Math All chapters MCQ with answers

Perimeter of the two sectors of circle Area of A  2m 2cm  1 3.14  1  22 14cm  22cm 4 27 2cm 2cm  0.86cm2 Total perimeter = 134 cm The perimeter of the given figure is 134 cm. Unshaded area  0.86cm2  2  1 cm 2 36. (d) Not available 4cm 4cm  9.72cm2 37. (a) Not available Shaded area  4cm 4cm  9.72cm2  6.28 cm2 38. (b) Not available 45. (c) Radius of circle  28 cm  2 14 cm 39. (a) Not available Area of circle  22 14cm14cm 40. (b) Not available 7 41. (a) Not available 42. (c) Not available  616 cm2 Radius of semicircle 14 cm  2  7 cm 43. (b) Radius =14 cm  2  7 cm  ShadedJaOreIaN 3@ 1iitw22ale7in7 T2e31lecmg2ram 27  616 cm2  231 cm2  385 cm2 Perimeter of shaded part of figure  7  7  3  1  22 14   2 7  14cm  66cm  80cm Area of a  1  22  7cm 7cm 46. (b) Area of rectangle  28 cm 23 cm 47  644 cm2 Radius of semicircle  28 cm  2 14 cm  38.5cm2 Radius of quadrant  23cm 16cm  7cm Area of unshaded region Area of a  1  7cm 7cm  (1  22 14cm14cm)  2 27 (2 1  22  7cm 7cm)  385cm2  24.5 cm2 47 Shaded area  644 cm2  385 cm2  259 cm2 Area of a  38.5 cm2  24.5 cm2 47. (c) Not available  14 cm2 Area of shaded region 14 cm2 8 112 cm2 44. (a) 48. (d) Not available 11

49. (a) Not available JOIN @iitwale in Telegram 50. (d) Not available 51. (c) Not available 52. (c) Not available 53. (b) Not available 54. (b) Not available 55. (a) Combine the shaded parts in the given figure as in the following figure. Radius of circle  28 cm  4  7 cm Area of quadrant  1  22  7  7  38.5 cm2 47 Area of shaded region =(1414)  38.5 38.5 196 cm2  77 cm2 119 cm2 12

Statistics Statistics 1. Find the weighted mean of first 'n' natural 7. The mean age of a combined group of men numbers, whose weights are and women is 25 years. If the mean age of proportional to the corresponding numbers. the group of men is 26 years and that of the group of women is 21 years, find the (a) 2n 1 percentage of men and women respectively 3 in the group. (a) 70, 30 (b) n 1 (b) 30, 70 2 (c) 80, 20 (d) 60, 40 (c) n(n 1) 2 (d) (n 1)(2n 1) 8. The mean of 8 numbers is 25. If 5 is 6 2. What is the mean of -8,-4, 4 and 8? subtracted from each number, what will the (a) 1 new mean be? (b) Zero (a) 20 (b) 15 (c) 8 (c) 160 (d) 2 (d) 2 9. If the mean of first 'n' odd natural numbers 3. Find the mean of the first six multiples of 3. is 'n' itself, what is the value of 'n'? (a) 63 (a) 2 (b) 11.5 (b) 3 (c) 10.5 (d) 60 (c) 1 JOIN @iitwale in Telegram (d) Any natural number 4. The A.M. of a set of 50 numbers is 38. If 10. If the mean of 'n' observations, two numbers of the set, namely 55 and 45 are discarded, find the mean of the 12,22,32,....,n2 is 46n , find the value of 'n'. remaining observations. 11 (a) 36 (b) 37.5 (a) 22 (b) 23 (c) 36.5 (c) 12 (d) 11 (d) 38.5 11. The A.M. of 'n' observations is M. If the sum of (n-4) observations is 'a', what is the mean of remaining 4 observations? 5. Find the mean of the first six prime (a) nM  a (b) nM  a numbers. 2 (a) 68.3 (b) 6.71 (c) nM  a (d) nM  a (c) 7 (d) 6.83 2 4 6. The A.M. of 'n' numbers of a series is X. If 12. Identify the mode of the given distribution. the sum of first (n - 1) terms is 'k'. what is the nth number? Marks 456 78 (a) nX  nk (b) nX  k Number of Students 3 5 10 6 1 (c) X  nk (d) X  k (a) 7 (b) 1 (c) 8 (d) 6

13. The hearts of 60 patients were examined 18. The mean weight of seven boys is 56 kg. through X-ray and observations obtained Individual weights of six boys (in kg) are are recorded. 52,57,55,60,59 and 55 respectively. Find the weight of the seventh boy. Length of No. of (a) 52 kg heart (in patients (b) 54 kg (c) 57 kg mm) (d) 59 kg 120 7 19. The mean of 150 items was found to be 60. 121 9 Later on, it was discovered that the values 122 15 of two items were taken as 52 and 8 instead 123 12 of 152 and 88 respectively. Find the correct 124 6 125 11 Find their median. mean. (a) 144 (b) 122 (a) 6.15 (b) 60.7 (c) 156 (d) 114 (c) 61.2 (d) 6.72 14. Marks obtained by 12 students in a test are 20. Given that x is the mean of x1, x2,....xn, find 37, 23, 16, 19, 34, 23, 5, 27, 36, 23, 20 the mean of x1 , x2 ,.... xn . and 38. Find the modal marks. aa a (a) 27 (b) 37 (a) x  a (b) x (c) 23 (d) 5 (c) ax (d) x 15. If 10, 13,15,18,(x 1),(x  3),30,32,35 and 41 21. In the freqJuOenIcNy d@istriibituwtioanal,ediisncreTteedleatgarias m are ten observations in the ascending order given. with median 24, find the value of 'x'. (a) 42 Variable (x) 0 1 2 3 4 5 (b) 22 (c) 10 Frequency x 20 40 40 20 4 (d) 32 (f) 16. The mean of six numbers is 23. If one of the If the mean is 2.5, what is the value of numbers is excluded, the mean of the frequency ' x ' ? remaining numbers is 20. Find the excluded (a) 0 (b) 1 number. (c) 3 (d) 4 (a) 138 (b) 100 22. If x1, x2,.....xn are 'n' observations such that (c) 20 (d) 38 nn (xi  3)  120 and (xi  5)  160 , find 11 'n'. (a) 40 (b) 20 (c) 60 (d) 70 17. If x is the mean of x1, x2,....xn , find the mean of (x1  2a),(x2  2a),(x3  2a),.....(xn  2a) . 23. The arithmetic mean of the scores of a (a) x  2a group of students in a test was 52%. The (b) x  2a brightest 20% of them secured a mean score of 80 and the dullest 25%, a mean score of (c) x  2a 31 %. Which of the following is the mean 2 score of the remaining 55%? (a) 45% (b) 50% (d) x  2a 2 (c) 51.4%(approx) (d) 54.6% (approx) 3

