maths super 10

Sample Paper-2 SP-11 16. Which of the following statement is true? (a) Every point on the number line represents a rational number. (b) Irrational numbers cannot be represented by points on the number line. (c) 272 is a rational number. (d) None of these. 17. Given ∆ABC ~ ∆DEF, if AB = 2DE and area of ∆ABC is 56 cm2, find the area of ∆DEF. (a) 14 sq.cm (b) 5 sq.cm (c) 18 sq.cm (d) 56 sq.cm 18. Given that L.C.M. (91, 26) = 182, then H.C.F. (91, 26) is (a) 13 (b) 26 (c) 17 (d) 9 19. One card is drawn from a well shuffled deck of 52 cards. I. The probability that the card will be diamond, is 1/2. II. The probability of an ace of heart is 1/52. III. The probability of not a heart is 3/4. IV. The probability of king or queen is 1/26. Which of the statement(s) is/are true? (a) I and II (b) II and III (c) III and IV (d) None of these 20. In what ratio is the line segment joining the points (3, 5) & (–4, 2) divided by y–axis? (a) 3 : 2 (b) 3 : 4 (c) 2 : 3 (d) 4:3 SECTION-B Section B consists of 20 quesions of 1 mark each. Any 16 quesions are to be attempted. 21. Find an acute angle q, when cos θ − sin θ = 1− 3 cos θ + sin θ 1+ 3 (a) 0° (b) 15° (c) 30° (d) 60° 22. If x = a (cosec q + cot q) and y = b(1− cos θ) , then xy = sin θ (a) aa22 +− b2 (b) a2 – b2 (c) ab (d) ba b2 23. Which of the following is not correct? (a) If the diagonals of a quadrilateral divide each other proportionally, then it is a trapezium. (b) The line segments joining the mid-points of the adjacent sides of a quadrilateral form a parallelogram. (c) If corresponding sides of two similar triangles are in the ratio 4 : 5, then corresponding medians of the triangles must be in the ratio 4 : 5. (d) None of the above 24. Find a point on the x-axis which is equidistant from the points (5, 4) and (–2, 3). (a) (2, 0) (b) (0, 3) (c) (–2, 2) (d) (3, 0) 25. Find the point of trisectionof the line joining the points (–2, –19) and (5, 4). (a) (2, –3) (b) (1, 2) (c) çççèæ13 , - 34 ÷ø÷÷ö (d) èçæçç83 ,131ø÷÷÷ö 3 26. If the mid point of the line joining (3, 4) and (k, 7) is(x, y) and 2x + 2y + 1 = 0. Find the value of k. (a) 10 (b) –15 (c) 15 (d) –10

SP-12 Mathematics 27. For which value of p, will the lines represented by the following pair of linear equations be parallel 3x – y – 5 = 0 (b) 10 6x – 2y – p = 0 (d) 1/2 (a) all real values except 10 (c) 5/2 28. If ABC and EBC are two equilateral triangles such that D is mid-point of BC, then the ratio of the areas of triangles ABC and BDE is (a) 2 : 1 (b) 1 : 2 (c) 1 : 4 (d) 4 : 1 29. If  a , 4  is the midpoint of the line segment joining A(–6, 5) and B(–2, 3), then what is the value of ‘a’?  3  (a) –4 (b) –12 (c) 12 (d) –6 30. A fair die is thrown once. The probability of getting a composite number less than 5 is (a) 1 (b) 1 (c) 2 (d) 0 3 63 31. ABC is an isosceles triangle in which AB = AC = 10 cm, BC = 12 cm. PQRS is a rectangle inside the isosceles triangle. Given PQ = SR = y cm and PS = QR = 2x cm, then x = (a) 6 − 3y (b) 6 + 6y (c) 6 + 4y 7x + 8y 4 3 (d) 4 32. If the zeroes of the polynomial f (x) = k2x2 – 17x + k + 2, (k > 0) are reciprocal of each other than value of k is (a) 2 (b) –1 (c) –2 (d) 1 33. The figure shows two concentric circleswith centre O and radii 3.5 m and 7 m. If ∠BOA = 40°, find the area of the shaded region. B DA C O (a) 767 cm2 (b) 756 (c) 73 (d) None of these 6  15 (2 + 2sin θ) (1− sin θ) 34. If cot θ =  8  , then evaluate (1+ cos θ) (2 − 2 cos θ) (a) 1 (b) 225 (c) 156 (d) –1 64 7 35. If a letter is chosen at random from the letter of English alphabet, then the probability that it is a letter of the word ‘DELHI’ is (a) 15 (b) 216 (c) 5 (d) 2261 26 36. What is the largest number that divides 70 and 125, leaving remainders 5 and 8 respectively? (a) 13 (b) 9 (c) 3 (d) 585

Sample Paper-2 SP-13 37. The diagonal BD of a parallelogram ABCD intersects the segment AE at the point F, where E is any point on the side BC. Then DC 4 1 F2 E 3 A B (a) FEAF  FB (b) DF × EF = FB × FA AB (d) (c) DF × EF = (FB)2 None of these 38. If P = (2, 5), Q = (x, –7) and PQ = 13, what is the value of ‘x’? (a) 5 (b 3 (c) –3 (d) –5 39. What is the largest number that divides 245 and 1029, leaving remainder 5 in each case? (a) 15 (b) 16 (c) 9 (d) 5 40. If p, q are two consecutive natural numbers, then H.C.F. (p, q) is (a) p (b) q (c) 1 (d) pq SECTION-C Case Study Based Questions: Section C consists of 10 quesions of 1 mark each. Any 8 quesions are to be attempted. Q 41. - Q 45 are based on case study-I Case Study-I Place a lighted bulb at a point O on the ceiling and directly below it a table in classroom. Place DABC shape cardboard parallel to the ground between the lighted bulb and the table. Then a shadow of DA′B′C′ is cost on the table such that DABC ~ DA′B′C′ shown in figure. If AB = 5 cm, A′B′ = 15 cm; B′C′ = 12 cm, AC = 3 cm, ∠B′ = 60° and ∠A = 80°. O A BC A¢ B¢ C¢

SP-14 Mathematics Answer the following questions. 41. Length of A′C′ is : (a) 3 cm (b) 4 cm (c) 9 cm (d) 12 cm 42. Length of BC is : (a) 4 cm (b) 12 cm (c) 3 cm (d) 15 cm 43. Measure of ∠A′ is : (a) 60° (b) 80° (c) 180° (d) 40° 44. Find the measure of ∠B. (a) 60° (b) 40° (c) 80° (d) 180° 45. Find the measure of ∠C. (a) 60° (b) 40° (c) 80° (d) 180° Q 46 - Q 50 are based on case study-II Case Study-II A two digit number is obtained by either multiplying sum of the digits by 8 and adding 1 or by multiplying the difference of the digits by 13 and adding 2. If x be the digit in ten’s place and y be the digit at unit place with x > y, then answer the following questions. 46. Find the equation corresponding to multiplying sum of the digits by 8 and adding 1. (a) 2x – 7y = 1 (b) 2x + 7y = 4 (c) 2x – 7y = 4 (d) 2x + 7y = 1 47. Find the equation corresponding to multiplying the difference of the digits by 13 and adding 2. (a) 14y – 3x = 2 (b) 3x – 14y = 4 (c) 14x – 3y = 2 (d) 3y – 14x = 6 48. What is the value of x ? (a) 2 (b) 3 (c) 4 (d) 5 49. What is the value of y ? (a) 0 (b) 1 (c) 3 (d) 4 50. What is the number ? (a) 21 (b) 31 (c) 41 (d) 51

OMR ANSWER SHEET Sample Paper No –  Use Blue / Black Ball pen only.  Please do not make any atray marks on the answer sheet.  Rough work must not be done on the answer sheet.  Darken one circle deeply for each question in the OMR Answer sheet, as faintly darkend / half darkened circle might by rejected. Start time : ____________________ End time ____________________ Time taken ____________________ 1. Name (in Block Letters) 2. Date of Exam SECTION-A 17. a    b    c    d 18. a    b    c    d 3. Candidate’s Signature 9. a    b    c    d 19. a    b    c    d 10. a    b    c    d 20. a    b    c    d 1. a    b    c    d 11. a    b    c    d 2. a    b    c    d 12. a    b    c    d 37. a    b    c    d 3. a    b    c    d 13. a    b    c    d 38. a    b    c    d 4. a    b    c    d 14. a    b    c    d 39. a    b    c    d 5. a    b    c    d 15. a    b    c    d 40. a    b    c    d 6. a    b    c    d 16. a    b    c    d 7. a    b    c    d 49. a    b    c    d 8. a    b    c    d SECTION-B 50. a    b    c    d 21. a    b    c    d 29. a    b    c    d 22. a    b    c    d 30. a    b    c    d 23. a    b    c    d 31. a    b    c    d 24. a    b    c    d 32. a    b    c    d 25. a    b    c    d 33. a    b    c    d 26. a    b    c    d 34. a    b    c    d 27. a    b    c    d 35. a    b    c    d 28. a    b    c    d 36. a    b    c    d 41. a    b    c    d SECTION-C 42. a    b    c    d 43. a    b    c    d 45. a    b    c    d 44. a    b    c    d 46. a    b    c    d 47. a    b    c    d 48. a    b    c    d No. of Qns. Attempted Correct Incorrect Marks

