5. (A) (i) II 6. (D) None of these 7. (A) AB 8. (C) G 9. (D) CF 10. (D) All are required III As per directions 6 people sit on line facing north. 12 3 456 North BE C F AD C sits to the left of F and C is not on the extreme of line. So, possible seats for C will be 2, 3 or 4, 5 and 4, 6 for F. D is not immediate neighbour of C, So if C is on 3, then F is on 4 then D can occupy 5th or 6th position. Between D and F there is one person, so, this person can be A or B, as A, E don't sit on extremes. As A is not an immediate neighbour of C, So, A sits at position 5 and D on extreme right. So, B is on extreme left and E is next to him at position 2. Hence, position are as shown above. 11. (A) Only person between A and C is F therefore, one person is sitting between A and C. So, the correct option is (A). 12. (C) Left end position is occupied by B So, the correct option is (C). 13. (A) If we make them sit in an alphabetical order, i.e., 12 3 456 AB CDEF Only one position i.e., 3 remains as it is (for C). P So, the correct option is (A). TS IV 14. (B) S and U are neighbours. QU So, the correct option is (B). R 15. (C) Q, R, U are in a right sequence. So, the correct option is (C). 16. (C) T is the other neighbour of P, a part from S. So, the correct option is (C). 17. (D) T and U are vertically opposite. So, the correct option is (D).

282 General Test for CUET V 18. (D) Here, the first person Q is sitting to the immediate right of the second S U person S. Hence, only option (D) is the correct option. Q 19. (B) From above diagram, we can find that the position of person V is second to the right of W. So (B) is the correct option. P V 20. (C) The position of person Q is third to the left of W. So, (C) is the correct option. R T W 21. (A) The position of person U is fourth to the left of R. So, (A) is the correct option. 22. (B) We can find, from the above diagram that only the person V is immediate right of T. So, (B) is the right option. VI 23. (D) Next to HCDB is G. So, option (D) is correct. 24. (C) In option (A), (B) and (D), first person is sitting immediate right of second person but in option (C) the first person is sitting immediate left of second person. 25. (A) We see G and E are immediate neighbour of A. So, option (A) is correct. 26. (D) We see F is at second position to the right of A. So, option (D) is correct. VII The given figure shows the arrangement of given seven letters: DC A G E B F 27. (C) Letter D is second to the left of letter A. 28. (D) It is clear from the diagram that letter G is in the middle of the letter arrangement. 29. (C) Clearly, letters E and F are adjacent to B.

XVII.  NON-VERBAL REASONING I. Series This chapter deals with the problems based on continuation of figures. There is a sequence of figures depicting a change step-by-step. A figure has to be selected from a separate set of answer figures that would continue the sequence. Illustrative Example Select the figure from amongst the answer Answer figures figures which will continue the series given in problem figures. Problem figures (Aa) (Bb) (Cc) (Dd) (A(a)) ((Bb)) ((Cc)) ((Dd)) Sol. Clearly we find that in one step, both the arrow and the small line segment turn to the other side of the main line and in the next step, the complete figure gets rotated through 90° ACW. So accordingly, the next figure after D of problem figure is (C). EXERCISE Select a figure from amongst the answer figures which will continue the series established by the four problem figures. 3. 1. Problem figures (aA) (Bb) (Cc) (Dd) (Aa) (Bb) (Cc) (dD) ((Aa)) ((Bb)) ((Cc)) ((Dd)) Answer figures 4. ((Aa)) ((Bb)) ((Cc)) ((Dd)) (aA) (Bb) (Cc) (Dd) 2. ((Aa)) ((Bb)) ((Cc)) ((Dd)) (aA) (Bb) (Cc) (Dd) 5. (A(a)) ((Bb)) ((Cc)) ((Dd)) (aA) (bB) (Cc) (Dd) 313

314 General Test for CUET ((Aa)) ((Bb)) ((Cc)) ((dD) ) II. Analogy Analogy implies ‘correspondence or relationship’. This chapter deals with the problems based on analogy, a pair of related figures is given and a similar relationship is to be established between two other figures, by selecting one of them from a set of alternatives. Illustrative Example Problem figures Answer figures ? ((Aa)) ((Bb)) ((Cc)) ((Dd)) (aA) (Bb) (Cc) (Dd) Sol. Clearly, figure (a) rotates 45° ACW to get figure (b). Similarly, figure (c) rotates 45° ACW to get (A) of the answer figure. EXERCISE Problem figures ? 1. (Aa) (Bb) (Cc) (Dd) ((Aa)) (bB)) ((Cc)) (Dd)) (bB) (Cc) Answer figures 4. ? (aA) (Dd) (A(a)) ((Bb)) ((Cc)) ((Dd)) 2. ? ((Aa)) ((Bb)) ((Cc)) ((Dd)) (Aa) (bB) (Cc) (dD) 5. ? (Aa) (Bb) (Cc) (Dd) ((Aa)) ((Bb)) ((Cc)) ((Dd)) 3. ? (Aa) (Bb) (Cc) (Dd) ((Aa)) ((Bb)) ((Cc)) ((Dd))

