The sum of exponents of the prime factors in the prime factorisation of 156 is
For any natural number N, 9ⁿ cannot end with which one of following digits?
LCM of 12 and 42 is 10m + 4, then value of 'm' is
4. If the sum and product of the zeroes of a quadratic polynomial are ‘3’ and ‘-10’, then the polynomial is:
5. If x – 2 is a factor of the polynomial x³ – 6x² + ax – 8, then the value of ‘a’ is
6. The pair of linear equations x + 2y – 5 = 0 and 3x + 12y – 10 = 0 has
7. Which of the following is not a quadratic equation?
8. If the sum and product of roots of equation kx² + 6x + 4k = 0 are equal, then value of ‘k’ is
9. If the numbers n – 3, 4n – 2 and 5n + 1 are in A.P., then value of ‘n’
10. If one root of the quadratic equationa(b - c)x^2 + b(c - a)x + c(a - b) = 0 is 1, then the other root is:
11. In an A.P., 25th term is 70 more than the 15th term, then the common difference is:
12. The points A(–5, 0), B(5, 0), and C(0, 4) are vertices of which triangle?
13. The X-axis divides the line joining the points A(2, –3) and B(5, 6) in ratio of
14. If 4 vertices of a parallelogram are (–3, –1), (a, b), (3, 3), and (4, 3) taken in order, then ratio of a : b is
15. In the given triangle △ABC, if DE ∥ BC, AE = a units, EC = b units, DE = x units and BC = y units, then which is true?
16. If the length of diagonals of a rhombus are 24 cm and 10 cm, then each side of the rhombus is:
17. In the given figure, PA is the tangent drawn from the external point P to the circle with center O. If the radius of the circle is 3 cm and PA = 4 cm, then length of PB is:
18. In 2 concentric circles, a chord of length 24 cm of the larger circle becomes a tangent to the smaller circle whose radius is 5 cm.
19. Area of the circle that can be inscribed in a square of side 10 cm is:
20. If the height of a conical tent is 3 m and the radius of its base is 4 m, then slant height is:
21. If the radius of the base of a right circular cylinder is halved, keeping the height same, then the ratio of volume of the new cylinder to the original cylinder is:
22. If tan A = √3, then sec A is
23. A chord of a circle of radius 6 cm is making an angle 60° at the center. Then length of the chord is
24. Value of tan 10° × tan 15° × tan 75° × tan 80° is
25. If tan θ + cot θ = 5, then value of tan²θ + cot²θ is
26. cos 36° × cos 54° – sin 36° × sin 54° =
27. If two towers of heights h₁ and h₂ subtend angles of 60° and 30° at the midpoint of the line segment joining their feet, then the ratio of their heights h₁ : h₂ is
28. The angles of elevation and depression of the top and bottom of a lighthouse from the top of a 60 m high building are 30° and 60°. Then the difference between the heights of the lighthouse and the building is
29. Which of the following cannot be the probability of an event?
30. If one card is drawn at random from a well-shuffled deck of 52 cards, then probability of getting a non-face card is
31. A lot consists of 144 ball pens of which 20 are defective and the others are good. Rafia will buy a pen if it is good but will not buy it if it is defective. The shopkeeper draws one pen at random and gives it to her. The probability that she will buy that pen is
32. A bag contains 3 red balls and 5 black balls. If a ball is drawn at random from the bag, then the probability of getting a red ball is
33. If the mean of the following frequency distribution is 15, then the missing frequency 'y' is:
34. Difference between mode and mean of data is k times the difference between median and mean. Then k is
35. Median of the first 10 prime numbers is
36. Which of the following is not an irrational number?
37. If ‘p’ and ‘q’ are positive integers such that p = a³b² and q = ab³, where a & b are prime numbers, then HCF(p, q) is
38. Which of the following is not a polynomial?
39. Degree of the polynomial ( 𝑥 + 1 ) ( 𝑥 2 − 𝑥 + 𝑥 − 1 ) (x+1)(x 2 −x+x−1) is
40. The value of k for which the pair of linear equations 𝑘 𝑥 − 𝑦 = 2 kx−y=2 and 6 𝑥 − 2 𝑦 = 3 6x−2y=3 has a unique solution is
41. The pair of equations y = 0 and y = –7 has
42. The 15th term of an A.P.: –10, –5, 0, 5, … is
43. The distance of the point P(2, 3) from the X-axis is (in units)
44. In a given △ABC, if DE ∥ BC, and 𝐴 𝐷 𝐷 𝐵 = 3 5 DB AD = 5 3 , and AC = 5.6 cm, then AE =
45. If a point P is 17 cm from the center of a circle of radius 8 cm, then the length of the tangent drawn to the circle from P is
46. Value of tan 2° × tan 4° × tan 6° × … × tan 88° is
47. If 𝑥 = 𝑎 sin 𝜃 x=asinθ, 𝑦 = 𝑏 tan 𝜃 y=btanθ, then the value of 𝑎 2 𝑥 2 − 𝑏 2 𝑦 2 x 2 a 2 − y 2 b 2 is
48. If the ratio of the length of a pole and its shadow is 1 : √3, then the angle of elevation of the Sun is
49. Two dice are thrown together. The probability of getting the same number on both dice is
50. The mean of 12 numbers is 19. If 4 is subtracted from each number, then the new mean is
51. Which term of the geometric progression 2, 2√2, 4, … is 128?
52. If the geometric progressions 162, 54, 18, … and 2/81, 2/27, 2/9, … have their nᵗʰ terms equal, then the value of 'n' is
53. If the points (a, 0), (0, b), and (1, 1) are collinear, then 1/ 𝑎 + 1/ 𝑏 = ?
54. Centroid of the triangle formed by the points (3, –5), (–7, 4), and (10, –k) is (k, –1). Then value of k is
55. If AM and PN are the altitudes of two similar triangles △ABC and △PQR and (AB)² : (PQ)² = 4 : 9, then AM : PN is
56. After how many decimal places will the decimal expansion of the rational number 23 / (2² × 5) terminate?
57. Value of 1 / log base √3 of 60 + 1 / log base √4 of 60 + 1 / log base √5 of 60 is
58. Which of the following collections is not a set?
59. If P = {3m : m ∈ N} and Q = {3ⁿ : n ∈ N} are two sets, then
60. If A and B are disjoint sets and n(A) = 4, n(A ∪ B) = 7, then the value of n(B) is