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Sample Paper 3 Time : 90 Minutes Max Marks : 40 General Instructions 1. The question paper contains three parts A, B and C. 2. Section A consists of 20 quesions of 1 mark each. Any 16 quesitons are to be attempted. 3. Section B consists of 20 quersions of 1 mark each. Any 16 quesions are to be attempted. 4. Section C consists of 10 quesions based two Case Studies. Attempt any 8 questions. 5. There is no negative marking. SECTION-A Section A consists of 20 questions of 1 mark each. Any 16 quesions are to be attempted. 1. Two numbers differ by 3 and their product is 54. Find the numbers. (a) 9 and 6 (b) – 9 and – 6 (c) Both (a) and (b) (d) 9 and – 4 2. ∆ABC ~ ∆PQR and area ∆ABC = 16 . If PQ = 18 cm and BC = 12 cm. then AB and QR are respectively area ∆PQR 9 (a) 9 cm, 24 cm (b) 24 cm, 9 cm (c) 32 cm, 6.75 cm (d) 13.5 cm, 16 cm 1 3. What is the maximum value of sec θ ? (a) 0 (b) 1 (c) –1 (d) –2 4. If the zeros of the polynomial f(x) = k2x2 – 17x + k + 2, (k > 0 ) are reciprocal of each other, then the value of k is (a) 2 (b) – 1 (c) – 2 (d) 1 5. If the value of a quadratic polynomial p(x) is 0 only at x = – 1 and p(– 2) = 2, then the value of p(2) is (a) 18 (b) 9 (c) 6 (d) 3 6. The probability of raining on day 1 is 0.2 and on day 2 is 0.3. The probability of raining on both the days is (a) 0.2 (b) 0.1 (c) 0.06 (d) 0.25 7. Which of the following statement is false? (a) All isosceles triangles are similar. (b) All quadrilateral triangles are similar. (c) All circles are similar. (d) None of the above

SP-18 Mathematics 8. A race track is in the form of a ring whose inner and outer circumference are 437m and 503m respectively. The area of the track is (a) 66 sq. cm (b) 4935 sq. cm (c) 9870 sq. cm (d) None of these 9. Which of the following will have a terminating decimal expansion? (a) 77 (b) 23 (c) 125 (d) 23 210 30 441 8 10. I. The L.C.M. of x and 18 is 36. II. The H.C.F. of x and 18 is 2. What is the number x ? (a) 1 (b) 2 (c) 3 (d) 4 11. Which of the following cannot be the probability of an event? (a) 2/3 (b) – 1/5 (c) 15% (d) 0.7 12. P, Q, R are three collinear points. The coordinates of P and R are (3, 4) and (11, 10) respectively and PQ is equal to 2.5 units. Coordinates of Q are (a) (5, 11/2) (b) (11, 5/2) (c) (5, –11/2) (d) (–5, 11/2) 13. A number lies between 300 and 400. If the number is added to the number formed by reversing the digits, the sum is 888 and if the unit’s digit and the ten’s digit change places, the new number exceeds the original number by 9. Then, the number is (a) 339 (b) 341 (c) 378 (d) 345 14. A fraction becomes 4 when 1 is added to both the numerator and denominator and it becomes 7 when 1 is subtracted from both the numerator and denominator. The numerator of the given fraction is (a) 2 (b) 3 (c) 5 (d) 15 15. The sum of the areas of two circles, which touch each other externally, is 153 π. If the sum of their radii is 15, then the ratio of the larger to the smaller radius is (a) 4 : 1 (b) 2 : 1 (c) 3 : 1 (d) None of these 16. The zeroes of the polynomial x2 – 3x – m(m + 3) are (a) m, m + 3 (b) –m, m +3 (c) m, –(m + 3) (d) –m, –(m + 3) 17. If a and b are zeroes of the polynomial 2t2 – 4t + 3, then the value of a2b + ab2 is : (a) 3 (b) 2 (c) 3 (d) 4 4 18. In the given figure, DE || BC. The value of EC is D 1.5 cmA1 cm E 3 cm BC (a) 1.5 cm (b) 3 cm (c) 2 cm (d) 1 cm 19. At present ages of a father and his son are in the ratio 7 : 3, and they will be in the ratio 2 : 1 after 10 years. Then the present age of father (in years) is (a) 42 (b) 56 (c) 70 (d) 77

Sample Paper-3 SP-19 20. The probability that a two digit number selected at random will be a multiple of ‘3’ and not a multiple of ‘5’ is (a) 2 (b) 4 (c) 1 (d) 4 15 15 15 90 SECTION-B Section B consists of 20 questions of 1 mark each. Any 16 quesions are to be attempted. 21. Solve 2x2 + 3y2 = 35; x2 + y2 =5 2 3 (a) x =± 4, y =± 9 (b) x = 3, y = 4 (c) x = 1, y = 1 (d) x =± 2, y =± 3 22. In ∆ABC, E divides AB in the ratio 3 : 1 and F divides BC in the ratio 3 : 2, then the ratio of areas of ∆BEF and ∆ABC is (a) 3 : 5 (b) 3 : 10 (c) 1 : 5 (d) 3 : 20 (b) 2 23. Given that sin θ + 2 cos θ = 1, then 2 sin θ – cos θ = (a) 0 (c) 1 (d) None of these 24. If α and β are the zeroes of the polynomial f(x) = x2 – 5x + k such that α – β = 1, the value of K is- (a) 12 (b) 6 (c) 4 (d) 1 25. If x + y = 1, then x3 + y3 + 3xy = ............... (a) 0 (b) 1 (c) 2 (d) None of these 26. The zeroes of the polynomial are p(x) = x2 –10x –75 (a) 5, – 15 (b) 5, 15 (c) 15, – 5 (d) – 5, – 15 27. If cosec x – cot x = 1 , where x ≠ 0, then the value of cos2x – sin2x is 3 (a) 16 (b) 9 (c) 8 (d) 7 25 25 25 25 28. The points (7, 2) and (–1, 0) lie on a line (a) 7y = 3x – 7 (b) 4y = x + 1 (c) y = 7x + 7 (d) x = 4y + 1 29. X’s salary is half that of Y’s. If X got a 50% rise in his salary and Y got 25% rise in his salary, then the percentage increase in combined salaries of both is (a) 30 (b) 33 1 (c) 37 1 (d) 75 3 2 30. The perimeter of a sector of a circle with central angle 90° is 25 cm. Then the area of the minor segment of the circle is. (a) 14 cm2 (b) 16 cm2 (c) 18 cm2 (d) 24 cm2 31. The perimeters of two similar triangles ABC and PQR are respectively 36 cm and 24 cm. If PQ = 10 cm, then AB = (a) 10 cm (b) 20 cm (c) 25 cm (d) 15 cm

SP-20 Mathematics 32. The least number which when divided by 15, leaves a remainder of 5, when divided by 25, leaves a remainder of 15 and when divided by 35, leaves a remainder of 25, is (a) 515 (b) 525 (c) 1040 (d) 1050 33. Out of one digit prime numbers, one number is selected at random. The probability of selecting an even number is (a) 1 (b) 1 (c) 4 (d) 2 2 4 9 5 34. A can do a piece of work in 24 days. If B is 60% more efficient than A, then the number of days required by B to do the twice as large as the earlier work is (a) 24 (b) 36 (c) 15 (d) 30 35. If n is an even natural number, then the largest natural number by which n (n + 1) (n + 2) is divisible is (a) 6 (b) 8 (c) 12 (d) 24 36. The least number which is a perfect square and is divisible by each of 16, 20 and 24 is (a) 240 (b) 1600 (c) 2400 (d) 3600 37. It is given that ∆ABC ~ ∆PQR with BC 1 . Then ar(∆PQR) is equal to QR = 3 ar(∆ABC) (a) 9 (b) 3 (c) 1 (d) 1 3 9 38. The figure given shows a rectangle with a semi-circle and 2 identical quadrants inside it. 28 cm 16 cm 23 cm What is the shaded area of the figure? (Use π = 22 ) 7 (a) 363 cm2 (b) 259 cm2 (c) 305 cm2 (d) 216 cm2 39. The value of k for which the system of linear equations x + 2y = 3, 5x + ky + 7 = 0 is inconsistent is (a) − 14 (b) 2 3 5 (c) 5 (d) 10 40. The probability of getting a number greater than 2 in throwing a die is (a) 2/3 (b) 1/3 (c) 4/3 (d) 1/4

Sample Paper-3 SP-21 SECTION-C Case Study Based Questions: Section C consists of 10 quesions of 1 mark each. Any 8 quesions are to be attempted. Q 41. - Q 45 are based on case study-I Case Study-I To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections-section A and section B of grade X. There are 64 students in section A and 72 students in section B. 41. What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B? (a) 144 (b) 128 (c) 576 (d) 272 42. If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (64, 72) is (a) 2 (b) 4 (c) 6 (d) 8 43. 72 can be expressed as a product of its primes as (a) 23 × 32 (b) 21 × 33 (c) 23 × 31 (d) 20 × 30 44. 5 × 13 × 17 × 19 + 19 is a (a) Prime number (b) Composite number (c) Neither prime nor composite (d) None of the above 45. If p and q are positive integers such that p = a2b3 and q = a3b2, where a, b are prime numbers, then the HCF (p, q) is (a) ab (b) a2b2 (c) a3b2 (d) a3b3 Q 46 - Q 50 are based on case study-II Case Study-II Due to heavy storm an electric wire got bent as shown in the figure. It followed a mathematical shape. Answer the following questions below. y 6 5 4 3 2 1 –6 –5 –4 –3 –2 –1 12345678 –1 –2 –3 –4 –5

SP-22 Mathematics 46. Name the shape in which the wire is bent parabola 0 (a) spiral (b) ellipse (c) linear (d) –4, 2 x2 + 2x + 3 47. How many zeroes are there for the polynomial (shape of the wire)? 0 (a) 2 (b) 3 (c) 1 (d) 48. The zeroes of the polynomial are (a) –1, 5 (b) –1, 3 (c) 3, 5 (d) 49. What will be the expression of the polynomial? (a) x2 + 2x – 3 (b) x2 – 2x + 3 (c) x2 – 2x – 3 (d) 50. What is the value of the polynomial if x = –1? (a) 6 (b) –18 (c) 18 (d)