Verbal and Non-Verbal Reasoning 315 III. Classification Here the problems are of ‘Odd-Man-Out’ type. A set of figures is given where all except one have similar features or correspondence. One is required to select the figure which differs from all other figures in the given set. The figure so selected is a odd-man-out. Illustrative Examples 1. 2. ((Aa)) ((Bb)) ((Cc)) ((Dd)) ((Aa)) ((Bb)) ((Cc)) ((Dd)) Sol. Clearly except figure (B), all other figures can be Sol. Looking carefully, all other figures except (D) rotated into each other. So, the answer is (B). are made of seven straight lines. In figure (D) there are eight straight lines. EXERCISE Find the odd-one-out. 6. ((Aa)) ((Bb)) ((Cc)) ((Dd)) 1. ((Aa)) ((Bb)) ((Cc)) ((Dd)) 7. ((Aa)) ((Bb)) ((Cc)) ((Dd)) 2. (A(a)) ((Bb)) ((Cc)) ((Dd)) 8. (A(a)) ((Bb)) ((Cc)) ((Dd)) 3. ((Aa)) ((Bb)) ((Cc)) ((Dd)) 9. 4. ((Aa)) ((Bb)) ((Cc)) ((Dd)) ((Aa)) ((Bb)) ((Cc)) ((Dd)) 10. 5. ((Aa)) ((Bb)) ((Cc)) ((Dd)) (A(a)) ((Bb)) ((Cc)) ((Dd))

316 General Test for CUET IV. Mirror Image The image of an objects as seen in a mirror, is called its mirror image. In this image, the right side of the object appears on the left side and vice versa. EXERCISE I. I n each of the following questions, you areK 3. PAINTED given a combination of alphabets and/or numbers WHITE (A) DETN IAP (B) DETNIAP followed by four alternatives (A), (B), (C) and (D). (C) DETNIAP (D) DE TNIAP Choose the alternative which most closely resembles the mirror-image of the given combination. 4. NATIONAL (A) LANOIT AN (B) LANOITAN 1. WHITE (C) LAN OITAN (D) LANOITAN (A) ETIHW (B) (C) ETIHW (D) E TIHW 5. JUDGEMENT (A) TNEMEGDUJ (B) TNEMEG DUJ 2. BRISK (C) TNEMEGDUJ (D) JUDGEMENT (A) KSIRB (B) KSIRB (C) K SIRB (D) SIRB II. In each of the following questions, choose the correct mirror image of the figure (X) from amongst the four alternatives (A), (B), (C) and (D). 1. (A(a)) (Bb)) ((Cc)) ((Dd)) (X(x) 2. ((Aa)) ((bB)) ((Cc)) ((Dd)) ((Xx)) 3. ((Aa)) ((Bb)) ((Cc)) ((Dd)) ((Xx)) ((Aa)) ((Bb)) ((Cc)) ((Dd)) ((Aa)) ((Bb)) ((Cc)) ((dD)) 4. ((Xx)) 5. ((Xx))

Verbal and Non-Verbal Reasoning 317 V.  Water Image The image of an object as seen in water is called its water image. It is the image obtained by turning the object inside down. EXERCISE I. In each of the following questions, a 3. (NAU) CRLAEEALRCUN (B) NUCLEAR combination of alphabet and/or numbers are followed (C) NUCLEAR (D) NUCLEAR by four alternatives (A), (B), (C) and (D). Choose the alternative which most closely resembles the water 4. QUARREL image of the given combination. (A) QUARREL (B) QUARR (C) QUARREL (D) QUA L 1. ACOUSTIC C (B) AC B (A) AC Y P (C) YLIMA YLI C ERR Y IMAF IC (D) ACUOSTICITSUO LE 5. U4P15BP715B7 U4 15B7 ITSUO 4U ITSUOCA 2. FAMILY (A) U4P15B7 (B) U4PI5 7 (A) L (B) F (C) (D) (C) FA M (D) FAMIL II. In each of the following questions, choose the correct water-image of the figure (X) from amongst the four alternatives (A), (B), (C) and (D) given along with it. 1. ((Aa)) (bB)) ((Cc)) (Dd)) (Xx)) ((Aa)) (bB)) ((Cc)) (Dd)) 2. ((Xx)) ((Aa)) ((bB)) ((Cc)) ((dD) ) 3. (A(a)) (B(b)) ((Cc)) (D(d)) ((Xx)) 4. (X(x)) 5. ((Aa)) ((Bb)) ((cC)) ((Dd)) ((Xx))

318 General Test for CUET VI. Paper Folding The problems on paper folding involve the process of selecting a figure which would most nearly match the pattern that would be formed when a transparent sheet carrying designs on either side of a dotted line is folded along this line. The figure has to be selected from a set of four alternatives (answer or response figures). Illustrative Example Find from amongst the four response figures, the one that resembles the pattern formed when the transparent sheet, carrying a design is folded along the dotted line. Transparent sheet Response figures ((Aa)) (Bb)) ((Cc)) ((dD) ) Sol. Clearly, left half is folded on the right half. Hence, triangle is inside the circle and circle is surrounding the dot. The correct answer is B. EXERCISE Transparent sheet Response figures 1. ((Aa)) ((Bb)) ((Cc)) ((dD) ) 2. ((Aa)) ((Bb)) ((Cc)) ((Dd)) 3. ((Aa)) ((bB)) ((Cc)) (Dd)) A 4. DA AD AD D AD ((Aa)) ((Bb)) ((cC) ) ((dD) )