24. The mean of 10 numbers is 7. If each 30. What is the mean of the first 'n' natural number is multiplied by 12, find the mean numbers? of new set of numbers. (a) 82 (b) 48 (a) n  1 (b) n(n 1) 2 (c) 78 (d) 84 (c) 1 (n 1) (d) (n 1) 25. The mean of the marks in Statistics of 100 2 2n students in class X was 72. The mean of 31. What is the arithmetic mean of 20 fours, 40 marks for boys was 75, while their number was 70. What is the mean of marks of girls fives, 30 sixes and 10 tens? (a) 50 (b) 25 in the class? (c) 5.6 (d) 33 (a) 35 (b) 65 (c) 68 (d) 86 32. Find the value of ' x ' if the mean of 26. The given data are the times (in minutes), it x  2,2x  3, 3x  4 and 4x  5 is x  2 . takes seven students to go to school from their homes. (a) 2 (b) 1 11 6 22 7 10 6 15 (c) 3 (d) -1 Which statement about the data is false? (a) Their median is 11. 33. What is the value of 'n' if the mean of first 9 (b) Their mean is 11. (c) Their range is 16. natural numbers is 5n ? (d) Their mode is 6. 9 (a) 7 (b) 8 (c) 9 27. From a series of 50 observations, an (d) 11 JOIN @iitwale in Telegram observation 45 is dropped, but the mean 34. Which of the following is true about the remains the same. What was the mean of 50 mode of a given data? observations? (a) It may or may not exist for a given data. (b) It is always unique. (a) 50 (b) 49 (c) It is very difficult to compute mode. (c) 45 (d) 40 (d) We cannot calculate mode without the empirical formula. 28. A person made 165 telephone calls in the month of May in a year. It was Friday on 1st 35. The A.M. of 12 observations is 15. If an May of the year. The average of telephone observation 20 is removed, what is the calls on Sundays of the month was 7. What arithmetic mean of the remaining was the average of the telephone calls per observations? day on the rest of the days of the month? (a) 165 (b) 5 (a) 14.5 (b) 13 31 (c) 15 (d) 13.5 (c) 7 (d) 137 27 36. The mean weight of a group of 10 students is 25 kg and the mean weight of another 29. The numbers 4 and 9 have frequencies x group of 10 students is 35 kg. What is the and (x 1) respectively. If their arithmetic mean weight of all the 20 students? (a) 30 kg mean is 6, what is the value of ' x ' ? (b) 35 kg (a) 2 (c) 25 kg (b) 3 (d) 20 kg (c) 4 (d) 5 4

37. The mean of the scores x1, x2,....., x6 is x . 44. What is the mode of the data 3,6,3,4,6,4, What is the mean of the scores 3,5,6,5, x and x2 ? 5x1,5x2,.....,5x6 ? (a) 4 or 5 only (b) 3 or 6 only (c) 3 or 5 only (d) 3, 4 or 6 (a) x  5 (b) x (c) x  5 5 45. What is the median of 1 , 2 , 3 , 1 and 7 ? 2 3 4 6 12 (d) 5x 38. Find x where 6 is the median of the scores (a) 3 (b) 7 6 4 12 x , x , x , x and x . (c) 2 (d) 1 2345 6 3 6 (a) 12 (c) 24 (b) 4 46. What is the median of the first 100 natural (d) 6 numbers? 39. The mode of a data exceeds its mean by 12. (a) 50.5 (b) 50 (c) 52 (d) 51 By how much does its mode exceed the median? (a) 8 (b) 12 47. If the difference of mode and median of a data is 24, what is the difference of median (c) 0 (d) 10 and mean? 40. In a class of 19 students, 7 boys failed in a (a) 24 (b) 6 (c) 12 (d) 30 math test. The scores of those who passed are 12,15,17,15,16,15,19,19,17,18,18 and 19 marks. What is the median marks of the 48. What is thJeOarIiNthm@eticiitmweaanleofin30T2e0 l3e2g1r6am and 27? 19 students in the class? (a) 23 (b) 24 (a) 15 (b) 12 (c) 16 (d) 19 (c) 25 (d) 26 41. If the median of x , x, x , x and x (where 49. Find the mode of 32, 20, 32, 16, 27 and 32. (a) 20 (b) 27 5 42 3 (c) 30 (d) 32 x  0 ) is 8, what is the value of ' x ' ? (a) 6 (b) 8 50. Find the median of 15 2 .15.03,15,15 1 and (c) 4 (d) 24 33 42. The mode of the observations 5, 4, 4, 3, 5, 15.3. x , 3, 4, 3, 5, 4, 3, and 5 is 3. What is their (a) 15 1 (b) 15.3 3 median? (a) 3 (b) 4 (c) 5 (d) 4.5 (c) 15 2 (d) 15.03 3 43. If the ratio of mean and median of a certain 51. If for a given data median is 125.6 and data is 2:3, what is the ratio of its mode and mean? mean is 128, find mode. (a) 3 : 2 (a) 120.8 (b) 128.0 (b) 5 : 2 (c) 108.2 (d) 180.2 (c) 3 : 5 (d) 2 : 3 52. what is the arithmetic mean of a  2 , a and a2? (a) a  2 (b) a (c) a  2 (d) 3a 5