OMR ANSWER SHEET Sample Paper No –  Use Blue / Black Ball pen only.  Please do not make any atray marks on the answer sheet.  Rough work must not be done on the answer sheet.  Darken one circle deeply for each question in the OMR Answer sheet, as faintly darkend / half darkened circle might by rejected. Start time : ____________________ End time ____________________ Time taken ____________________ 1. Name (in Block Letters) 2. Date of Exam SECTION-A 17. a    b    c    d 18. a    b    c    d 3. Candidate’s Signature 9. a    b    c    d 19. a    b    c    d 10. a    b    c    d 20. a    b    c    d 1. a    b    c    d 11. a    b    c    d 2. a    b    c    d 12. a    b    c    d 37. a    b    c    d 3. a    b    c    d 13. a    b    c    d 38. a    b    c    d 4. a    b    c    d 14. a    b    c    d 39. a    b    c    d 5. a    b    c    d 15. a    b    c    d 40. a    b    c    d 6. a    b    c    d 16. a    b    c    d 7. a    b    c    d 49. a    b    c    d 8. a    b    c    d SECTION-B 50. a    b    c    d 21. a    b    c    d 29. a    b    c    d 22. a    b    c    d 30. a    b    c    d 23. a    b    c    d 31. a    b    c    d 24. a    b    c    d 32. a    b    c    d 25. a    b    c    d 33. a    b    c    d 26. a    b    c    d 34. a    b    c    d 27. a    b    c    d 35. a    b    c    d 28. a    b    c    d 36. a    b    c    d 41. a    b    c    d SECTION-C 42. a    b    c    d 43. a    b    c    d 45. a    b    c    d 44. a    b    c    d 46. a    b    c    d 47. a    b    c    d 48. a    b    c    d No. of Qns. Attempted Correct Incorrect Marks

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Sample Paper 4 Time : 90 Minutes Max Marks : 40 General Instructions 1. The question paper contains three parts A, B and C. 2. Section A consists of 20 quesions of 1 mark each. Any 16 quesitons are to be attempted. 3. Section B consists of 20 quersions of 1 mark each. Any 16 quesions are to be attempted. 4. Section C consists of 10 quesions based two Case Studies. Attempt any 8 questions. 5. There is no negative marking. SECTION-A Section A consists of 20 questions of 1 mark each. Any 16 quesions are to be attempted. 1. If x + y = 1, then x3 + y3 + 3xy = ............... (a) 0 (b) 1 (c) 2 (d) None of these 2. Find a point on the x-axis which is equidistant from the points (5, 4) and (–2, 3). (a) (2, 0) (b) (0, 3) (c) (–2, 2) (d) (3, 0) 3. Two numbers differ by 3 and their product is 54. Find the numbers. (a) 9 and 6 (b) – 9 and – 6 (c) Both (a) and (b) (d) 9 and – 4 4. A railway half -ticket costs half the full fare but the reservation charges are the same on a half ticket as on full ticket. One reserved first class ticket from station A to station B costs ` 2125. Also, one reserved first class ticket and one reserved half first class ticket from A to B costs ` 3200. Find the full fare from station A to B and also the reservation charges for a ticket. (a) ` 1100, ` 15 (b) ` 2100, ` 25 (c) ` 1000, ` 25 (d) ` 2000, ` 40 5. tan θ − cot θ is equal to sin θ cos θ (a) sec2 θ + cosec2 θ (b) cot2 θ – tan2 θ (c) cos2 θ – sin2 θ (d) tan2θ – cot2θ 6. I. The L.C.M. of x and 18 is 36. II. The H.C.F. of x and 18 is 2. What is the number x ? (a) 1 (b) 2 (c) 3 (d) 4 7. In the figure, ABC is a triangle in which AD bisects ∠A, AC = BC, ∠B = 72° and CD = 1cm. Length of BD (in cm) is C D AB

SP-26 Mathematics (a) 1 (b) 1 (c) 5– 1 (d) 3 +1 2 2 2 8. C is the mid-point of PQ, if P is (4, x), C is (y, –1) and Q is (–2, 4), then x and y respectively are (a) – 6 and 1 (b) – 6 and 2 (c) 6 and – 1 (d) 6 and – 2 9. If in a lottery, there are 5 prizes and 20 blanks, then the probability of getting a prize is (a) 52 (b) 54 (c) 1 (d) 1 5 10. If a = 23 × 3, b = 2 × 3 × 5, c = 3n × 5 and L.C.M. (a, b, c) = 23 × 32 × 5, then n = (a) 1 (b) 2 (c) 3 (d) 4 11. The area of a circular ring formed by two concentric circles whose radii are 5.7 cm and 4.3 cm respectively is (Take π = 3.1416) (a) 43.98 sq.cm (b) 53.67 sq. cm (c) 47.24 sq.cm (d) 38.54 sq.cm 12. The areas of two similar triangles are 81 cm2 and 49 cm2 respectively, then the ratio of their corresponding medians is (a) 7 : 9 (b) 9 : 81 (c) 9 : 7 (d) 81 : 7 13. If cos θ + 1 cos θ =4, then 1− sin θ + sin θ (a) cos θ = 3 (b) sin θ =12 (c) θ = 60° (d) tan θ = 1 2 3 14. The ratio in which the point (2, y) divides the join of (– 4, 3) and (6, 3) and hence the value of y is (a) 2 : 3, y = 3 (b) 3 : 2, y = 4 (c) 3 : 2, y = 3 (d) 3 : 2, y = 2 15. In a number of two digits, unit’s digit is twice the tens digit. If 36 be added to the number, the digits are reversed. The number is (a) 36 (b) 63 (c) 48 (d) 84 16. Two coins are tossed simultaneously. The probability of getting at most one head is (a) 14 (b) 12 (c) 3 (d) 1 4 17. ∆ABC is an equilateral triangle with each side of length 2p. If AD ⊥ BC, then the value of AD is (a) 3 (b) 3 p (c) 2p (d) 4p 18. Lowest value of x2 + 4x + 2 is (a) 0 (b) –2 (c) 2 (d) 4 19. Ratio in which the line 3x + 4y = 7 divides the line segment joining the points (1, 2) and (–2, 1) is (a) 3 : 5 (b) 4 : 6 (c) 4 : 9 (d) None of these

Sample Paper-4 SP-27 20. In the adjoining figure, OABC is asquare of side 7 cm. OAC is a quadrant of a circle with O as centre. The area of the shaded region is OC AB (a) 10.5 cm2 (b) 38.5 cm2 (c) 49 cm2 (d) 11.5 cm2 SECTION-B Section B consists of 20 questions of 1 mark each. Any 16 quesions are to be attempted. 21. If the value of a quadratic polynomial p(x) is 0 only at x = – 1 and p(– 2) = 2, then the value of p(2) is (a) 18 (b) 9 (c) 6 (d) 3 22. Which of the following is not correct? (a) If the diagonals of a quadrilateral divide each other proportionally, then it is a trapezium. (b) The line segments joining the mid-points of the adjacent sides of a quadrilateral form a parallelogram. (c) If corresponding sides of two similar triangles are in the ratio 4 : 5, then corresponding medians of the triangles must be in the ratio 4 : 5. (d) None of the above 23. If 5θ and 4θ are acute angles satisfying sin 5θ = cos 4θ, then 2sin 3θ – 3 tan 3θ is equal to (a) sin2θ (b) 1 (c) 1 (d) 0 2 3 24. Determine the value of k for which the following system of equations becomes consistent : 7x – y = 5, 21x – 3y = k. (a) k = 15 (b) k = 11 (c) k = 4 (d) k = 11 4 (d) 2 25. If α and β are the zeroes of the polynomial f(x) = x2 – 5x + k such that α – β = 1, the value of K is- (a) 12 (b) 6 (c) 1 26. 2 tan 30° is equal to 1+ tan2 30° (a) sin 30° (b) cos 60° (c) 1 (d) 3 2 2 27. Find the largest number of four digits exactly divisible by 12, 15, 18 and 27. (a) 9720 (b) 9728 (c) 9270 (d) 7290 28. The point on the X-axis which is equidistant from the points A(–2, 3) and B(5, 4) is (a) (0, 2) (b) (2, 0) (c) (3, 0) (d) (–2, 0)

SP-28 Mathematics 29. The length of the side of a square whose diagonal is 16 cm, is (a) 8 2 cm (b) 2 8 cm (c) 4 2 cm (d) 2 2 cm 30. If 3x + 4y : x + 2y = 9 : 4, then 3x + 5y : 3x – y is equal to (a) 4 : 1 (b) 1 : 4 (c) 7 : 1 (d) 1 : 7 31. An urn contains 6 blue and ‘a’ green balls. If the probability of drawing a green ball is double that of drawing a blue ball, then ‘a’ is equal to (a) 6 (b) 18 (c) 24 (d) 12 32. If x = 0.7 , then 2x is (a) 1.4 (b) 1.5 (c) 1.54 (d) 1.45 33. The point which divides the line joining the points A (1, 2) and B(–1, 1) internally in the ratio 1 : 2 is (a)  –31 , 5  (b)  13 , 5  (c) (–1, 5) (d) (1, 5) 3  3  34. x and y are 2 different digits. If the sum of the two digit numbers formed by using both the digits is a perfect square, then value of x + y is (a) 10 (b) 11 (c) 12 (d) 13 35. The areas of two similar triangles ABC and PQR are in the ratio 9 : 16. If BC = 4.5 cm, then the length of QR is (a) 4 cm (b) 4.5 cm (c) 3 cm (d) 6 cm 36. If cosec A + cot A = 11 , then tan A 2 (a) 2221 (b) 1165 (c) 44 (d) 11 117 117 37. The centroid of the triangle whose vertices are (3, –7), (–8, 6) and (5, 10) is (a) (0, 9) (b) (0, 3) (c) (1, 3) (d) (3, 5) 38. A single letter is selected at random from the word “PROBABILITY”. The probability that the selected letter is a vowel is (a) 2 (b) 3 (c) 4 (d) 0 11 11 11 39. On dividing a natural number by 13, the remainder is 3 and on dividing the same number by 21, the remainder is 11. If the number lies between 500 and 600, then the remainder on dividing the number by 19 is (a) 4 (b) 6 (c) 9 (d) 13 40. If ∆ABC ~ ∆APQ and ar (∆APQ) = 4 ar (∆ABC), then the ratio of BC to PQ is (a) 2 : 1 (b) 1 : 2 (c) 1 : 4 (d) 4 : 1

Sample Paper-4 SP-29 SECTION-C Case Study Based Questions: Section C consists of 10 quesions of 1 mark each. Any 8 quesions are to be attempted. Q 41. - Q 45 are based on case study-I Case Study-I Students of class X make a design such that, the area of an equilateral triangle ABC is 17320.5 cm2. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle. (Use p = 3.14 and 3 = 1.73205) A BC Answer the following questions. 41. Find the length of side of DABC. (a) 200 cm (b) 105.5 cm (c) 210.3 cm (d) 200.5 cm 42. Find the radius circle. (b) 20 cm (c) 10 cm (d) 100 cm (a) 200 cm 43. Find the area of each sector. (a) 5233.3 cm2 (b) 5223.3 cm2 (c) 4233.3 cm2 (d) 522.2 cm2 44. Find the area of the shaded region. (a) 17320.5 cm2 (b) 1620.5 cm2 (c) 15700 cm2 (d) 31400 cm2 45. Find the perimeter of DABC. (a) 60 cm (b) 400 cm (c) 600 cm (d) 300 cm Q 46 - Q 50 are based on case study-II Case Study-II On school sport day, a sport teacher make a racing track whose left and right ends are semicircular shown in figure.