Verbal and Non-Verbal Reasoning 319 5. ((Aa)) ((bB)) ((Cc)) ((dD) ) VII. Paper Cutting The problems on paper cutting contain a set of three figure X, Y and Z showing the manner in which a piece of paper has been folded. In each of the first two figures, a dotted line together with an arrow on it has been given indicating the line along which the paper is to be folded and the direction of the fold respectively. In the third figure, there are marks showing the position and nature of the cut made in the folded sheet. The candidate has to select one of the figures from the set of four answer figures a, b, c and d, that would most nearly match the pattern when the paper is unfolded. It will be interested to see that the designs of the cut will appear on each fold made in the paper. Illustrative Example Consider the three figures marked X, Y and Z showing one fold in X, another in Y and cut in Z. From amongst the four alternative figures A, B, C and D, select the one showing the unfolded position of Z. XYZ ((Aa)) ((Bb)) ((Cc)) ((Dd)) Sol. Clearly in Z, a triangle has been punched in the folded sheet, so punched triangle will be created in each quarter of the paper. Thus when the paper is unfolded, four triangle will appear symmetrically over it and the paper will then appear as shown in figure (D). EXERCISE In the following Questions 1 to 5, choose a figure out of (A), (B), (C) and (D) which would most closely resemble the unfolded form of figure Z. 1. XY Z ((Aa)) ((Bb)) ((Cc)) ((Dd))

320 General Test for CUET 2. X YZ ((Aa)) ((bB)) ((cC)) ((Dd)) 3. X YZ ((Aa)) ((bB)) ((cC) ) ((dD) ) 4. YZ X (A(a)) ((Bb)) ((Cc)) ((dD) ) 5. YZ X (A(a)) (B(b)) (C(c)) (D(d))

Verbal and Non-Verbal Reasoning 321 VIII. Dot Situation The problems on dot situation involve a trace of similar conditions in the alternative figures as indicated in the problem figure. The problem figure contains dots placed in the spaces enclosed between the combinations of square, triangle, rectangle and circle. Selecting one of these dots we observe the region in which the dot is enclosed i.e., to which of the four figures is this region common. The candidate now has to look for such a region in the four alternatives given. After having found it, the same procedure has to be repeated to find the other dot. Illustrative Example From amongst the figures marked (A), (B), (C) and (D) select the figure which satisfies the same conditions of placement of dots as in figure (X). (X) (A(a)) ((Bb)) (Cc)) ((Dd)) Sol. In figure (X) the dot lies in the region common to the circle and the triangle only. Such a region is present in figure (C). EXERCISE In the following questions, from the figures marked (A), (B), (C) and (D), select the one which satisfies the same conditions of placements of dots as in figure (X). 1. ((Aa)) ((Bb)) ((Cc)) ((Dd)) ((Aa)) ((Bb)) ((Cc)) ((Dd)) (X) 2. (X) 3. ((Aa)) ((Bb)) ((Cc)) ((Dd)) (X)

322 General Test for CUET 4. ((Aa)) (Bb)) ((Cc)) ((Dd)) (X) 5. (X) ((Aa)) ((Bb)) ((Cc)) ((Dd)) IX. Problems on Dice In these problems, more than two positions of a dice are given. After observing these figures, one has to find the number or a symbol opposite to a given number or symbol. Illustrative Example A dice is thrown three times and its three different positions are given below. I II III How many dots lie opposite 2 dots? (A) 1 (B) 2 (C) 5 (D) 6 From dice (II) and (III) we conclude that 1, 6, 3 and 4 dots lie adjacent to 5 dots, so 2 dots must be opposite 5 dots. Conversely 5 dots must lie opposite 2 dots. So, the answer is (C). EXERCISE 1. Three positions of a dice are given. Based on them, find out which number is found opposite the number 2 in the given cube. 6 5 4 I II III 14 36 12 I II III (A) 1 (B) 3 (A) 6 (B) 5 (C) 5 (D) 6 (C) 3 (D) 1 3. The three different positions of a dice are depicted on the next Page. Find the number of 2. Three different positions of a dice are shown dots on the face opposite to the face with one below. How many dots lie opposite 2 dots? dot.