53. The mean of 9, 11, 13, p, 18 and 19 is p. (c) 14 (d) 8 Find the value of 'p'. 55. Which of the following is calculated using (a) 12 (b) 13 (c) 14 (d) 15 mid-values of classes? (a) Mean (b) Median 54. What is the mode of 10, 2, 8, 6, 7, 8, 9, 10, (c) Mode (d) Range 10, 11 and10? (a) 10 (b) 12 JOIN @iitwale in Telegram 6

Answer - Keys 1. A 2. B 3. C 4. B 5. D 6. B 7. C 8. A 9. D 10. D 11. D 12. D 13. B 14. C 15. B 16. D 17. A 18. B 19. C 20. D 21. D 22. B 23. C 24. D 25. B 26. A 27. C 28. B JO2I9N. @Biitwale i3n0T. eleCgram 31. C 32. D 33. C 34. A 35. A 36. A 37. D 38. B 39. A 40. A 41. D 42. B 43. B 44. C 45. B 46. A 47. C 48. C 49. D 50. B 51. A 52. B 53. C 54. A 55. A 7

Solutions 1. (a) Not available 15. (b) Not available 2. (b) Not available 16. (d) Not available 3. (c) Not available 17. (a) Not available 18. (b) Not available 4. (b) Not available 19. (c) Not available 5. (d) Not available 20. (d) Not available 6. (b) Let the numbers be 21. (d) Not available x1, x2, x3.....xn .Then 22. (b) Not available X1 n X1 n i1 23. (c) Not available  X  x1  x2  x3  .....  xn1  xn 24. (d) Total of 10 numbers n 107  7J0OIN @iitwale in Telegram  k  xn [ x1  x2  x3  .....  xn1  k] n If each number is multiplied by 12, New total  7012  xn  cX  k New mean  7012  84 7. (c) Not available 10 8. (a) Not available 25. (b) Mean marks of girls Total marks of all students 9. (d) Not available  -Total marks of boys 10. (d) Not available Total number of girls 11. (d) Not available  1950  65 30 12. (d) Mode is 6 as it has the highest frequency. 26. (a) Arranging the given data in ascending order, we get, 6, 6, 7, 10, 11, 15, 22 13. (b) Not available mean  6  6  7 10 1115  22 7 14. (c) The given data arranged in ascending  77  11 order is 5,16,19,20,23,23,23,27, 34, 36, 7 37,38. Mode = 6 By observation, we find that 23 occurs the Median = 4th value = 10 most number of times. Range = 22 - 6 = 16 Mode = 23 or Modal marks = 23 8

27. (c) Not available 40. (a) Not available 28. (b) Not available 41. (d) Not available 29. (b) Not available 42. (b) Not available 30. (c) Not available 43. (b) Not available 31. (c) Not available 44. (d) Not available 32. (d) Given that the mean of x  2 , 45. (b) Not available 2x  3,3x  4 and 4x + 5 is x  2 46. (a) Not available  10x 14  x  2 4 47. (c) Not available  6x  6  x  1 48. (c) Not available 33. (c) Mean of first 9 natural numbers 49. (d) Not available  1 2  .....  9  45  5 50. (b) Not avJaOilabINle @iitwale in Telegram 99 51. (a) Given median = 125.6 and mean Given mean of first 9 natural numbers is 5n . =128. 9 Mode = 3 Median - 2 Mean  (3125.6)  (2128)  5n  5  n  95 9  376.8  256 9 5  120.8 34. (a) Mode of a given data may or may not 52. (b) Mean  a  2  a  a  2  3a  a exist sometimes. 33 35. (a) The A.M. of 12 observations is 15. 53. (c) Given mean = p  Sum of 12 observations  9 1116  p 18 19  p 6 1215 180  p 14 An observation 20 is removed  Mean of the remaining observations 54. (a) Mode = Observation with the highest frequency =10  180  20  160  14.5 (12 1) 11 55. (a) Mean is calculated using the mid-values of classes. 36. (a) Not available 37. (d) Not available 38. (b) Not available 39. (a) Not available 9

Triangles 1. In the figure, ABC  DAC  90 , BC = 3 5. ABCD is a parallelogram in which EF is cm, AD = 2 cm and AB = 1 cm. What is drawn parallel to BC such that the measure of AC + CD? AE  (4x  3)cm , AF  (8x  7)cm , BE  (3x 1)cm and CF(5x  3)cm . (a) 2( 5  7)cm What is the value of 'x'? (b) 5( 2  7)cm (a) 1 (b) -1 (c) 2( 7  5)cm (d) 7( 2  2)cm (c) -5 (d) 1 2 2. A paper is cut in the following shape. 6. In ABC , if AD  AE and ADE  ACB , DB EC what type of triangle is ABC ? (a) Right triangle (b) Acute angled triangle (c) IOsobstcuesleJesOatnrIgiaNlendg@lteriainitgwleale (d) in Telegram 7. The altitudes of two similar triangles are 4 cm and 6 cm. If the area of one triangle is Which of the following is the correct 36 cm2 , what is the area of the other? statement? (a) AE2  AD2  ED2 (a) 16cm2 (b) 36cm2 (b) AC2  AD2  DE2 (c) AC2  AB2  AD2 (c) 49 cm2 (d) 25 cm2 (d) AE2  AB2  BC2 8. The ratio of areas of two similar triangles is 3. In the given figure what is the value of ' x ' if 81 :49. If the median of one triangle is 4.9 AB || CD ? cm, what is the median of the other? (a) 4.9 cm (b) 6.3 cm (c) 7 cm (d) 9 cm 9. The perimeters of two similar triangles ABC and DEF are 24 cm and 32 cm respectively. If DE = 12 cm, find AB. (a) 9cm (b) 35cm (a) 2 units (b) 4 units (c) 18cm (d) 28cm (c) 3 units (d) 5 units 10. BC and EF are the corresponding sides of two similar triangles ABC and DEF. If BC = 4. In ABC , DE || BC and AD  3 . What is the 9.1 cm, EF = 6.5 cm and the perimeter of DB 5 AEF is 35 cm, find the perimeter of ABC . length of AE if AC  4.8cm ? (a) 15cm (b) 49cm (a) 1.4cm (b) 1.8cm (c) 45 cm (d) 35 cm (c) 2.2 cm (d) 3.6 cm