SP-30 Mathematics The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide then answer the following questions. 46. Find the radius of inner semicircular end. (a) 30 m (b) 60 m (c) 10 m (d) 40 m 47. Find the radius of outer semicircular end (a) 30 m (b) 50 m (c) 40 m (d) 70 m 48. The distance around the track along its inner edge is: (a) 423.57 m (b) 400.57 m (c) 400.32 m (d) 400 m 49. The distance around the track along its outer edge is: (a) 462.43 m (b) 461.43 m (c) 463 m (d) 463.43 m 50. Find the area of the track. (a) 4320 m2 (b) 4230 m2 (c) 2340 m2 (d) 4120 m2

OMR ANSWER SHEET Sample Paper No –  Use Blue / Black Ball pen only.  Please do not make any atray marks on the answer sheet.  Rough work must not be done on the answer sheet.  Darken one circle deeply for each question in the OMR Answer sheet, as faintly darkend / half darkened circle might by rejected. Start time : ____________________ End time ____________________ Time taken ____________________ 1. Name (in Block Letters) 2. Date of Exam SECTION-A 17. a    b    c    d 18. a    b    c    d 3. Candidate’s Signature 9. a    b    c    d 19. a    b    c    d 10. a    b    c    d 20. a    b    c    d 1. a    b    c    d 11. a    b    c    d 2. a    b    c    d 12. a    b    c    d 37. a    b    c    d 3. a    b    c    d 13. a    b    c    d 38. a    b    c    d 4. a    b    c    d 14. a    b    c    d 39. a    b    c    d 5. a    b    c    d 15. a    b    c    d 40. a    b    c    d 6. a    b    c    d 16. a    b    c    d 7. a    b    c    d 49. a    b    c    d 8. a    b    c    d SECTION-B 50. a    b    c    d 21. a    b    c    d 29. a    b    c    d 22. a    b    c    d 30. a    b    c    d 23. a    b    c    d 31. a    b    c    d 24. a    b    c    d 32. a    b    c    d 25. a    b    c    d 33. a    b    c    d 26. a    b    c    d 34. a    b    c    d 27. a    b    c    d 35. a    b    c    d 28. a    b    c    d 36. a    b    c    d 41. a    b    c    d SECTION-C 42. a    b    c    d 43. a    b    c    d 45. a    b    c    d 44. a    b    c    d 46. a    b    c    d 47. a    b    c    d 48. a    b    c    d No. of Qns. Attempted Correct Incorrect Marks

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Sample Paper 5 Time : 90 Minutes Max Marks : 40 General Instructions 1. The question paper contains three parts A, B and C. 2. Section A consists of 20 quesions of 1 mark each. Any 16 quesitons are to be attempted. 3. Section B consists of 20 quersions of 1 mark each. Any 16 quesions are to be attempted. 4. Section C consists of 10 quesions based two Case Studies. Attempt any 8 questions. 5. There is no negative marking. SECTION-A Section A consists of 20 questions of 1 mark each. Any 16 quesions are to be attempted. ( )1. If three points (0, 0) 3, 3 and (3, λ) form an equilateral triangle, then λ is equal to (a) 2 (b) – 3 (c) − 3 (d) 3 2. If the sum of the zeros of the polynomial f(x) = (k2 – 14) x2 – 2x – 12 is 1, which is one of the possible values of ‘k’? (a) 14 (b) –14 (c) 2 (d) ± 4 3. ABCD is a square. F is the mid-point of AB, BE is one-third of BC. If the area of the ∆FBE is 108 sq. cm find the length AC.   (a) 36 2 cm (b) 37 2 cm (c)  36 2 cm (d) (36)2 cm 4. Express the number 0.3178 in the form of rational number. 3178 (b) 3178 (c) 3178 (d) 999 (a) 99 999 1000 3178 5. The product of two irrationals is (a) a rational number (b) an irrational number neither A nor B (c) either A or B (d) 6. In DABC, AB = AC, P and Q are points on AC and AB respectively such that BC = BP = PQ = AQ. Then, ∠AQP is equal to (use p =180º) (a) 27π (b) 37π (c) 4π (d) 5π 7 7 7. If the circumference of a circle increases from 4π to 8π, then its area is (a) halved (b) doubled (c) tripled (d) quadrupled 8. (1 + tan θ + sec θ) (1 + cot θ– cosec θ) = (a) 0 (b) 1 (c) 2 (d) –1

SP-34 Mathematics 9. If the point P (p, q) is equidistant from the points A (a + b, b – a) and B (a – b, a + b), then (a) ap = by (b) bp = ay (c) ap + bq = 0 (d) bp + aq = 0 10. In a classroom, one-fifth of the boys leave the class and the ratio of the remaining boys to girls is 2 : 3. If further 44 girls leave the class, then the ratio of boys to girls is 5: 2. How many more boys should leave the class so that the number of boys equals that of girls? (a) 16 (b) 24 (c) 30 (d) 36 11. In the adjoining figure, OACB is a quadrant of a circle of radius 7 cm. The perimeter of the quadrant is B C (a) 11 cm OA (d) 36 cm (b) 18 cm (c) 25 cm 12. Let ABC be a triangle and M be a point on side AC closer to vertex C than A. Let N be a point on side AB such that MN is parallel to BC and let P be a point on side BC such that MP is parallel to AB. If the area of the quadrilateral BNMP is equal 5 to 18 of the area of DABC, then the ratio AM/MC equals 18 (d) 125 (b) 6 (c) 5 (a) 5 13. The points A (– 4, – 1), B (–2, – 4), C (4, 0) and D (2, 3) are the vertices of a (a) Parallelogram (b) Rectangle (c) Rhombus (d) Square 14. For what value of p, the following pair of linear equations in two variables will have infinitely many solutions ? px + 3y – (p – 3) = 0, 12x + py – p = 0 (a) 6 (b) – 6 (c) 0 (d) 2 15. If a circular grass lawn of 35m in radius has a path 7m wide running around it on the outside, then the area of the path is (a) 1450 m2 (b) 1576 m2 (c) 1694 m2 (d) 3368 m2 16. 9 sec2 A – 9 tan2 A = (a) 1 (b) 9 (c) 8 (d) 0 17. Three - digit numbers formed by using digits 0, 1, 2 and 5 (without repetition) are written on different slips with distinct number on each slip, and put in a bowl. One slip is drawn at random from the bowl. The probability that the slip bears a number divisible by 5 is (b) 94 (c) 2 (d) 13 (a) 95 3 18. The value of 0.235 is : (b) 929303 (c) 235 (d) 929305 (a) 920303 999

Sample Paper-5 SP-35 19. The figure below shows two concentric circles with centre O. PQRS is a square inscribed in the outer circle. It also circum- scribes the inner circle, touching it at point B, C, D and A. The ratio of the perimeter of the outer circle to that of polygon ABCD is (a) π (b) 3π (c) π (d) p 4 2 2 20. Let P be an interior point of a DABC. Let Q and R be the reflections of P in AB and AC, respectively. If Q, A, R are collinear, then ∠A equals (a) 30° (b) 60° (c) 90° (d) 120° SECTION-B Section B consists of 20 questions of 1 mark each. Any 16 quesions are to be attempted. 21. If α and β are the zeros of the polynomial f(x) = x2 + ax – b, find the polynomial having zeros 1 and 1 .  (a) abx2 + bx – a (b) x2  a x  1 (c) abx2 – bx + a (d) x2  b x  1 b b a a 22. A class of 20 boys and 15 girls is divided into n groups so that each group has x boys and y girls. Values of x, y and n respectively are (a) 3, 4 and 8 (b) 4, 3 and 6 (c) 4, 3 and 7 (d) 7, 4 and 3 23. Triangle ABC is an isosceles triangle right angled at B. ∆ADB and ∆AEC are equilateral triangle then. (a) Area (∆ABD) = 1 Area (∆CAE) (b) Area (∆ABD) = Area (∆CAE) 2 (c) Area (∆ABD) = 3 Area (∆CAE) (d) 2Area (∆ABD) = Area (∆CAE) 24. A polynomial of degree 7 is divided by a polynomial of degree 4. Degree of the quotient is (a) less than 3 (b) 3 (c) more than 3 (d) more than 5 25. Find a point on the x-axis which is equidistant from the points (5, 4) and (–2, 3). (a) (2, 0) (b) (0, 3) (c) (–2, 2) (d) (3, 0) 26. A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought? (a) 40 (b) 240 (c) 480 (d) 750 27. 2 tan 30° = 1− tan2 30° (a) cos 60° (b) sin 60° (c) tan 60° (d) sin 30° 28. If the value of a quadratic polynomial p(x) is 0 only at x = –1 and p(–2) = 2, then the value of p(2) is (a) 18 (b) 9 (c) 6 (d) 3