Verbal and Non-Verbal Reasoning 323 (A) 4 (B) 5 (C) 6 (D) Cannot be determined I II III (A) 2 (B) 3 5. (C) 4 (D) 6 4. Given below are three different positions of dice. What numbers occur at the bottom face in the Find the number of dots on the face opposite the three positions of the same die? face bearing 3 dots. (A) 6, 6, 2 (B) 5, 6, 1 (C) 5, 5, 5 (D) 6, 5, 2 I II III X. Counting of Geometrical Figures in a Complex Figure In this top, a complex figure is given and it is asked to find the number of straight lines, the number of triangles or the number of squares or any other geometrical figure are contained in the complex figure. Illustrative Example 1. How many triangles are contained in the given The simplest triangles are ABE, BEF, EFC, CDE figure? and AED i.e., 5 in number. Sol. In the large given square, there is no triangle The triangles composed of two components each formed. A square within this, contains four are ABF, BCE, ACE and ABD i.e., 4 in number. triangles. There are other four smaller squares, The triangles composed of three components each containing 2 triangles, hence there are 4 + 8 each are AFC and BCD i.e., 2 in number. i.e., 12 triangles. There is only one triangle ABC composed of five 2. How many straight lines and the triangles are components. contained in the following figure. Thus, there are 5 + 4 + 2 + 1 = 12 triangles in the Sol. Clearly there are six straight lines. figure. B Hence, the answer is (6, 12). F E AD C

324 General Test for CUET EXERCISE 1. Count the number of squares in the following 4. How many triangles are there in the following figure: figure? (A) 18 (B) 14 (C) 10 (D) 9 2. How many parallelograms are there in the (A) 47 (B) 45 following figure? (C) 41 (D) 39 5. How many rectangles are contained in the following figure? (A) 20 (B) 24 (C) 28 (D) 30 3. What is the number of rectangles in the following figure? (A) 8 (B) 17 (C) 18 (D) 20 (A) 6 (B) 7 (C) 9 (D) 11 XI. Cubes and Boxes Illustrative Examples 1. Count the number of cubes in the given figure. (A) 6 (B) 8 (C) 10 (D) 12 Sol. C learly, there is 1 column containing 3 cubes, 2 columns containing 2 cubes each and 3 columns of 1 cube each. Hence, there are 3 × 1 + 2 × 2 + 1 × 3 = 10 cubes in the given figure. So, the answer is (C).

Verbal and Non-Verbal Reasoning 325 2. Select from the alternatives, the box that can be formed by folding the sheet shown in figure (X): 2 51 3 1 2 3 4 1 5 4 4 63 6 3 6 1 ((Aa)) ((Bb)) ((Cc)) ((Dd)) (X) Sol. Clearly when the sheet in figure (X) is folded to form a box (cube) then: The number 2 will lie opposite the number 4; the number 1 will lie opposite the number 6 and the number 5 will lie opposite the number 3. Figure (A) has the numbers 1 and 6 on adjacent faces, figure (B) has numbers 3 and 5 on adjacent faces and the figure (C) has the numbers 2 and 4 on the adjacent faces. So, these three alternatives are not possible. Since, the numbers 1, 3 and 4 can appear on adjacent faces, so figure (D) is possible. Hence, only box shown in figure (D) can be formed by folding figure (X). 3. Select from the alternatives, the box that can be formed by folding the sheet shown in figure (X): (A) (B) (C) (D) (X) Sol. Clearly when the sheet in figure (X) is folded to form a box (cube) then the dot and the shading must lie opposite to each other. Hence, the figures (A), (C) and (D) which bear the dot and the shading on adjacent faces cannot possibly be formed by folding the sheet in figure (X). Therefore, only cube (B) can be formed. Hence, the answer is (C). EXERCISE 1. Count the number of blocks in the following 2. Count the number of cubes in the given figure. figure. (A) 6 (B) 7 (A) 8 (B) 9 (C) 8 (D) 9 (C) 12 (D) 15

326 General Test for CUET 3. Count the number of cubes in each of the (A) 64 (B) 66 (D) 70 following figure. (C) 68 DIRECTIONS FOR QUESTIONS 4–10 The sheet of paper shown in the figure (X) given on the left hand side, in each problem, is folded to form a box. Choose from amongst the alternatives (A), (B), (C) and (D), the boxes that are similar to the box that will be formed. 4. ((Aa)) ((Bb)) ((Cc)) ((Dd)) (X) 5. ((Aa) ((bB)) (Cc)) (Dd) (D) c and d only (X) (B) b, c and d only (C) d only (A) a and c only 6. (Aa) ((bB)) (cC)) ((Dd) (B) b, c and d only (C) d only (D) c and d only (X) D (A) a and b only A F E A E F F E (dD) B E D C (D) a, b, c and d 7. B E B CD (X) (aA)) (Bb) ((cC)) (A) a only (B) b only (C) a and c only

Verbal and Non-Verbal Reasoning 327 8. (X) ((Aa)) ((Bb)) ((Cc)) ((Dd)) 9. When the following figure is folded to form a cube, how many dots would lie opposite the face bearing five dots? (A) 1 (B) 2 (C) 3 (D) 4 10. How many dots lie opposite the face having three dots, when the given figure is folded to form a cube? (A) 2 (B) 4 (C) 5 (D) 6 I. Series 2. (B) ANSWER KEY 4. (D) 5. (D) 1. (A) 2. (D) 2. (D) 3. (C) 4. (D) 5. (B) II. Analogy 7. (A) 1. (C) 2. (D) 3. (C) 4. (B) 5. (C) 2. (C) 9. (C) 10. (B) III. Classification 3. (B) 1. (D) 8. (C) 4. (B) 5. (C) 6. (B) 4. (B) 5. (C) 3. (B) IV. Mirror Image 3. (D) I. 1. (D) II. 1. (A)