11. A man cycles 15 m towards east, turns right 18. In similar triangles ABC and FDE .DE = and cycles 8 m. How far is he from the 4 cm, BC = 8 cm and area of starting point? (a) 7m (b) 17m FDE  25 cm2 . What is the area of ABC ? (c) 23m (d) 19m (a) 144cm2 (b) 121 cm2 (c) 100cm2 (d) 81 cm2 12. At what height does the tip of a 34m long 19. Given AO  BO  1 and AB  8cm ,find DC ladder placed at a distance of 16 m from a OC OD 4 wall, touch the wall? (a) 29 m (b) 34 m (c) 30m (d)18 m 13. At some point of time on a summer evening, an 8 m tall flag post casts a 15 m long shadow. What is the distance between the tips of the flag post and its image? (a) 15m (b) 28m (a) 10cm (b) 32cm (c) 23m (d) 17m (c) 6 cm (d) 2 cm 14. What is the area of a square of diagonal 20. Given that PB  AB and QA  AB PO=4 12cm? cm and QO  7cm , if area of QAO is (a) 36cm2 (b) 9cm2 245 cm2 , what is the area of PBO ? (c) 72cm2 (d) 144 cm2 (a) 60 cm2 (b) 40 cm2 (c) 125cmJ2 OIN @iit(wd)a8l0ecmin2 Telegram 15. Two 15 m strings are tied to a peg between two poles 9 m and 12 m long from their types. What is the distance between the 21. A girl of height 90 cm is walking away from the base of a lamp post at a speed of 1.2 poles? m/sec. If the lamp is 3.6 m above the (a) 18m (b) 21 m (c) 20 m (d) 23 m ground, find the length of the girls shadow after 4 seconds. (a) 4.8m (b) 1.2m 16. The areas of two similar triangles are 81 (c) 1.6m (d) 3.6m cm2 and 49 cm2 respectively. If the altitude of the bigger triangle is 4.5 cm, find the corresponding altitude of the smaller 22. In the given figure, PD || BC and AD  CE triangle. DC BE (a) 3 cm (b) 2.5 cm . Identify the correct statement. (c) 4 cm (d) 3.5 cm 17. X and Y are points on the sides AB and AC respectively of ABC If AB = 5.6 cm, AX = 1.4 cm, AC = 7.2 (a) AD  DC cm, and XY || BC , what is the measure of (b) PE | | AC AY? (b) 1.6cm (c) PB  CE (a) 2.4 cm (d) PD  AC (c) 1.8 cm (d) 3.6cm 3

23. In the given figure, AB  BC , DE  AC 28. In the given figure, ABE~DCE . and GF  BC . Find the difference between ABE and AEB . (a) 130 (b) 15 (c) 35 (d) 115 Which of the following is correct? 29. In ABC, B  90 and AD  CB (a) GFC  DAE (produced). Identify the correct statement. (b) ADE GCF (a) AC2  AB2  BC2  2BC.AD (c) GCF  ABC (b) AC2  AB2  BC2  2BC.AB (d) AED EGF (c) AB2  AC2  BC2  2BC.BD 24. Lf ABC ~ DEF , BC=3cm,EF  4cm and 30. In the figure, DE | | BC . Find AE. area of ABC  54cm2 , find the area of DEF . (b) 16cm2 (a) 96 m2 (c) 96cm2 (d) 69cm2 25. In ABC, A  90 , AN  BC , BC = 12 JOIN @iitwale in Telegram cm and AC = 5 cm. Find the ratio (a) 6 cm (b) 4 cm ar(ANC) : ar(ABC) (c) 5 cm (d) 3 cm (a) 122 : 52 (b) 32 :122 (c) 52 :122 (d) 32 : 52 31. Two triangles BAC and BDC, right angled at A and D respectively, are drawn on the 26. In trapezium ABCD, AB || CD . If OA  x  4 , same base BC and on the same side of BC. If AC and DB intersect at P, which of the OB  3x 19,OC  4 and OD  x  3 , find following statements is true? (a) AP PC  DP PB 'x'. (a) 10 units (b) 9 units (b) AP  DP (c) 12 units (d) 8 units PC PB 27. In the given figure, if ABE  ACD , (c) AP PB  DP PC identify the correct statement. (d) Both (b) and (c) 32. In ABC , D is a point on AB and E is a point on BC such that DE | | AC and area of DBE  1 area of ABC . Find AD . 2 AB (a) ADE~BED (a) 1 2 (b) 2 1 (b) ABC~ADE 2 2 (c) DEC ~ ABC (c) 2 1 (d) 2 1 (d) BDE ~ BAE 2 2 4