SP-36 Mathematics 29. If the sector of a circle of diameter 10 cm subtends an angle of 144° at the centre, then the length of the arc of the sector is (a) 2π cm (b) 4π cm (c) 5π cm (d) 6π cm 30. x and y are two non-negative numbers such that 2x + y = 10. The sum of the maximum and minimum values of (x + y) is (a) 6 (b) 9 (c) 10 (d) 15 31. sin 2A = 2 sin A is true when A = (a) 0° (b) 30° (c) 45° (d) 60° 32. Given that 1 = 0.142857 , which is a repeating decimal having six different digits. If x is the sum of such first three positive 7 integers n such that 1 = 0.abcdef , where a, b, c, d, e and f are different digits, then the value of x is n (a) 20 (b) 21 (c) 41 (d) 42 33. For an event E, P (E) + P (E ) = q, then (a) 0 ≤ q < 1 (b) 0 < q ≤ 1 (c) 0 < q < 1 (d) None of these 34. A boat travels with a speed of 15 km/hr in still water. In a river flowing at 5 km/hr, the boat travels some distance downstream and then returns. The ratio of average speed to the speed in still water is (a) 8 : 3 (b) 3 : 8 (c) 8 : 9 (d) 9 : 8 35. Which of the following relationship is the correct ? (a) P (E) + P (E) = 1 (b) P (E) – P(E) = 1 None of these (c) P(E) = 1 + P (E) (d) 36. 1− tan2 45° = 1+ tan2 45° (a) tan 90° (b) 1 (c) sin 45° (d) 0 37. The sum of two numbers is 528 and their H.C.F. is 33, then find the number of pairs of numbers satisfying the above conditions. (a) 4 (b) 5 (c) 6 (d) 2 38. A man can row a boat in still water at the rate of 6 km per hour. If the stream flows at the rate of 2 km/hr, he takes half the time going downstream than going upstream the same distance. His average speed for upstream and down stream trip is (a) 6 km/hr (b) 16/3 km/hr (d) none of the above (c) Insufficient data to arrive at the answer 39. 2 tan 30° = 1+ tan2 30° (a) sin 60° (b) cos 60° (c) tan 60° (d) sin 30°

Sample Paper-5 SP-37 40. The unit digit in the expression 55725 + 735810 + 22853 is (a) 0 (b) 4 (c) 5 (d) 6 SECTION-C Case Study Based Questions: Section C consists of 10 quesions of 1 mark each. Any 8 quesions are to be attempted. Q 41. - Q 45 are based on case study-I Case Study-I Soniya and Anuj are students of class X and they given a polynomial such that “If one zero of the polynomial 3x2 – 8x + 2k + 5 is four times the other 4x2 – 12x + 3k + 8. Then, answer the following questions. 41. Find the sum of zeroes. (a) 3 (b) 4 (c) 12 (d) 152 3 42. For quadratic polynomial ax2 + bx + c, a ≠ 0, write the formula to find product of zeroes. (a) ba (b) – b (c) – c (d) ac a a 43. If α and β be the zeroes of given polynomial. Then, what is the relation between α and β? (a) α + β = 4 (b) αβ = 4 (c) β = 4α (d) α2 = 16β 44. If α and β be the zeroes of the given polynomial, then find value of α. (a) 15 (b) 7 (c) 2 (d) 53 4 5 45. Find the value of k. If α and β be the zeroes of given polynomials. (a) 5765 (b) – 56 (c) 75 (d) 6755 75 56 Q 46 - Q 50 are based on case study-II Case Study-II In a classroom, 4 friends are seated at the points P, Q, R and S as shown in figure. Then answer the following questions. 10 9 8 7Q 6 Rows 5 P R 4 3 2 S 1 1 2 3 4 5 6 7 8 9 10 Columns

SP-38 Mathematics (d) (6, 7) 46. The coordinate of P is : (d) 6 unit (d) 5 unit (a) (4, 3) (b) (3, 4) (c) (6, 1) (d) Parallelogram 47. The distance of PQ is : (c) 2 3 unit (d) (6, 4) (c) 6 unit (a) 3 2 unit (b) 4 unit (c) Rhombus 48. The distance of PR is : (c) (6, 2) (a) 7 unit (b) 6 2 unit 49. The name of quadrilateral is : (a) Square (b) Rectangle 50. The mid point of QS is : (a) (5, 4) (b) (7, 4)

OMR ANSWER SHEET Sample Paper No –  Use Blue / Black Ball pen only.  Please do not make any atray marks on the answer sheet.  Rough work must not be done on the answer sheet.  Darken one circle deeply for each question in the OMR Answer sheet, as faintly darkend / half darkened circle might by rejected. Start time : ____________________ End time ____________________ Time taken ____________________ 1. Name (in Block Letters) 2. Date of Exam SECTION-A 17. a    b    c    d 18. a    b    c    d 3. Candidate’s Signature 9. a    b    c    d 19. a    b    c    d 10. a    b    c    d 20. a    b    c    d 1. a    b    c    d 11. a    b    c    d 2. a    b    c    d 12. a    b    c    d 37. a    b    c    d 3. a    b    c    d 13. a    b    c    d 38. a    b    c    d 4. a    b    c    d 14. a    b    c    d 39. a    b    c    d 5. a    b    c    d 15. a    b    c    d 40. a    b    c    d 6. a    b    c    d 16. a    b    c    d 7. a    b    c    d 49. a    b    c    d 8. a    b    c    d SECTION-B 50. a    b    c    d 21. a    b    c    d 29. a    b    c    d 22. a    b    c    d 30. a    b    c    d 23. a    b    c    d 31. a    b    c    d 24. a    b    c    d 32. a    b    c    d 25. a    b    c    d 33. a    b    c    d 26. a    b    c    d 34. a    b    c    d 27. a    b    c    d 35. a    b    c    d 28. a    b    c    d 36. a    b    c    d 41. a    b    c    d SECTION-C 42. a    b    c    d 43. a    b    c    d 45. a    b    c    d 44. a    b    c    d 46. a    b    c    d 47. a    b    c    d 48. a    b    c    d No. of Qns. Attempted Correct Incorrect Marks

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Sample Paper 6 Time : 90 Minutes Max Marks : 40 General Instructions 1. The question paper contains three parts A, B and C. 2. Section A consists of 20 quesions of 1 mark each. Any 16 quesitons are to be attempted. 3. Section B consists of 20 quersions of 1 mark each. Any 16 quesions are to be attempted. 4. Section C consists of 10 quesions based two Case Studies. Attempt any 8 questions. 5. There is no negative marking. SECTION-A Section A consists of 20 questions of 1 mark each. Any 16 quesions are to be attempted. 1 1. Let P(x) be a polynomial of degree 3 and P(n) = 2 for n = 1, 2, 3, 4. Then the value of P(5) is (a) 0 (b) 1 (c) − 52 (d) 53 5 2. If the area of a square inscribed in a semicircle is 2cm2, then the area of the square inscribed in a full circle of the same radius is ______ (a) 5 cm2 (b) 10 cm2 (c) 5 2 cm2 (d) 25 cm2 3. Which of the following points is 10 units from the origin? (a) (– 6, 8) (b) (– 4, 2) (c) (– 6, 5) (d) (6, 4) 4. The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is (a) 25 (b) 72 (c) 63 (d) 36 5. Find the largest number of four digits exactly divisible by 12, 15, 18 and 27. (a) 9720 (b) 9728 (c) 9270 (d) 7290 6. A circle passes through the vertices of a triangle ABC. If the vertices are A(–2, 5), B(–2, –3), C(2, –3), then the centre of the circle is (a) (0, 0) (b) (0, 1) (c) (–2, 1) (d) (0, –3) 7. The value of (sin 45° + cos 45°) is (d) 1 (a) 12 (b) 2 (c) 23

SP-42 Mathematics 8. In a right angled triangle ∆ABC, length of two sides are 8 cm and 6 cm, then which among the given statements is/are correct? A (a) Length of greatest side is 10cm BC (c) ∠BAC = 45° (b) ∠ACB = 45° (d) Pythagoras theorem is not applicable here. 9. Product of two co-prime numbers is 117. Their L.C.M. should be (a) 1 (b) 117 (c) equal to their H.C.F. (d) Lies between 1 to 117 10. The centre of the circle passing through the ponts (6, – 6), (3, – 7) and (3, 3) is (a) (3, 2) (b) (–3, –2) (c) (3, – 2) (d) (–3, 2) 11. Let a and b be co-prime, thus a2 and b2 are: (a) co-prime (b) not co-prime (c) odd numbers (d) even numbers 12. Which among the following is/are correct? (I) If the altitudes of two similar triangles are in the ratio 2 : 1, then the ratio of their areas is 4 : 1. (II) PQ || BC and AP : PB = 1 : 2. Then, area (∆APQ) = 1 area (∆ABC) 4 (III) The areas of two similar triangles are respectively 9cm2 and 16cm2. The ratio of their corresponding sides is 3 : 16. (a) I (b) II (c) III (d) None of these 13. If Anish is moving along the boundary of a triangular field of sides 35 m, 53 m and 66 m and you are moving along the boundary of a circular field whose area is double the area of the triangular field, then the radius of the circular field is (Take 22 π = 7 ) (a) 14 3 m (b) 3 14 m (c) 28 3 m (d) 7 3 m 14. The pair of equations 5x – 15y = 8 and 3x – 9y = 24 has 5 (a) one solutio (b) two solutions (c) infinitely many solutions (d) no solution tan 30° (d) 1 15. The value of cot 60° is 11 (a) 2 (b) 3 (c) 3 33 16. The decimal expansion of the rational number 22.5 will terminate after (a) one decimal place (b) two decimal places (c) three decimal places (d) more than 3 decimal places 17. Which among the following is/are correct? (a) The ratios of the areas of two similar triangles is equal to the ratio of their corresponding sides. (b) The areas of two similar triangles are in the ratio of the corresponding altitudes.