328 General Test for CUET V. Water Image 2. (D) 3. (D) 4. (A) 5. (C) I. 1. (B) 4. (B) 5. (B) 4. (B) 5. (B) II. 1. (C) 2. (A) 3. (D) 4. (B) 5. (B) VI. Paper Cutting 4. (A) 5. (C) 4. (C) 5. (C) 1. (C) 2. (A) 3. (B) 4. (B) 5. (C) VII. Paper Cutting 4. (A) 5. (C) 9. (C) 10. (D) 1. (B) 2. (C) 3. (B) V III. Dot Situation 1. (D) 2. (B) 3. (C) IX. Problems on Dice 1. (A) 2. (C) 3. (D) X. Counting of Geometrical Figures in a Complex Figure 1. (B) 2. (D) 3. (C) XI. Cubes and Boxes 1. (B) 2. (D) 3. (C) 6. (D) 7. (B) 8. (D)

Mock Test Paper –1 Directions (Q. No. 1–4): Complete the passage given Malnutrition most commonly ___1___ between below by selecting the most suitable word/phrase from each the ages of six months and two years. This happens list to fill the corresponding gap. in spite of the child’s food requirements being less The world economy is in recession, the deepest than those of ___2___ child. Malnutrition is often attributed to poverty, but it has been found that even and the most widespread .......1....... the 1940. There are in households where adults eat adequate quantities of food, more than 50 per cent of children-under- .......2....... of .......3....... in the industrial countries, but five ___3___ consume enough food. The child’s dependence on someone else to feed ___4___ is most serious economic .......4....... anticipate the rate of primarily responsible for malnutrition. growth and leaves of economic activity will remain low. 1. Which of these fits gap 1? (A) since (B) in 7. Which of these fits gap 4? (C) by (D) for (A) them (B) him/her 2. Which of these fits gap 2? (C) him (D) her (A) glimmers (B) risks 8. Which of these fits gap 3? (C) tips (D) studies (A) does not (B) need not 3. Which of these fits gap 3? (C) do not (D) dare not (A) downfall (B) development 9. Which of these fits gap 1? (C) slackness (D) recovery (A) comes (B) in often 4. Which of these fits gap 4? (C) noticed (D) occurs (A) findings (B) surveys 10. Which of these fits gap 2? (C) journalists (D) analysts (A) a rich (B) a poor Directions (Q. No. 5–6): Select the most appropriate (C) an older (D) a smarter alternative in the following questions: Directions (Q. No. 11–15): Rearrange the following given 5. ‘Assault’ stands for sentences, in a proper order and answer the questions that follow. (A) reply (B) encounter 1. He ordered that tents be erected on the eastern (C) revenge (D) attack side for the fighting forces, and a little away on the western slopes tents be put up for the family 6. To look down upon is meant for members of the officers who had accompanied (A) to look front them. (B) to look down (C) to treat with contempt 2. He thought that the very presence of the British on the outskirts of Kittur would terrorise the (D) to look at rulers and people of Kittur, and that they would lay down their arms. Directions (Q. No. 7–10): In the following passage numbered blank spaces are left. For each blank space four 3. During the afternoon and evening of 20th words or phrases (1, 2, 3, 4) are given. Choose the most October, the British soldiers were busy making suitable word or phrase to fill the corresponding gap. arrangements for these camps. M-1

M-2 General Test for CUET 4. He was quite confident that he would be able to (C) Kanshi Ram crush the revolt in no time. (D) Lal Krishna Adwani 5. Thackeray reached Kittur along with a small 21. What is Zilla Parishad? British army force and a few of his officers. (A) District Panchayat (B) Block Panchayat 11. Which sentence should come second in the paragraph? (C) Gram Sabha (D) None of these (A) 1 (B) 2 22. Which country of South-East Asia has made rapid economic growth? (C) 3 (D) 4 (A) India (B) China (E) 5 (C) Nepal (D) Pakistan 12. Which sentence should come third in the 23. ‘Banking and Insurance’ belongs to which of the paragraph? following sectors? (A) 1 (B) 2 (A) Secondary (B) Primary (C) 3 (D) 4 (C) Tertiary (D) IT sector (E) 5 24. What was Dhanraj Pillay associated with? 13. Which sentence should come first in the (A) Hockey (B) Football paragraph? (C) Cricket (D) Lawn Tennis (A) 1 (B) 2 25. Which one of these is related to football? (C) 3 (D) 4 (A) Out (B) LBW (E) 5 (C) Scissor kick (D) Gully 14. Which sentence should come last in the 26. The author of the book ‘Geetanjali’ is paragraph? (A) Bankim Chandra Chattopadhyay (A) 1 (B) 2 (B) Mrinal Sen (C) 3 (D) 4 (C) Rabindranath Tagore (E) 5 (D) R.C. Dutt 15. Which sentence should come fourth in the paragraph? 27. The highest sporting award of India is (A) 1 (B) 2 (A) Arjuna Award (C) 3 (D) 4 (B) Khel Ratna Award (E) 5 (C) C.K. Naydu Award 16. When was the train used first? (D) Eklavya Award (A) 200 years ago (B) 250 years ago 28. Number of children dying per one thousand birth is called (C) 150 years ago (D) 300 years ago (A) mortality rate 17. Which was the capital of Kosala? (B) death rate (A) Hastinapur (B) Ayodhya (C) birth rate (C) Karnal (D) Delhi (D) birth and death ratio 18. What is the name given to the full moon night? 29. Which ocean contains many volcanoes? (A) Amavasya (B) Poornima (A) Indian Ocean (B) Arctic Ocean (C) Both (A) and (B) (D) None of these (C) Pacific Ocean (D) Atlantic Ocean 19. When does the longest day and the shortest night occur in the northern hemisphere? 30. Which country bagged the maximum number of medals at the 2022 Winter Olympic Games? (A) June 21 (B) September 23 (A) South Korea (B) China (C) December 22 (D) March 21 (C) Germany (D) Norway 20. Who was the chairman of the drafting committee of the Constituent Assembly of India? 31. Who has been appointed as the new Director of the NCERT? (A) Dr. Bhim Rao Ambedkar (A) Divesh Prasad Saklani (B) Mayawati (B) Rajesh Prasad Saklani