33. In the given figure, RSP~RPQ .Identify 37. In the given figure, ABC is right angled at the true statement. A. (a) RS  Rp2 (b) RP  RQ  RS2 What is the length of AD in terms of 'b' and RQ (d) RQ RS  RP 'c'? (c) RS  RQ  RP2 (a) AC (b) bc b2  c2 b2  c2 34. In ABC,A  90 and AD±BC. If AB= 5 cm, BC = a cm and AC = b cm, find the (c) bc (d) bc length of BD in cm. b2  c2 c2  b2 (a)  b2  a2  25  (b)  a2  b2  25  38. In the given figure, quad. ABCD ~ quad  a    PQRS. Find the value of 'z'.    2a  (c)  a2  b2  25  (d)  a2  b2  25       2b   2a  35. If ABC is an equilateral triangle of side 'a' JOIN @iitwale in Telegram and D is a point on BC such that BD = - BC, what is the length of AD? (a) 7 a (b) 3 a2 (a) 5 4 (b) 45 3 7 6 4 (c) 7 a (d) 7 a2 (c) 5 5 (d) 35 3 3 6 3 36. In the given figure, AD -L BC, BC = a, CA 39. ABC is an isosceles triangle right- angled = b, and AB = c. at B. Similar triangles ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of ABC and ACD . (b) 3 :1 (a) 1 :2 (c)1:3 (d) 4:1 If BD  1 CD , what is the value of 2b2 ? 40. If ABC ~ DFE,A  30o,C  50o, AB  5cm, 3 AC  8cm and DF  7.5 cm . Which of the following is true ? (a) a2  2c2 (a) DE 12cm, F  50 (b) 2a2  c2 (c) c2  2a2 (b) DE 12cm, F 100 (d) 2a2  2c2 (c) EF 12cm, D 100 (d) EF 12cm, D  30 5

41. In the given figure, AD is the bisector of 46. In ABC,DE | |BC,AD  6cm,BD  9cm and BAC . If AB= 10 cm, AC = 14cm and BC AE  8cm . = 6 cm, find the length of DC. (a) 2 cm (b) 3.5 cm Find the length of AC. (c) 2.5 cm (d) 4 cm (a) 20 cm (b) 12 cm (c) 15 cm (d) 18 cm 42. In the given figure, AO  BO  1 and AB = 47. The lengths of the diagonals of a rhombus OC OD 2 are 16 cm and 12 cm. What is the length of the side of the rhombus? 5 cm. Find the value of DC. (a) 9cm (b) 10cm (c) 8 cm (d) 20 cm (a) 5 cm (b) 15cm 48. In the given figure, two line segments AC (c) 10 cm (d) 8 cm and BD intersect each other at point P, such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, 43. In the given figure, AABC is right angled at A. DEFG is a square, BD = 12 cm and EC FPiDnd=P5BAcJmO., INAP@B iit5w0aalned inCTDePle3g0ra. m = 27 cm. What is the length of the side of square? (a) 70 (b) 80 (c) 90 (d) 100 49. If ABC and PQR are similar and (a) 27 cm (b) 19 cm BC  1 , find ar(PQR) . (c) 12 cm (d) 18 cm QR 3 ar(BCA) (a) 9 (b) 3 44. ABC is right-angled at C. If p is the length (c) 1 (d) 1 3 9 of perpendicular from C to AB and AB = c, BC = a and CA = b, which of the following is true? 50. Aman drives 13 km in the north west (a) pc  ab (b) pb  ab direction, turns left and drives 5 km. How far is he from the starting point? (c) pc  bc (d) pb  ac (a) 10km (b) 18km 45. ABC is right angled at C and AC  3BC . (c) 12 km (d) 11 km What is the value of ABC ? (a) 30 (b) 90 (c) 60 (d) 45 6

51. Given xy  4cm , QR  8 cm and area of PXY  25sq.cm , what is the area of PQR ? (a) 49 cm2 (b) 81 cm2 (c) 64cm2 (d) 100cm2 52. What is the ratio of areas of two similar triangles whose corresponding sides are in the ratio 15:19? (a) 15 : 19 (b) 15:19 (c) 225:361 (d) 125:144 53. Identify the incorrect statement. JOIN @iitwale in Telegram (a) A right angled triangle may have 1,1 and 2 as its sides. (b) 1, 2, 3 are the sides of a right angled triangle. (c) The ratio of corresponding sides of two squares whose areas are in the ratio 4:1 is 2 :1. (d) 17,8 and 15 are the sides of a right angled triangle. 54. Points P and Q on the sides AB and AC of ABC are such that PQ||BC , AP: PB = 2 :3 and AQ = 4 cm. What is the measure of AC? (a) 12cm (b) 16cm (c) 10cm (d) 15cm 55. The side of an equilateral triangle is 10 cm. What is its altitude? (a) 5 2cm (b) 5 3cm (c) 12cm (d) 5cm 56. The diagonals of a rhombus are 16 cm and 12 cm. What is the measure of its side? (a) 10cm (b) 12cm (c) 8cm (d) 16cm 7

Answer - Keys 1. A 2. A 3. C 4. B 5. A 6. C 7. A 8. B 9. A 10. B 11. B 12. C 13. D 14. C 15. B 16. D 17. C 18. C 19. B 20. D 21. C 22. B 23. B 24. C 25. C 26. D 27. B 28. D JO2I9N. @Aiitwale i3n0T. eleDgram 31. A 32. B 33. C 34. B 35. C 36. D 37. B 38. C 39. A 40. B 41. B 42. C 43. D 44. A 45. C 46. A 47. B 48. D 49. A 50. C 51. D 52. C 53. A 54. C 55. B 56. A 8

Solutions 1. (a) In Perimeter of ABC is 49 cm. ABC, AC  AB2  BC2  10 cm In ACD,CD  AD2  AC2 11. (b) Not available  14cm  AC  CD  10  14 cm Let the starting point of the man be A, AB is  2( 5  7)cm the distance cycled due east, BC is the distance cycled after taking a right turn. 2. (a) Not available  The required distance is AC, which is given by 3. (c) Not available 152  82  289 17 m 4. (b) Not available 12. (c) 5. (a) Not available 6. (c) Not available 7. (a) If ABC ~ DEF , then JOIN @iitwale in Telegram ar(ABC)  AP2 where AP and DQ are the Let ' x ' m be the height at which the ladder ar (DEF ) DQ2 touches the wall. According to Pythagoras' theorem, corresponding altitudes. x2  342 162 Area of the other triangle 16 cm2  x  342 162  30m 8. (b) Let the median of the other triangle be 13. (d) Not available ' x ' cm. Then 81 : 49  (4.9)2 : x2 14. (c) Not available  x  9  4.9  6.3 15. (b) Not available 7 The other median = 6.3 cm 9. (a) Let AB be ' x ' cm. 16. (d) Not available Then 32  12  x  9cm 17. (c) Not available 24 x 10. (b) Given BC = 9.1 cm, EF = 6.5 cm and 18. (c) Since ABC ~ DEF , perimeter of ADEF is 35 cm. Let the perimeter of ABC be ' x ' cm area of ABC   BC 2 area of DEF  DE   35  6.5  x  49cm x 9.1  area of ABC   8 2  25  100cm2  4  9