Sample Paper-6 SP-43 (c) The ratio of area of two similar triangles are in the ratio of the corresponding medians. (d) If the areas of two similar triangles are equal, then the triangles are congruent. 18. A bag contains card numbers 3, 4, 5, 6, 7....27. One card is drawn, then probability of prime number card is (a) 295 (b) 287 (c) 285 (d) 15 19. A line l passing through the origin makes an angle q with positive direction of x-axis such that sin θ= 3 . The coordinates 5 of the point, which lies in the fourth quadrant at a unit distance from the origin and on perpendicular to l, are (a)  53 , − 4 (b)  54 ,−53 (c) (3, –4) (d) (4, –3) 5  20. The area of a circular path of uniform width ‘d’ surrounding a circular region of radius ‘r’ is (a) πd(2r + d) (b) π(2r + d) r (c) π(d + r)d (d) π(d + r)r SECTION-B Section B consists of 20 questions of 1 mark each. Any 16 quesions are to be attempted. 21. If ∆ABC is an equilateral triangle such that AD ⊥­ BC, then AD2 = A. 3a42 B. 3a22 C. 34 BC2 D. 23 a (a) A and C (b) A (c) D (d) B and C 22. A boat takes 3 hours to travel 30 km downstream and takes 5 hours to return to the same spot upstream. Find the speed of the boat in still water. (km/hr) (a) 10 km/hr (b) 8 km/hr (c) 6 km/hr (d) 5 km/hr 23. From the data (1, 4, 7, 16, 27, 29) if 29 is removed, the probability of getting a prime number is (a) 12 (b) 15 (c) 52 (d) 13 24. P is a point on the graph of y = 5x + 3. The coordinates of a point Q are (3, –2). If M is the mid point of PQ, then M must lie on the line represented by (a) y = 5x + 1 (b) y = 5x – 7 (c) y = 52 x – 7 (d) y = 5 x + 1 2 2 2 25. If the perimeter of a semi-circular protractor is 36 cm, then its diameter is (a) 10 cm (b) 14 cm (c) 12 cm (d) 16 cm 26. The polynomial, f(x) = (x – 1)2 + (x – 2)2 + (x – 3)2 + (x – 4)2 has minimum value, when x = ................... (a) 40 (b) 20 (c) 10 (d) 2.5 27. In village Madhubani 8 women and 12 girls can paint a large mural in 10 hours. 6 women and 8 girls can paint it in 14 hours. The number of hours taken by 7 women and 14 girls to paint the mural is (a) 10 (b) 15 (c) 20 (d) 35

SP-44 Mathematics 28. In a triangle ABC, ∠BAC = 90°; AD is the altitude from A on to BC. Draw DE perpendicular to AC and DF perpendicular to AB. Suppose AB = 15 and BC = 25. Then the length of EF is (a) 12 (b) 10 (c) 5 3 (d) 5 5 29. If the points (a, 0), (0, b) and (1, 1) are collinear then which of the following is true : (a) 1a + 1 = 2 (b) 1a − 1b = 1 (c) 1a − 1b = 2 (d) 1a + 1b = 1 b 30. The value of (sin 30° + cos 30°) – (sin 60° + cos 60°) is (a) –1 (b) 0 (c) 1 (d) 2 31. If one zero of the quadratic polynomial x2 + 3x + k is 2, then the value of k is (a) 10 (b) –10 (c) 5 (d) –5 32. A box contains four cards numbered as 1, 2, 3 and 4 and another box contains four cards numbered as 1, 4, 9 and 16. One card is drawn at random from each box. What is the probability of getting the product of the two numbers so obtained , more than 16? (a) 85 (b) 12 (c) 83 (d) 14 33. The distances of a point from the x-axis and the y-axis are 5 and 4 respectively. The coordinates of the point can be (a) (5, 4) (b) (5, 0) (c) (0, 4) (d) (4, 5) 34. 1+ tan2 A = L 1+ cot 2 A (a) sec2 A (b) –1 (c) cot2 A (d) tan2 A 35. Consider the following two statements: I. Any pair of consistent linear equations in two variables must have a unique solution. II. There do not exist two consecutive integers, the sum of whose squares is 365. Then, (a) both I and II are true (b) both I and II are false (c) I is true and II is false (d) I is false and II is true 36. If the radius of a circle is diminished by 10%, then its area is diminished by (a) 10% (b) 19% (c) 36% (d) 20% 37. Let D be a point on the side BC of a triangle ABC such that ∠ADC = ∠BAC. If AC = 21 cm, then the side of an equilateral triangle whose area is equal to the area of the rectangle with sides BC and DC is (a) 14 × 31/2 (b) 42 × 3–1/2 (c) 14 × 33/4 (d) 42 × 31/2 38. If one of the zeroes of the quadratic polynomial (k –1) x2 + kx + 1 is –3, then the value of k is (a) 43 (b) −34 (c) 32 (d) −32 39. (sec A + tan A) (1 – sin A) = (a) sec A (b) sin A (c) cosec A (d) cos A

Sample Paper-6 SP-45 40. The equations 1 + 1 = 15 and 1 - 1 = 5 are such that ax = 1 and by = 1. The values of ‘a’ and ‘b’ respectively are x y x y (a) 10, 5 (b) 10, –5 (c) –5, 10 (d) 5, 10 SECTION-C Case Study Based Questions: Section C consists of 10 quesions of 1 mark each. Any 8 quesions are to be attempted. Q 41. - Q 45 are based on case study-I Case Study-I Class X students of a secondary school in Krishnagar have been allotted a rectangular plot of a land for gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1m from each other. There is a triangular grassy lawn in the plot as shown in the fig. The students are to sow seeds of flowering plants on the remaining area of the plot. BC P R Q AD Considering A as origin, answer question (i) to (v) 41. Considering A as the origin, what are the coordinates of A? (a) (0, 1) (b) (1, 0) (c) (0, 0) (c) (4, 5) (d) (–1, –1) (c) (6, 0) (c) (0, 16) 42. What are the coordinates of P? (d) (6, 10) (a) (4, 6) (b) (6, 4) (d) (5, 4) 43. What are the coordinates of R? (a) (6, 5) (b) (5, 6) (d) (7, 4) 44. What are the coordinates of D? (a) (16, 0) (b) (0, 0) (d) (16, 0) 45. What are the coordinate of P if D is taken as the origin? (a) (12, 2) (b) (–12, 2) (c) (12, 3) Q 46 - Q 50 are based on case study-II Case Study-II Rakesh and Mohit playing a card game. Rakesh picked up a card from properly mixed cards numbered from 1 to 25. Then answer the following questions :

SP-46 Mathematics 46. The probability of getting prime numbers is : (a) 295 (b) 1205 (c) 275 (d) 285 47. The probability of getting multiple of 3 is : (a) 275 (b) 285 (c) 265 (d) 295 48. The probability of getting multiple of 2 is : (a) 1205 (b) 1235 (c) 1225 (d) 1215 49. The probability of getting multiple of 2 and 3 is : (a) 235 (b) 245 (c) 225 (d) 1265 50. The probability of getting multiple of 2 or 3 is : (a) 1265 (b) 245 (c) 235 (d) 1205

OMR ANSWER SHEET Sample Paper No –  Use Blue / Black Ball pen only.  Please do not make any atray marks on the answer sheet.  Rough work must not be done on the answer sheet.  Darken one circle deeply for each question in the OMR Answer sheet, as faintly darkend / half darkened circle might by rejected. Start time : ____________________ End time ____________________ Time taken ____________________ 1. Name (in Block Letters) 2. Date of Exam SECTION-A 17. a    b    c    d 18. a    b    c    d 3. Candidate’s Signature 9. a    b    c    d 19. a    b    c    d 10. a    b    c    d 20. a    b    c    d 1. a    b    c    d 11. a    b    c    d 2. a    b    c    d 12. a    b    c    d 37. a    b    c    d 3. a    b    c    d 13. a    b    c    d 38. a    b    c    d 4. a    b    c    d 14. a    b    c    d 39. a    b    c    d 5. a    b    c    d 15. a    b    c    d 40. a    b    c    d 6. a    b    c    d 16. a    b    c    d 7. a    b    c    d 49. a    b    c    d 8. a    b    c    d SECTION-B 50. a    b    c    d 21. a    b    c    d 29. a    b    c    d 22. a    b    c    d 30. a    b    c    d 23. a    b    c    d 31. a    b    c    d 24. a    b    c    d 32. a    b    c    d 25. a    b    c    d 33. a    b    c    d 26. a    b    c    d 34. a    b    c    d 27. a    b    c    d 35. a    b    c    d 28. a    b    c    d 36. a    b    c    d 41. a    b    c    d SECTION-C 42. a    b    c    d 43. a    b    c    d 45. a    b    c    d 44. a    b    c    d 46. a    b    c    d 47. a    b    c    d 48. a    b    c    d No. of Qns. Attempted Correct Incorrect Marks

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Sample Paper 7 Time : 90 Minutes Max Marks : 40 General Instructions 1. The question paper contains three parts A, B and C. 2. Section A consists of 20 quesions of 1 mark each. Any 16 quesitons are to be attempted. 3. Section B consists of 20 quersions of 1 mark each. Any 16 quesions are to be attempted. 4. Section C consists of 10 quesions based two Case Studies. Attempt any 8 questions. 5. There is no negative marking. SECTION-A Section A consists of 20 questions of 1 mark each. Any 16 quesions are to be attempted. 1. The distance between which of the following two points is 2 units? (a) (–2, –3) and (–2, –4) (b) (0, 4) and (0, 6) (c) (7, 2) and (6, 2) (d) (4, –3) and (2, 3) 2. Which of the following is/are a polynomial? (a) x2 + 1 (b) 2x2 – 3 x +1 (c) x3 – 3x + 1 3 x (d) 2x 2 – 5x 3. In Fig. DE || BC. If AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, find the value of x. C E A DB (a) 4 (b) 7 (c) 5 (d) 2 4. Two dice are rolled, then probability of getting a total of 9 is (a) 13 (b) 19 (c) 190 (d) 98 5. Which of the following statement(s) is/are always true? (a) The sum of two distinct irrational numbers is rational. (b) The rationalising factor of a number is unique. (c) Every irrational number is a surd. (d) None of these