Mock Test Paper –1 M-3 (C) Rahul Prasad Saklani 42. Divide ` 12540 in A, B and C such that A shall (D) Dinesh Prasad Saklani receive 3 of B and C together and B may receive 7 32. When was National Development Council established? 2 of what A and C together receive. 7 (A) 1952 (B) 1971 (C) 1958 (D) 1964 (A) 3762, 2280, 6498 (B) 3762, 6498, 2280 33. What is the capital of Nagaland ? (C) 2280, 6498, 3762 (D) none of these (A) Chandigarh (B) Kohima 43. Convert 33 1 % into common fraction. 3 (C) Ranchi (D) Bengaluru 34. The capital of Chile is (A) 12 (B) 13 (A) Roseau (B) Santiago (C) St. George (D) Guatemala City (C) 14 (D) 15 35. Who invented the Seed Drill? 44. An article was sold at 15% profit. If that article would have been sold at 25% loss, then ` 20 less (A) Jethro Tull (B) Arlo Guthrie would have been got. Find the C.P. of the article. (C) Woodie Guthrie (D) Thomas Hines 36. Look at the series in the following question and (A) ` 50 (B) ` 40 fill in the blank. (C) ` 100 (D) ` 60 72, 76, 73, 77, 74, —, 75, ... 45. The C.I. of a sum of money for 2 years is (A) 70 (B) 71 ` 396 and S.I. is ` 384. Find the rate percent. (C) 75 (D) 78 (A) 6 14 % (B) 3 34 % 37. Simplify 23 × 19 × 85 . 19 17 (C) 3% (D) 6% (A) 17 (B) 19 46. A can do a piece of work in 10 days and B can do it in 15 days. In how many days will A and B (C) 115 (D) 23 together finish the work? 38. The numbers which are exactly divisible by 2 (A) 20 days (B) 12 days are known as (A) prime numbers (C) 8 days (D) 6 days (B) rational numbers 47. A man rows 15 kilometres down the stream in 3 hours 45 minutes and 5 kilometres up stream in (C) whole numbers 2 hours 30 minutes. Find his speed in still water. (D) even numbers 39. The L.C.M. of two numbers which are prime to (A) 4 km/hr (B) 2 km/hr each other is their (C) 3 km/hr (D) 5 km/hr (A) sum (B) difference 48. The sum of age’s of Manoj and his mother is 63 years. Four years back his mother’s age was 4 (C) product (D) quotient times that of Manoj’s age at that time. What is the present age in years of Manoj’s mother? 40. The value of the expression 1 2 is (A) 48 (B) 46 4 2 – 2 + (C) 42 (D) 40 +5 2 2+ 6 49. The average height of 30 girls out of a class of 40 7 is 160 cm and that of the remaining girls is 156 cm. The average height of the whole class is (A) 197 (B) 197 (A) 159 cm (B) 160 cm (C) 165 cm (D) 170 cm (C) 1 (D) 2 50. In what ratio should water and 66% wine solution be mixed to obtain 55% wine solution? 41. Find the least number by which if we divide 2816, the quotient becomes a perfect square. (A) 2 : 5 (B) 1 : 5 (A) 14 (B) 16 (C) 2 : 3 (D) 1 : 4 (C) 28 (D) 21