19. (b) In AOD and DOC ,  x  4  3x 19 AO  BO  1 and AB  8cm 4 x3 OC OD 4 AOB  DOC  x 11or 8 (Vertically opposite angles) The required value of ' x ' is 8 units.  AOB ~ DOC. (S.A.S. similarity)  Corresponding sides are proportional 27. (b) Not available  AO  BO  AB  1 OC OD DC 4 28. (d) Not available  DC  4AB  48cm  32cm 29. (a) Not available 20. (d) Given QA  AB and PB  AB , PO = 4 30. (d) Not available cm, QO = 7 cm and area of QAO  245 cm2 . 31. (a) Not available According to the given problem, APB ~ JPOBDPICNAB@iitwale in Telegram  AP  In QAO and PBO , DP PC DC QAO  BPO, AQO  PBO  AP PC  PB DP  QAO ~ PBO (A.A. corollary) area (QAO) (QO)2 49 32. (b) Not available area(PBO) (PO)2 16     area PBO  245 16  80cm2 33. (c) Not available 49 34. (b) Not available 21. (c) Not available 35. (c) Not available 22. (b) Not available 36. (d) Not available 23. (b) Not available 37. (b) 1 b2  c2  AD  1 bc 22 24. (c) Not available  AD  bc 25. (c) Not available b2  c2 26. (d) Since the diagonals of a trapezium Hence, the length of AD in terms of 'b' and divide each other proportionally, 'c' is bc OA  OB b2  c2 OC OD 38. (c) Not available 10

39. (a) Not available According to the problem, BC2  BA2  AC2 40. (b) Not available A man is 12 km from his starting point. 41. (b) Not available 42. (c) Not available 51. (d) Not available 43. (d) Not available 44. (a) Not available 52. (c) Not available 45. (c) Not available 46. (a) Not available 53. (a) Not available 47. (b) The diagonals of a rhombus are 54. (c) Not available perpendicular to each other 55. (b) Not available 56. (a) The diagonals of a rhombus bisect each other perpendicularly. JOIN @iitwale in Telegram side of rhombus  64  36 10cm  AOB is a right angled triangle with OA = 8 cm and OB = 6 cm.  AB  OA2  OB2  64  36  100 10cm 48. (d) PB  AP PC DP  APB ~ DPC  B 180o  (50o  30o )  B 100o 49. (a) ABC ~ PQR (Given)  ar(ABC)  BC2  1 ar(PQR) QR2 9  ar(PQR)  9 ar(BCA) 50. (c) 11

Introduction to Trigonometry 1. ABC is right angled at A. If AC = 8 cm and 8. ABC is an isosceles triangle with the unequal AB = 6 cm, what is the value of cosec B? side measuring 12 cm. If both the equal sides (a) 5 (b) 3 measure 19 cm, what is the measure of BAC ? 4 4 (a) 36.8 (b) 68 (c) 4 (d) 4 (c) 38 (d) 60 3 5 9. ABCD is a trapezium in which AB = 8 cm, AD 2. ABC is right angled at A .lf BC  2 and AB = 4 cm and CD = 3 cm. = AC =1, what is the measure of B ? (a) 60 (b) 45 (c) 30 (d) 90 3. What is the value of tor which tan  cot ? (a) 60 (b) 45 (c) 90 (d) 0 4. Given sin  1  4 , what is the value What is the length of BC to the nearest whole sin number? (a) 20 (b) 16 (a) 5 cm (b) 41cm (c) 14 (d) 4 (c) 8 cm (d) 7 cm 5. Given sin2  1 , what is the value of 10. The figure JshOowIsNan@isoisictewleas tlreianignleTABeCle. Fginrdam sin2  the length of the perpendicular from A to BC. sin  cos ? (a) 25 (b) 31 31 25 (c) 24 (d) 31 25 24 6. Find the value of cos30 cos45  sin30 sin45 . (a) 6 1 (a) 5.45 cm (b) 4.55 cm 2 (c) 5.6 cm (d) 4.54 cm (b) 6  2 11. If sec  2p and tan  2 find the value 4 p (c) 6  2  p2  1  . 8 2 p2   (d) 2( 3 1)  4 (a) 1 (b) 1 2 2 7. What is the value of (c) 1 (d) 1 4 8 tan 7 tan 23 tan 60 tan 67 tan 83 ? (a) 1 (b) 3 12. What is the value of if 3 tan 2  3  0 ? 3 (d)  (a) 45 (b) 90 (c) 1 (c) 30 (d) 60

