Mathematics Past Paper PDF

Roll No. : Time - Date : MM - 45 1. If the prime factorisation of a natural number N is 24 × 34 × 5...

Roll No. : Time - Date : MM - 45 1. If the prime factorisation of a natural number N is 24 × 34 × 53 × 7, then number of consecutive zeroes in N 1 are (a) 5 (b) 4 (c) 3 (d) 2 2. If product of two numbers is 3691 and their LCM is 3691, then their HCF = 1 (a) 2 (b) 3691 (c) 1 (d) 3 3. 1 If p and q are two co-prime numbers, then the HCF and LCM of p and q is (a) HCF = p, LCM = pq (b) HCF = 1, LCM = pq (c) HCF = q, LCM = pq (d) HCF = pq, LCM = pq 4. 1 HCF of 52 × 32 and 35 × 53 is: (i)53 × 35 (a) (ii) (b) 5 × 33 (iii) (c) 53 × 32 (iv) (d) 52 × 32 5. Given that LCM (91, 26) = 182, then HCF (91, 26) is 1 (i) 11 (ii) 26 (iii) 13  (iv) 91 6. What will be the least possible number of the planks, if three pieces of timber 42 m, 49 m and 63 1 m long have to be divided into planks of the same length? (i) 5 (ii) 6 (iii) 7 (iv) None of these 7. The HCF and LCM of two numbers are 33 and 264 respectively. When the first number is divided 1 by 2 the quotient is 33. The other number is (i) 66 (ii) 130 (iii) 132 (iv) 196 8. The LCM and HCF of two non-zero positive numbers are equal, then the numbers must be 1 (i) composite (ii) prime (iii) co-prime (iv) equal 9. The least number which when divided by 18, 24, 30 and 42 will leave same remainder 1, would be 1 (i) 2520 (ii) 2519 (iii) 2521 (iv) 2522 10. In a school there are two sections, section A and section B of class X. There are 45 students in 1 section A and 36 students in section B. The minimum numbers of books required for their class library so that they can be distributed equally among the students of section A or section B are (i) 280 (ii) 180  (iii) 90 (iv) 120 11. The largest number which divides 71 and 126 leaving remainder 6 and 9 respectively is 1 (i) 65 (ii) 875 (iii) 13 (iv) 1750 12. The smallest number, which when increased by 14 is exactly divisible by 165 and 770, is 1 (i) 2297 (ii) 2310 (iii) 2296 (iv) 2295 13. The exponent of 2 in prime factorisation of 288 is 1 (i) 2 (ii) 3 (iii) 4 (iv) 5 14. The sum of exponents of 2 and 3 in prime factori-sation of 3600 is 1 (i) 5 (ii) 6 (iii) 7 (iv) 4 15. The graph of x = p(y) is given below, for some polynomial p(y). The number of zeroes of p(y) is/are 1  (i) 1 (ii) 2 (iii) 3 (iv) 4 16. If one zero of p(x) = ax2 + bx + c is zero, then the value of c is 1 (i) 1 (ii) 2 (iii) 3 (iv) 0 17. Zeroes of a polynomial can be determined graphically. Number of zeroes of a polynomial is equal to 1 number of points where the graph of polynomial (i) intersects y-axis (ii) intersects x-axis (iii) intersects y-axis or intersects x-axis (iv) none of these 18. The graph of the polynomial p(x) cuts the x-axis at 2 places and touches it at 4 places. The number of zeroes 1 of p(x) is (i) 2 (ii) 6 (iii) 4 (iv) 8 19. The graph of y = x3 – 4x cuts x-axis at (–2, 0), (0, 0) and (2, 0). The zeroes of x3 – 4x are 1 0,(i) 0, 0  (ii) –2, 2, 2 (iii) –2, 0, 2 (iv) –2, –2, 2 20. If p(x) = ax2 + bx + c and a + b + c = 0, then one zero is 1 (i) (ii) (iii) (iv) none of these 21. If the product of the zeroes of x2 – 3kx + 2k2 – 1 is 7, then values of k are 1 (i) ± 1 (ii) ± 2 (iii) ± 2 (iv) ± 4 22. If one of the zeroes of the quadratic polynomial (k – 1)x2 + kx + 1 is –3, then the value of k is 1 23. If the zeroes of the quadratic polynomial x2 + (a + 1) x + b are 2 and –3, then 1 (a) a = –7, b = –1 (b) a = 5, b = –1 (c) a = 2, b = –6 (d) a = 0, b = –6 24. Which of the following is not the graph of a quadratic polynomial? 