M-4 General Test for CUET 51. In how many ways can the letters of the word 60. If in a certain language, HOUSE is coded as REPEAT be arranged? INVRF, how is CROWD coded in that code? (A) 2240 (B) 232230 (A) BGNVC (B) DQPVK (C) 360 (D) 235760 (C) DQPVE (D) DSPXE 52. The radii of two wheels of a railway train 61. Which number is required to replace the are 1.4 m and 2.1 m respectively. How many question mark? revolutions more the one will make than the other in running 34.320 km? ?2 93 (A) 600 (B) 700 74 (C) 900 (D) 1300 55 53. Examine the nature of the roots of the equation x2 + 2x + 1 = 0 (A) imaginary, unequal (A) 10 (B) 11 (B) real, rational and equal (C) 12 (D) 13 (C) real, unequal, rational 62. Pointing out to a lady, Ramesh said, “She is the daughter of the women who is the mother of (D) real, unequal, irrational the husband of my mother”. How is the lady related to Ramesh? 54. How many straight lines can be drawn through a point parallel to a given straight line? (A) no (B) 1 (A) Aunt (B) Grand Daughter (C) 2 (D) any number (C) Daughter (D) Sister 55. Which of the following statements are true? 63. Which number indicates teachers who are neither doctor nor engineer? (i) Statistics is the science of estimates and probabilities R (ii) Statistics is the science of counting (iii) Statistics is an art but not a science 1 (iv) Statistics deals with individual study 475 (A) (iii) (B) all 36 2 S (C) none (D) (i) and (ii) T 56. Newspaper : Editor :: Film : ? R = Engineer, S = Doctor, T = Teacher (A) Actor (B) Director (A) 7 (B) 3 (C) Audience (D) Producer (C) 5 (D) 2 57. If the following four words are arranged in an 64. Directions: Given below are the two statements alphabetical order, which word will come in the followed by two conclusions. Disregarding commonly second last? known facts, taking statements to be thoroughly true, mark your answer as: (A) Mirror (B) Dear (C) Supreme (D) Radiation A. Only I follows 58. Find out the next term in the series B. Only II follows 240, 120, 40, 10, ___ C. Both I and II follow (A) 5 (B) 20 D. Neither I nor II follows (C) 4 (D) 2 Statements: 59. Complete the series I. All bats are blind. ABC, BCD, CDE, DEF, ___ II. All snakes are blind. (A) DFE (B) EFG Conclusions: (C) GHI (D) GIH I. Some snakes are bats. II. No snake is a bat.

Mock Test Paper –1 M-5 65. Directions: Study the given information carefully (iv) G is between E and F and answer the question: (v) D is sitting third from the south end (i) A, B, C, D, E, F and G are sitting on a wall and all of them are facing east. Who is sitting to the right of E? (ii) C is to the immediate right of D (A) A (B) C (iii) B is at an extreme end and has E as his neighbour. (C) D (D) None of these Directions: Questions 66–70 are based on hypothetical data given in Table below. Table: Employees Working in Various Departments of Reliance Industries Departments (Number of Employees) Years Production Marketing Corporate Accounts Research 1999 150 25 50 45 75 2000 225 40 45 62 70 2001 450 65 30 90 73 2002 470 73 32 105 70 2003 500 80 35 132 74 2004 505 75 36 130 75 66. In which year did the total number of employees 70. Which department had less than 10% of the reach (approximately) twice the total number employees through all the years shown in the of employees that the company had in the year table? 1999? (A) Marketing (B) Corporate (A) 2000 (B) 2001 (B) Accounts (D) None of these (C) 2002 (D) 2003 71. Find the odd term in the following: 67. In which department did the number of (A) Blade (B) Axe employees (approximately) remain the same during the years 1999 and 2004? (C) Dish (D) Scissors (A) Production (B) Corporate 72. A man is facing West. He turns 45° in the clockwise direction and then another 180° in the (C) Research (D) None of these same direction and then 270° in the anticlockwise direction. Which direction is he facing now? 68. In how many years was the number of employees working in the production department more (A) South-East (B) South-West than 50% of the total employees? (C) South (D) North-West (A) 2 (B) 3 73. Find the odd-one-out. (C) 4 (D) 5 69. In which year did each department have a larger number of employees than it had in the ((Aa)) immediately preceding year? (A) 2002 (B) 2004 ((Bb)) ((Cc)) ((Dd)) (C) 2001 (D) 2003

M-6 General Test for CUET 74. In the following question, choose the correct water-image of the figure (X) from amongst the four alternatives (A), (B), (C) and (D) given along with it. ((Cc)) (Dd)) (Xx)) ((Aa)) (bB)) 75. Count the number of squares in the following figure: (A) 18 (B) 14 (C) 10 (D) 9