13. Given sin  cos  3 , what is the value of 19. Graphs of y  sin x and y  cos x , where tan  cot ? 0  x   intersect at a point. Find abscissa. 2 (a) 1 (b) 2 2 3 (a)  (b)  6 4 (c) 3 (d) 1 2 (c)  (d) 0 3 14. If tan 26o  tan19o  cos 60o , what is the x(1 tan 26o tan19o ) 20. Find the value of sin 15 . value of x ? (a) 3 1 (b) 3 1 (a) 1 (b) 2 2 2 (c) 2 (d) 3 (c) 3 1 (d) 3 1 22 22 2 2 3 4 x 1  15. If sin 1 . 2 . 3 .... x 2   1, 0  x 100 , find the value of x . 21. What is the value of sin0  cos30  tan45  cosec 60  cot90 ? (a) 91 (b) 80 (a) 7 3  6 (b) 6  7 3 (c) 49 (d) 46 6 6 16. What is the angle between the hour and minute (c) 0 (d) 2 hands of a clock at 02 :15 hours? 22. If sin  J1O, IwNhat@arieittwhearleespeinctivTeeploessgibrleam (a) 15 (b) 1o 7 2 2 values of 9 between 0 and 2 ? (c) 221o 2 (d) 30 (a) 210 and 300 (b) 240 and 330 (c) 240 and 300 (d) 210 and 330 17. C is the centre of a circle of radius 3 units, and 23. In terms of radians. what is the equivalent of 45  is the angle as shown in the given figure. If ? sin  cos2   x2 1 ,find the value of x. (a) 25 (b) 0.25 x2 (c) 180o (d) 45o 45o  24. Find the value of 1 cos A 1 cos A (a) 2 (b) 4 (a) sec A  cot A (b) cosec A  cot A (c) 6 (d) 8 (c) 0 (d) 1 18. If tan  sec  2 , 0     find the value of 25. Find the value of 2 5cos  4  3  5sin the tan . 3  5sin 4  5cos (a) - 1 (b) 5 (a) 3 (b) 5 (c) 1 (d) 0 4 4 26. If x  3cos Acos B, y  3cos Asin B and z  3 sin A (c) 3 (d) 5 2 2 , find the value of x2  y2  z2 . (a) 3 (b) 6 (c) 12 (d) 9 3

27. Find the value of 1 tan 75o 34. If sec  b tan  p , what is the value of cos ? 1 tan 75o (a) p2 1 (b) p2 1 (a)  2 (b) 3 P2 1 (P2 1)2 3 (c) 2 p (d) 4 p2 (c)  3 (d) 1 P2 1 (P2 1)2 3 35. What is the numerical value of the expression 28. If 8 tan A =15, find the value of sinA  cosA sin 9o  cos81o ? sinA  cosA sin 48o cos 42o (a) 7 (b) 11 (a) 1 (b) 1 23 23 (c) 0 2 (d) -1 (c) 13 (d) 17 36. Find the value of the expression 23 23 [cosec(75o  )  sec(15o  )  29. If 4sin  3cos ,find sec2  . tan(55o  )  cot(35o  )] 4(1 tan2  ) (a) - 1 (b) 0 (a) 25 (b) 25 (c) 1 (d) 3 16 28 2 (c) 1 (d) 5 37. If cos(   )  0 , what is the value of 4 6 sin(   ) ? 30. Find the value of (a) cos  JOIN @iit((wdb))acsliones22in Telegram (c) sin cos1ocos2cos3.....cos89cos90o . (a) 1 (b) 1 38. If cos9  sin a and 9  90o , what is the 2 value of tan 5 a? (c) 1 2 (d) 0 (a) 1 (b) 3 3 31. If tan x  x , where x and y are whole numbers, (c) 1 (d) 1 y 2 find sin x . 39. If ABC is right angled at C, find the value of (a) y (b) x cos(A  B) . y2  x2 x2  y2 (a) 0 (b) 1 (c) y (d) x (c) 1 (d) 3 x2  y2 y2  x2 2 2 32. Find sin3   cos3  40. If sin A  sin2 A  1 , find the value of the sin  cos expression (cos2 A  cos4 A) . (a) 1  sin cos (b) 1 sinc cos (a) 1 (b) 1 (c) 1 sin tan (c) 2 2 (d) 1 (d) 3 33. If x  a sec  b tan and y  b sec  a tan , 41. Given that sin  1 and cos = 1 , find the 22 find x2  y2 . value of (   ) . (a) 4absec  a tan (b) a2  b2 (a) 0 (b) 30 (c) b2  a2 (d) a2  b2 (c) 60 (d) 90 4

42. Find the value of the expression 50. If 3 tan  3sin , find the value of sin2   cos2  . sin2 22o  sin2 68o  sin2 63o  cos 63o sin 27o cos2 22o  cos2 68o (a) 3 (b) 2 (c) 1 (d) 0 43. If sin  cos  0 , find the value of (sin4   cos4  ) (a) 1 (b) 3 (a) 2 (b) 1 4 3 3 (c) 1 2 (d) 1 (c) 1 (d) 1 4 2 3 44. Find the value of sin(45o  )  cos(45o  ) . (a) 2cos (b) 0 51. If cos ec  13 , find the value of 12 (c) 2sin (d) 1 2sin  3cos 45. What is the value of 4sin  9cos sin25  sin210  sin280  sin285 ? (a) 0 (b) 1 (c) 2 (d) 3 46. If sin B  1 , find the value of 3cosB  4cos3B. JOIN @iitwale in Telegram 2 (a) 1 (b) 1 (a) 0 (b) 1 2 (d) 0 (c) 3 (d) 2 (c) 2 47. If tan x  sin 45cos 45  sin30 , find the value 52. Find the value sin230cos2 45  4tan230 of x . (a) 30o (b) 60  1 sin2 90o  2cos2 90o  1 (c) 45 (d) 90 2 24 (a) 1 (b) 2 48. If sin(A  B) 1 and cos(A-B)  3 , find A (c) 2 (d) 3 2 53. Find the value of 2 (cos4 30o  sin4 45o ) and B. 3 (a) 45,45 3(sin2 60o  sec2 45o )  1 cot2 30o 4 (b) 90,45 (a) 15 (b) 3 (c) 45, 30 4 4 (d) 60, 30 49. If 4tan 1, find the value of 4sin  2cos (c) 2 65 (d) 4 17 4sin  3cos 4 24 (a) 1 (b) 1 54. If cos3x  cos 30 sin 60  sin 30 cos 60 2 6 (c) 2 (d) 1 , find the value of x. 3 3 (a) 60 (b) 45 (c) 20 (d) 30 5

55. In ABC , if B  90,AB  5 cm and AC =10 57. If 2(cos  sec )  5 , what is the value of cm, find A and C cos2   sec2  ? (a) 25 (b) 5 2 4 (c) 17 (d) 4 4 17 (a) 90, 45 (b) 60, 30 58. How is cot expressed in terms of sin ? (c) 45, 0 (d) 90, 60 (a) 1 (b) 1 sin2  56. lf sin  cos  3 1 find the acute angle . 1 sin2  sin sin  cos 3 1 (c) 1 (d) sin sin 1 sin2  (a) 90 (b) 45 (c) 30 (d) 60 JOIN @iitwale in Telegram 6