1 25. A quadratic polynomial, the product and sum of whose zeroes are 5 and 8 respectively is 1 (a) k [x2 – 8x + 5] (b) k [x2 + 8x + 5] (c) k[x2 – 5x + 8] (d) k[x2 + 5x + 8] 26. A quadratic polynomial, the product and sum of whose zeroes are 5 and 8 respectively is 1 (a) k [x2 – 8x + 5] (b) k [x2 + 8x + 5] (c) k [x2 – 5x + 8] (d) k [x2 + 5x + 8] 27. The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 is 1 (a) inconsistent (b) consistent (c) dependent consistent (d) none of these 28. The pair of equations y = 0 and y = –7 has 1 (a) one solution (b) two solutions (c) infinitely many solutions (d) no solution 29. A pair of linear equations which has a unique solution x = 2, y = –3 is 1 (a) x + y = –1; 2x – 3y = –5 (b) 2x + 5y = –11; 4x + 10y = –22 (c) 2x – y = 1 ; 3x + 2y = 0 (d) x – 4y – 14 = 0; 5x – y – 13 = 0 30. The difference between a two digit number and the number obtained by interchanging the digits 1 is 27. What is the difference between the two digits of the number? (a) 9 (b) 6 (c) 12 (d) 3 31. The pair of equations ax + 2y = 7 and 3x + by = 16 represent parallel lines if 1 (a) a = b (b) 3a = 2b (c) 2a = 3b (d) ab = 6 32. The equations ax + by + c = 0 and dx + ey + c = 0 represent the same straight line if 1 (a) ad = be (b) ac = bd (c) bc = ad (d) ab = de 33. Using the following equations: + 6y = 10; – 6y = 5, find the value of p if p = 5x. 1 (a) 1 (b) 2 (c) 3 (d) 4 34. The value of k for which the system of equations x + y – 4 = 0 and 2x + ky = 3, has no solution, is 1 (a) – 2 (b) ≠ 2 (c) 3 (d) 2 35. If a pair of linear equations in two variables is consistent, then the linens represented by two 1 equations are: (a) intersecting (b) parallel (c) always coincident (d) intersecting or coincident 36. Which of the following cannot be the probability of an event? 1 (a) 1.5 (b) (c) 25% (d) 0.3 37. A coin is tossed twice. The probability of getting both heads is 1 38. A fair dice is rolled. Probability of getting a number x such that 1 ≤ x ≤ 6, is 1 (a) 0 (b) > 1 (c) between 0 and 1 (d) 1 39. The sum of the probabilities of all elementary events of an experiment is p, then 1 (a) 0 < p < 1 (b) 0 ≤ p < 1 (c) p = 1 (d) p = 0 40. If an event cannot occur, then its probability is 1 41. An event is very unlikely to happen. Its probability is closest to 1 (a) 0.0001 (b) 0.001 (c) 0.01 (d) 0.1 42. Match the columns: 1 (1) Probability of sure event (A) (2) Probability of impossible (B) 0 event (3) A and B are complementary (C) 1 events (D) P(B) = 1 – P(A) (E) P(A) = P(B) (a) (1) → (A), (2) → (B), (3) → (C) (b) (1) → (B), (2) → (A), (3) → (C)  (c) (1) → (C), (2) → (B), (3) → (E) (d) (1) → (C), (2) → (B), (3) → (D) 43. A card is drawn from a well-shuffled deck of 52 playing cards. The probability that the card will 1 not be an ace is 44. An experiment whose outcomes has to be among a set of events that are completely known but 1 whose exact outcomes is unknown is a (a) sample space (b) elementary event (c) random experiment (d) none of these 45. The experiments which when repeated under identical conditions produce the same results or 1 outcomes are known as (a) random experiments (b) probabilistic experiment (c) elementary experiment (d) deterministic experiment 46. For an event E, P(E) + = q, then 1 (a) 0 ≤ q < 1 (b) 0 < q ≤ 1 (c) 0 < q < 1 (d) none of these 47. A man is known to speak truth 3 out of 4 times. He throws a die and a number other than six 1 comes up. Find the probability that he reports it is a six. 48. One ticket is selected at random from 100 tickets numbered 0.0, 01, 02,......, 99. Suppose x is the 1 sum of digits and y is the product of digits, then probability that x = 9 and y = 0 is Verify that x = 3 is a zero of the polynomial. 1 p(x) = 2x3 – 5x2 – 4x + 3