ANSWERS Mock Test Papers Mock Test Paper –1 1. (A) 2. (A) 3. (C) 4. (D) 5. (D) 6. (C) 7. (B) 8. (C) 9. (D) 10. (C) 11. (B) 12. (D) 13. (E) 14. (C) 15. (A) 16. (A) 17. (B) 18. (B) 19. (A) 20. (A) 21. (A) 22. (B) 23. (C) 24. (A) 25. (C) 26. (C) 27. (B) 28. (A) 29. (C) 30. (D) 31. (A) 32. (A) 33. (B) 34. (B) 35. (A) 36. (D) 37. (C) 38. (D) 39. (C) 40. (B) 41. (A) 42. (A) 43. (B) 44. (A) 45. (A) 46. (D) 47. (C) 48. (A) 49. (A) 50. (B) 51. (C) 52. (D) 53. (B) 54. (B) 55. (D) 56. (B) 57. (D) 58. (D) 59. (B) 60. (C) 61. (B) 62. (A) 63. (D) 64. (D) 65. (D) 66. (B) 67. (C) 68. (D) 69. (D) 70. (A) 71. (C) 72. (B) 73. (D) 74. (C) 75. (B) Mock Test Paper –2 1. (A) 2. (B) 3. (C) 4. (D) 5. (B) 6. (B) 7. (B) 8. (A) 9. (C) 10. (A) 11. (B) 12. (E) 13. (D) 14. (C) 15. (A) 16. (A) 17. (A) 18. (B) 19. (B) 20. (A) 21. (A) 22. (D) 23. (C) 24. (D) 25. (B) 26. (B) 27. (D) 28. (C) 29. (A) 30. (C) 31. (B) 32. (A) 33. (C) 34. (D) 35. (B) 36. (B) 37. (D) 38. (C) 39. (C) 40. (B) 41. (A) 42. (A) 43. (C) 44. (C) 45. (D) 46. (A) 47. (D) 48. (A) 49. (B) 50. (D) 51. (B) 52. (A) 53. (A) 54. (B) 55. (B) 56. (A) 57. (C) 58. (B) 59. (A) 60. (A) 61. (C) 62. (A) 63. (B) 64. (A) 65. (A) 66. (B) 67. (B) 68. (C) 69. (B) 70. (B) 71. (D) 72. (A) 73. (B) 74. (A) 75. (D) Mock Test Paper –3 1. (A) 2. (B) 3. (C) 4. (C) 5. (B) 6. (C) 7. (C) 8. (B) 9. (A) 10. (B) 11. (C) 12. (B) 13. (D) 14. (E) 15. (A) 16. (A) 17. (C) 18. (A) 19. (A) 20. (A) 21. (A) 22. (C) 23. (B) 24. (A) 25. (D) 26. (A) 27. (B) 28. (A) 29. (A) 30. (D) 31. (B) 32. (C) 33. (D) 34. (A) 35. (B) 36. (C) 37. (D) 38. (A) 39. (B) 40. (A) 41. (C) 42. (D) 43. (C) 44. (B) 45. (D) 46. (B) 47. (A) 48. (C) 49. (B) 50. (B) 51. (D) 52. (A) 53. (D) 54. (B) 55. (D) 56. (C) 57. (B) 58. (A) 59. (C) 60. (D) 61. (B) 62. (D) 63. (D) 64. (B) 65. (C) 66. (A) 67. (B) 68. (A) 69. (D) 70. (A) 71. (D) 72. (B) 73. (B) 74. (D) 75. (C) M-31

M-32 General Test for CUET Mock Test Paper –4 1. (A) 2. (B) 3. (C) 4. (D) 5. (C) 6. (C) 7. (A) 8. (D) 9. (C) 10. (B) 11. (E) 12. (C) 13. (A) 14. (D) 15. (B) 16. (D) 17. (B) 18. (B) 19. (D) 20. (A) 21. (A) 22. (C) 23. (D) 24. (C) 25. (A) 26. (B) 27. (C) 28. (D) 29. (B) 30. (A) 31. (C) 32. (A) 33. (C) 34. (B) 35. (D) 36. (A) 37. (A) 38. (B) 39. (D) 40. (B) 41. (A) 42. (B) 43. (C) 44. (A) 45. (D) 46. (D) 47. (C) 48. (A) 49. (A) 50. (D) 51. (D) 52. (A) 53. (D) 54. (B) 55. (B) 56. (A) 57. (D) 58. (A) 59. (C) 60. (B) 61. (B) 62. (C) 63. (D) 64. (D) 65. (D) 66. (B) 67. (D) 68. (C) 69. (B) 70. (A) 71. (D) 72. (B) 73. (B) 74. (B) 75. (B) Mock Test Paper –5 1. (B) 2. (B) 3. (C) 4. (D) 5. (B) 6. (A) 7. (D) 8. (B) 9. (B) 10. (B) 11. (B) 12. (A) 13. (E) 14. (D) 15. (C) 16. (A) 17. (C) 18. (A) 19. (C) 20. (B) 21. (B) 22. (C) 23. (C) 24. (A) 25. (A) 26. (C) 27. (A) 28. (C) 29. (C) 30. (B) 31. (B) 32. (C) 33. (D) 34. (A) 35. (B) 36. (B) 37. (B) 38. (B) 39. (A) 40. (B) 41. (D) 42. (A) 43. (B) 44. (D) 45. (C) 46. (A) 47. (B) 48. (A) 49. (B) 50. (D) 51. (C) 52. (C) 53. (D) 54. (A) 55. (A) 56. (A) 57. (C) 58. (D) 59. (B) 60. (A) 61. (A) 62. (A) 63. (A) 64. (C) 65. (D) 66. (C) 67. (C) 68. (B) 69. (A) 70. (A) 71. (C) 72. (B) 73. (C) 74. (C) 75. (A)