Answer - Keys 1. A 2. B 3. B 4. C 5. B 6. D 7. B 8. A 9. B 10. A 11. A 12. C 13. D 14. C 15. D 16. C 17. A 18. A 19. B 20. D 21. A 22. D 23. D 24. C 25. D 26. D 27. C 28. A JO2I9N. @Biitwale i3n0.TeleDgram 31. B 32. A 33. B 34. C 35. C 36. B 37. B 38. C 39. A 40. A 41. D 42. B 43. C 44. B 45. C 46. D 47. C 48. D 49. B 50. B 51. C 52. B 53. D 54. C 55. B 56. D 57. D 58. B 7

Solutions 1. (a) In ABC ,by sin  BD  6   18.41o Pythagoras' theorem, AB 19 AC  82  62 10cm  BAC  2(BAD)  218.41o  36.82  36.8 9. (b)  cos ec  Hypotenuse  5 side opposite to 4 2. (b) sin B  AC  1 BC  CE2  EB2 BC 2  16  25  41cm From the tables, sin 45  1 . 10. (a) The perpendicular from A to BC bisects 2 BC at D. The length of Therefore sin45  sinB  B  45 AD  ABJ2OIBND2@ ii6tw2(a2l.e5)2in Telegram 3. (b) Not available  29.75  5.45 4. (c) Not available 11. (a) Not available 5. (b) Not available 12. (c) Not available 6. (d) Not available 13. (d) Not available 7. (b) Not available 14. (c) Not available 8. (a) In ABC , AB = AC = 19 cm and BD = 15. (d) Not available DC = 6 cm. 16. (c) The minute hand moves 6 in one minute. It will move 30 in 5 minutes (from 2 to 3). Also the hour hand moves 30 in one hour. It will move  30 15 o in 15 minutes, i.e.,  60  So, the angle between the two hands is  30o   7 1 o  22 1o .  2  2 In ABD , 8

17. (a)   30 (The angle subtended in the arc 25. (d) Not available is half the angle subtended at the centre.) 26. (d) x  3cos Acos B, y  3cos Asin B and sin  cos2   x2 1 (Given) z  3sin A x2 x2  y2  z2  (3cos Acos B)2  (3cos Asin B)2  (3sin A)2  x2  1  sin 30o  cos2 30o  9[cos2 A1 sin2 A]  91  9 x2 27. (c) tan 45o  tan 75o  1   3 2  1  3 1 tan 45o tan 75o 2  2  2 4  tan(45o  75o )  tan120o   3   1  5 1 1  x2 x2 4 4 28. (a) tan A  15 8 18. (a) Solving the question from the options, sin A  cos A  tan A 1 we get sin A  cos A tan A 1  15  8  7 tan  3  sec  5 4 4 15  8 23 (Pythagoras theorem) 29. (b) JOIN @iitwale in Telegram  tan  sec  3  5  8  2 44 4 Which satisfies the given equation. 19. (b) When 0     , 4sin  3cos 2  tan  3  sec  5 sin   cos   1 44 4 42  5 2 The graphs intersect at  .  4  4  sec2   4(1 tan2  )  2  20. (d) sin 15  sin(45  30) 4 1   3    sin 45  cos 30  cos 45 sin 30   4  3  1  3 1 22 22 22 25 21. (a) Not available  16  25  25 1 9  4(7) 28 22. (d) Not available 4  16  23. (d) Not available 30. (d) cos1cos2cos3.....cos45.... ... (cos 90  2)cos(90  l)cos 90 24. (b) Not available coslcos2.....cos45... ...sin2sin lsin0  0 31. (b) Not available 9

32. (a) Not available  cos285  cos280  sin280  sin285 11 2 33. (b) Not available 46. (d) Not available 34. (c) Not available 47. (c) Not available 35. (c) Not available 48. (d) Not available 36. (b) cosec(75  )  sec(15  ) tan(55  )  cot(35  ) 49. (b) We have 4 tan   3  sec(15  )  sec(l5  ) Now, 4sin  2cos 4 sin cot(35  )  cot 35    0 4sin  3cos cos  sin 37. (b) cos(   )  0 cos      90 4  3    90   sin(   )  sin(90o     )  32  1  sin(90o  2 )  cos 2 33 6 38. (c) cos9  sin 50. (b) Not available cos(9)  cos(90 )  9   90o 51. (c) Not available  10  90o    9o JOIN @iitwale in Telegram  tan5  tan 45 1 52. (b) Not available 39. (a) A  B  C 180 53. (d) Not available A  B  90 [ Since C  90 ]  cos(A  B)  cos 90  0 54. (c) Not available 40. (a) Not available 55. (b) In ABC, B  90AB = 5 cm, AC = 10 cm 41. (d) Not available Now, in right angled ABC 42. (b) Not available cos A  AB  5  1  cos60o AC 10 2 43. (c) Not available  A  60o 44. (b) Not available  C 180o  (A  B) 45. (c) sin25  sin210  sin280  sin285 180  (60  90) 180 150  30 56. (d) sin  cos  3 1 sin  cos 3 1  (sin  cos )  (sin  cos ) (sin  cos )  (sin  cos )  ( 3 1)  ( 3 1) ( 3 1)  ( 3 1) 10

[Applying Componendo-Dividendo on both sides]  2sin  2 3  tan  3 2cos 2   60o  tan  tan 60o  57. (c) Given 2(cos  sec )  5  cos  sec  5 2  cos2   sec2   2 cos sec   5 2  2   cos2   sec2   25  2  17 44  cos2   sec2   17 4 58. (b) cot  cos  cos2   1 sin2  sin sin sin JOIN @iitwale in Telegram 11

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