SP-50 Mathematics 6. I. If x – y = xy = 1 – x – y, then x + y is 5 3 II. The system of equations 3x + 2y = a and 5x + by = 4 has infinitely many solutions for x and y, then a = 4, b = 3 III. If x + y =2 and ax – by = a2 – b2, then x = a, y = b a b Which is true? (a) I only (b) II only (c) III only (d) None of these. 7. If 13 tan q = 12, then find the value of 2sin θ cosθ cos2 θ − sin2 θ (a) 32152 (b) 215 (c) 1321 (d) 32152 8. From a bag containing 100 tickets numbered 1, 2, 3, ........., 100 one ticket is drawn. If the number on this ticket is x, then the probability that x+ 1 > 2 is ...... (a) 0 x (b) 0.99 (c) 1 (d) None of these 9. A right triangle has hypotenuse of length p cm and one side of length q cm. If p – q = 1, find the length of the third side of the triangle. (a) 2q +1cm (b) 2(q +1) cm (c) 2q +1cm (d) 2q + q2 cm 10. Suppose we have two circles of radius 2 each in the plane such that the distance between their centers is 2 3 . The area of the region common to both circles lies between (a) 0.5 and 0.6 (b) 0.65 and 0.7 (c) 0.7 and 0.75 (d) 0.8 and 0.9 11. Which of the following statement(s) is/are not correct? 73 (a) 54 is a non-terminating repeating decimal. (b) If a= 2 + 3 and b = 2 – 3 , then a + b is irrational. (c) If 19 divides a3, then 19 divides a, where a is a positive integer. (d) Product of L.C.M. and H.C.F. of 25 and 625 is 15625. 12. Which of the following given options is/are correct? (a) Degree of a zero polynomial is ‘0’. (b) Degree of a zero polynomial is not defined. (c) Degree of a constant polynomial is not defined. (d) A polynomial of degree n must have n zeroes. 13. If cot θ =  15 , then evaluate (2 + 2sin θ) (1− sin θ)  8  (1+ cos θ) (2 − 2 cos θ) (a) 1 (b) 225 (c) 1576 (d) –1 64 14. A coin is tossed. Then the probability of getting either head or tail is (a) 1 (b) 1 (c) 12 (d) 14 3 15. Which of the following is / are not correct ? Three points will form : (a) an equilateral triangle, if all the three sides are equal. (b) an isosceles triangle, if any two sides are equal. (c) a collinear or a line, if sum of two sides is equal to third side. (d) a rhombus, if all the four sides are equal.

Sample Paper-7 SP-51 16. A circle is inscribed in a right angled triangle of perimeter 7p . Then the ratio of numerical values of circumference of the circle to the area of the right angled triangle is (a) 4 : 7 (b) 3 : 7 (c) 2 : 7 (d) 1 : 7 17. In the given figure, S and T trisect the side QR of a right triangle PQR. Then which of the following is correct? P y Q x Sx T x R (a) 8PT 2 = 3PR2 + 5PS2 (b) 8PR 2 = 8PT2 + 8PS2 (c) 8PT 2 – 4PR2 = 6PS2 (d) 8PT 2 = 7RP2 – 6PS2 18. The product of unit digit in (795 – 358) and (795 + 358) is (a) 8 (b) lies between 3 and 7 (c) 6 (d) lies between 3 and 6 19. Which of the following given options is/are correct? (a) 2 +3 is a polynomial (b) x + 5 is a polynomial x (c) 2 4 is a polynomial (d) 5x2 + 1 x + 3 is a polynomial 3x – 2 7 20. If 5θ and 4θ are acute angles satisfying sin 5θ = cos 4θ, then 2sin 3θ – 3 tan 3θ is equal to (a) sin2θ (b) 12 (c) 13 (d) 0 SECTION-B Section B consists of 20 questions of 1 mark each. Any 16 quesions are to be attempted. 21. Which of the following is / are correct? Four points will form : (a) a rectangle, if opposite sides and diagonals are not equal. (b) a parallelogram, if opposite sides are not equal. (c) a square, if all the four sides and diagonals are equal. (d) a right angle triangle, if sum of squares of any two sides is equal to square of third largest side. 22. Two dice are rolled simultaneously. Find the probability that they show different faces. (a) 43 (b) 16 (c) 13 (d) 56

SP-52 Mathematics 23. In the given figure PA, QB and RC, each are perpendicular to AC. R P Q z x y AB C Which of the following is correct ? (a) y + z = x (b) x +1 z = 1y (c) 1y= 1x + 1z (d) None of these 24. If x = a, y = b is the solution of the equations x – y = 2 and x + y = 4, then the values of a and b are, respectively. (a) 3 and 5 (b) 5 and 3 (c) 3 and 1 (d) – 1 and – 3 25. If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is (a) –2 (b) 2 (c) –1 (d) 1 26. How much time the minute hand of a clock will take to describe an angle of 2π radians? 3 (a) 15 minutes (b) 20 minutes (c) 10 minutes (d) 25 minutes 27. The value of c for which the pair of equations cx – y = 2 and 6x + 2y = 3 will have infinitely many solutions is (a) 3 (b) – 3 (c) – 12 (d) no value 28. Which of the following is/are not correct? (a) If the diagonals of a quadrilateral divide each other proportionally, then it is a trapezium. (b) The line segments joining the mid-points of the adjacent sides of a quadrilateral form a parallelogram. (c) If corresponding sides of two similar triangles are in the ratio 4 : 5, then corresponding medians of the triangles must be in the ratio 4 : 5. (d) None of the above 29. A line is of length 10 units and one end is (2, –3). If the abscissa of the other end is 10, what is the ordinate? (a) 3 or 9 (b) –3 or –9 (c) 3 or –9 (d) –3 or 9 30. The probability of an event can not be (a) positive (b) negative (c) zero (d) one 31. If sin A + sin2A = 1, then the value of the expression (cos2A + cos4A) is (a) 1 (b) 1 (c) 2 (d) 3 2 32. Which of the following statement(s) is/are not correct? (a) There are infinitely many even primes. (b) Let ‘a’ be a positive integer and p be a prime number such that a2 is divisible by p, then a is divisible by p. (c) Every positive integer different from 1 can be expressed as a product of non-negative power of 2 and an odd number. (d) If ‘p’ is a positive prime, then p is an irrational number. 7 33. If the radius of a circle is cm, then the area of the circle is equal to π (a) 49 cm2 (b) p cm2 π (c) 154 cm2 (d) 49 cm2

Sample Paper-7 SP-53 34. The zeroes of the quadratic polynomial x2 + 99x + 127 are (a) both positive (b) both negative (c) one positive and one negative (d) both equal 35. Which of the following points will be collinear with the points (–3, 4) and (2, –5)? (a) (0, 0) (b) (7, –14) (c) (0, –1) (d) (3, 1) 36. Given that sin θ = a , then cos θ is equal to b b (b) ba (c) b2b− a2 (d) b2a− a2 (a) b2 − a2 37. Which of the following statement(s) is/are not correct? (a) Every integer is a rational number. (b) The sum of a rational number and an irrational number is an irrational number. (c) Every real number is rational. (d) Every point on a number line is associated with a real number. 38. A die is thrown once then, (a) the probability of getting an odd number is 2 (b) the probability of getting multiple of 3 is 1/3 3 (d) the probability of getting number greater than 5 is 1/3 (c) the probability of getting a prime number is 2/3 39. Two triangles are similar if (a) their corresponding angles are equal. (b) their corresponding sides are equal. (c) both are right triangle. (d) None of the above 40. A circle drawn with origin as the centre passes through  13 , 0  . The point which does not lie in the interior of the circle is  4  (a)  −43 ,1 (b)  2, 73  (c)  3, −21  (d)  −6, 52  SECTION-C Case Study Based Questions: Section C consists of 10 quesions of 1 mark each. Any 8 quesions are to be attempted. Q 41. - Q 45 are based on case study-I Case Study-I Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut shown in figure. 1.8 m 2.4 m

SP-54 Mathematics Answer the following questions. 41. How much string does she have out? (a) 1 m (b) 2 m (c) 3 m (d) 4 m 42. Find the length of CD. (a) 1 m (b) 1.2 m (c) 1.5 m (d) 2 m 43. Find the length of her fishing rod. (a) 1.5 m (b) 1.2 m (c) 1 m (d) 0.8 m 44. Both triangles are similar by similarity criterion is: (a) AAA (b) SSS (c) ASA (d) SAS 45. If she pulls in the string at the rate of 5 cm per second, then time taken to pulls all string. (a) 1 min. (b) 30 sec. (c) 30 min. (d) 40 sec. Case Study-II Q 46 - Q 50 are based on case study-II A compound angle is that which is made of up of algebraic sum of two or more angles. sin(A + B) = sin A cos B + cos A sin B tan(A + B) = tan A + tan B , tan (A – B) = tan A – tan B 1 – tan A tan B 1+ tan A⋅ tan B cos (A + B) = cos A cos B – sin A sin B cos (A – B) = cos A cos B + sin A sin B 46. The value of sin 75° is 3 –1 3+ 3 (c) 0 3 +1 (a) 2 2 (b) 2 2 (d) 2 2 47. The value of tan 15° is 3+ 1 (b) 22– 23 (c) 33 +–11 (d) 2 + 3 (a) 3 – 1 48. The value of tan 75° is (a) 2 1 (c) 0 3 +1 2– 3 (b) 1 – 3 (d) 3 –1 49. The value of cos 15° is (a) 23 +21 (b) 23 –21 (c) 3 2+ 2 (d) 3 2– 2 50. The value of cos 75° is (a) 3 +1 (b) 23 –21 (c) 33 +–11 (d) 33 +–11 22

OMR ANSWER SHEET Sample Paper No –  Use Blue / Black Ball pen only.  Please do not make any atray marks on the answer sheet.  Rough work must not be done on the answer sheet.  Darken one circle deeply for each question in the OMR Answer sheet, as faintly darkend / half darkened circle might by rejected. Start time : ____________________ End time ____________________ Time taken ____________________ 1. Name (in Block Letters) 2. Date of Exam SECTION-A 17. a    b    c    d 18. a    b    c    d 3. Candidate’s Signature 9. a    b    c    d 19. a    b    c    d 10. a    b    c    d 20. a    b    c    d 1. a    b    c    d 11. a    b    c    d 2. a    b    c    d 12. a    b    c    d 37. a    b    c    d 3. a    b    c    d 13. a    b    c    d 38. a    b    c    d 4. a    b    c    d 14. a    b    c    d 39. a    b    c    d 5. a    b    c    d 15. a    b    c    d 40. a    b    c    d 6. a    b    c    d 16. a    b    c    d 7. a    b    c    d 49. a    b    c    d 8. a    b    c    d SECTION-B 50. a    b    c    d 21. a    b    c    d 29. a    b    c    d 22. a    b    c    d 30. a    b    c    d 23. a    b    c    d 31. a    b    c    d 24. a    b    c    d 32. a    b    c    d 25. a    b    c    d 33. a    b    c    d 26. a    b    c    d 34. a    b    c    d 27. a    b    c    d 35. a    b    c    d 28. a    b    c    d 36. a    b    c    d 41. a    b    c    d SECTION-C 42. a    b    c    d 43. a    b    c    d 45. a    b    c    d 44. a    b    c    d 46. a    b    c    d 47. a    b    c    d 48. a    b    c    d No. of Qns. Attempted Correct Incorrect Marks

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Sample Paper 8 Time : 90 Minutes Max Marks : 40 General Instructions 1. The question paper contains three parts A, B and C. 2. Section A consists of 20 quesions of 1 mark each. Any 16 quesitons are to be attempted. 3. Section B consists of 20 quersions of 1 mark each. Any 16 quesions are to be attempted. 4. Section C consists of 10 quesions based two Case Studies. Attempt any 8 questions. 5. There is no negative marking. SECTION-A Section A consists of 20 questions of 1 mark each. Any 16 quesions are to be attempted. 1. A boat goes 12 km. upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time. Find the speed of the boat in still water and the speed of the stream. (a) 4 km/hr, 5 km/hr (b) 3 km/hr, 1 km/hr (c) 6 km/hr, 2 km/hr (d) 7 km/hr, 2 km/hr ( ) ( )2. Find the distance between the points 3 +1, 2 -1 and 3 -1, 2 +1 . (a) 3 (b) 2 3 (c) 2 (d) 2 2 3. If in fig. O is the point of intersection of two chords AB and CD such that OB = OD, then triangles OAC and ODB are A D 45° O C B (a) equilateral but not similar (b) isosceles but not similar (c) equilateral and similar (d) isosceles and similar 4. If the H.C.F of 210 and 55 is expressible in the form 210 × 5 + 55y, find y. (a) 20 (b) 19 (c) – 91 (d) – 19 5. A child has a die whose six faces show the number as given below: 122346 The die is thrown once. What is the probability of getting an even number? (d) 3 (a) 16 (b) 32 (c) 0

SP-58 Y Mathematics 6. Which of the following is/are not graph of a quadratic polynomial ? Y Y (a) X¢ O A B X (b) (c) X¢ A O B X (d) X¢ O X Y¢ Y¢ Y¢ 7. The two opposite vertices of a square are (–1, 2) and (3, 2). Find the co-ordinates of the other two vertices. (a) (1, 0), (1, 2) (b) (1, 0), (2, 1) (c) (1, 4), (1, 0) (d) (4, 1), (1, 0) 8. I. If 3x – 5y = –1 and x – y = – 1, then x = –2, y = –1 II. 2x + 3y = 9, 3x + 4y = 5 ⇒ x = –21, y = 17 III. 2ax=+ by 2, ax=– by 4 ⇒ x = 2a, y = 2b Which is true? (a) I (b) II (c) III (d) None of these 9. In figure given below , O is a point inside ∆PQR such that ∠POR = 90°, OP = 6 cm and OR = 8 cm. If PQ = 24 cm, QR = 26 cm. Then P 24 cm 6 cm O (a) ∠QRP = 90° Q 8 cm R (d) ∆PQR is an isosceles (b) ∠PRQ = 90° ∠QPR = 90° 26 cm (c) 10. If the ratio of the areas of the two circles is 25 : 16, then the ratio of their circumferences is (a) 1265 (b) 54 (c) 5 500 4 (d) 625 11. If p is a terminating decimal, what can you say about q ? q (a) q must be in the form 2n (b) q must be in the form 5m (c) q must be in the form 2n.5m (d) q must be in the form 2n.5m, where n and m are non negative integers. 12. Identify the ratio in which the line joining (4, 5) and (– 10, 2) is cut by the Y-axis. (a) – 5 : 2 (b) 3 : 5 (c) – 5 : 3 (d) 2:5 13. From a normal pack of cards, a card is drawn at random, find the probability of getting a jack or a king. (a) 572 (b) 143 (c) 2 3 13 (d) 13 14. The graph of y = x2 – 6x + 9 is : (a) a parabola open upward (b) a parabola open downward (c) a straight line (d) None of these

Sample Paper-8 SP-59 15. Identify the incorrect statement. (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. 16. Two dice are thrown at a time, then find the probability that the difference of the numbers shown on the dice is 1. (a) 136 5 (c) 7 (d) 7 (b) 18 36 18 17. Which of the following is not a rational number? (a) 2 (b) 4 (c) 9 (d) 16 18. If the sector of a circle of diameter 14cm subtends an angle of 30° at the centre, then its area is (a) 49π (b) 4192π (c) 242 (d) 121 3π π 19. What is a system of simultaneous equations called if it has no solution? (a) Consistent system (b) Independent system (c) Inconsistent system (d) Dependent system 20. Find the probability for a randomly selected number of 1, 2, 3, 4,.....25 to be a prime number. 4 7 89 (a) 25 (b) 25 (c) 25 (d) 25 SECTION-B Section B consists of 20 questions of 1 mark each. Any 16 quesions are to be attempted. 21. If a and b are the zeroes of the quadratic polynomial f (x) = ax2 + bx + c then evaluate 1 + 1 . (a) a2 – b2 (c) α3 β3 3abc – b3 –b c (b) c3 a (d) a 22. Find the chance that a non-leap year contains 53 Saturdays. 12 35 (a) 7 (b) 7 (c) 7 (d) 7 23. What is the value of ‘x’ if (4, 3) and (x, 5) are points on the circumference of a circle with centre O(2, 3)? (a) 4 (b) 2 (c) –2 (d) 0 24. Which of the following is not correct? 1 (a) 7 is rational having non-terminating is repeating decimal fraction. (b) 1310 is rational non-terminating repeating decimal. (c) 9311 is rational having non-terminating repeating decimal. (d) 11235 is rational having non-terminating repeating decimal. 25. In DABC, ∠B = 90° and D is the midpoint of BC. Then (a) AC2 = AD2 + 3CD2 (b) AC2 + AD2 = CD2 (c) 3AC2 = AD2 + CD2 (d) AD2 = CD2 = 3AC2 26. Solve for x and y : 3 + 4y= 1; 4 + 2y= 11 x x 12 (a) x = 1, y = 2 (b) x = 6 , y = 8 (c) x = 4, y = 5 (d) x = 7, y = 3

SP-60 Mathematics 27. Which of the following statement is/are not correct? (a) A chord divides the interior of a circle into two parts. (b) An arc of a circle whose length is less than that of a semicircle of the same circle is a called a minor arc. (c) Circles having the same centre but different radii are called concentric circles. (d) A line segment joining any two points of a circle is called an arc. 28. When two dice are thrown, find the probability of getting a number always greater than 4 on the second dice. 2 (b) 13 32 (a) 3 (c) 5 (d) 5 29. Find a and b if x + 1 and x + 2 are factors of p (x) = x3 + 3x2 − 2αx + β (a) 3, –1 (b) –1, 0 (c) 0, –3 (d) 5, 6 30. A ladder 15 m long reaches a window which is 9 m above the ground on one side of the street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12 m high. Find the width of the street. E D 15m 15m 9 m 12 m A CB (a) 21 m (b) 18 m (c) 22 m (d) 12 m 31. If a pair of linear equations is inconsistent, then the lines will be (a) parallel (b) always coincident (c) intersecting (d) coincident 32. If ABC and EBC are two equilateral triangles such that D is mid-point of BC, then the ratio of the areas of triangles ABC and BDE is (a) 2 : 1 (b) 1 : 2 (c) 1 : 4 (d) 4 : 1 33. If the mid-point of the line segment AB (shown in the adjoining figure) is (4, –3), then the coordinates of A and B are Y A O X B (a) (8, 0) and (– 6, 0) (b) (8, 0) and (0, – 6) (c) (0, 8) and (– 6, 0) (d) (0, 8) and (0, – 6) 34. For what value of ‘x’ does 6x end with 5? (a) 0 (b) 1 (c) 5 (d) Never ends with 5 35. Which of the following is/are not correct? (a) Area of a circle with radius 6 cm, if angle of sector is 60°, is 132 cm2. 14 (b) If a chord of circle of radius 14 cm makes an angle of 60° at the centre of the circle, then area of major sector is 512.87 cm2. (c) The ratio between the circumference and area of a circle of radius 5 cm is 2 : 5. (d) Area of a circle whose radius is 6 cm, when the length of the arc is 22 cm, is 66 cm2.