Secure a perfect score in the objective section with our dedicated 10th Maths Chapter-Wise Additional One Marks Test Question Papers. While standard book-back multiple-choice questions are straightforward, public exams frequently feature creative, book-inside, and application-based one-marks to test your conceptual depth. This resource portal offers unit-by-unit online tests and printable question papers packed with custom-crafted MCQs, formula applications, and shortcut problems from all eight chapters. Use these targeted mock tests to boost your problem-solving speed, eliminate careless errors, and confidently tackle the compulsory one-mark questions!
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CLASS: 10TH | CHAPTER: 1-8
1. If { (x, 2), (4, y) } represents an identity function, then (x, y) is
(A) (2, 4) (B) (4, 2) (C) (2, 2) (D) (4, 4)
2. If { (7, 11), (5, a) } represents a constant function, then the value of 'a' is
(A) 7 (B) 11 (C) 5 (D) 9
3. Given f(x) = (-1)x is a function from ℕ to ℤ. Then the range of f is
(A) {1} (B) ℕ (C) {1, -1} (D) ℤ
4. If f = {(6, 3), (8, 9), (5, 3), (-1, 6)}, then the pre-images of 3 are
(A) 5 and -1 (B) 6 and 8 (C) 8 and -1 (D) 6 and 5
5. Let A = {1, 3, 4, 7, 11}, B = {-1, 1, 2, 5, 7, 9} and f: A → B be given by f = {(1, -1), (3, 2), (4, 1), (7, 5), (11, 9)}. Then f is
(A) one-one (B) onto (C) bijective (D) not a function
7. If A = {5, 6, 7}, B = {1, 2, 3, 4, 5} and f: A → B is defined by f(x) = x - 2, then the range of f is
(A) {1, 4, 5} (B) {1, 2, 3, 4, 5} (C) {2, 3, 4} (D) {3, 4, 5}
8. If f(x) = x2 + 5, then f(-4) =
(A) 26 (B) 21 (C) 20 (D) -20
9. If the range of a function is a singleton set, then it is
(A) a constant function (B) an identity function (C) a bijective function (D) an one-one function
10. If f: A → B is a bijective function and if n(A) = 5, then n(B) is equal to
(A) 10 (B) 4 (C) 5 (D) 25
1. Which one of the following is not true?
(A) A sequence is a real valued function defined on ℕ.
(B) Every function represents a sequence.
(C) A sequence may have infinitely many terms.
(D) A sequence may have a finite number of terms.
2. The 8th term of the sequence 1, 1, 2, 3, 5, 8, ... is
(A) 25 (B) 24 (C) 23 (D) 21
3. The next term after 1/20 in the sequence 1/2, 1/6, 1/12, 1/20, ... is
(A) 1/24 (B) 1/22 (C) 1/30 (D) 1/18
4. If a, b, c, l, m are in A.P., then the value of a - 4b + 6c - 4l + m is
(A) 1 (B) 2 (C) 3 (D) 0
5. If a, b, c are in A.P., then (a - b)/(b - c) is equal to
(A) a/b (B) b/c (C) a/c (D) 1
6. If the nth term of a sequence is 100n + 10, then the sequence is
(A) an A.P. (B) a G.P. (C) a constant sequence (D) neither A.P. nor G.P.
7. If a1, a2, a3, ... are in A.P. such that a4/a7 = 3/2, then the 13th term of the A.P. is
(A) 3/2 (B) 0 (C) 12a1 (D) 14a1
8. If the sequence a1, a2, a3, ... is in A.P., then the sequence a5, a10, a15, ... is
(A) a G.P. (B) an A.P. (C) neither A.P. nor G.P. (D) a constant sequence
9. If k + 2, 4k - 6, 3k - 2 are the three consecutive terms of an A.P., then the value of k is
(A) 2 (B) 3 (C) 4 (D) 5
10. If a, b, c, l, m, n are in A.P., then 3a + 7, 3b + 7, 3c + 7, 3l + 7, 3m + 7, 3n + 7 form
(A) a G.P. (B) an A.P. (C) a constant sequence (D) neither A.P. nor G.P.
11. If the third term of a G.P. is 2, then the product of first 5 terms is
(A) 52 (B) 25 (C) 10 (D) 15
12. If a, b, c are in G.P., then (a - b)/(b - c) is equal to
(A) a/b (B) b/a (C) a/c (D) c/b
13. If x, 2x + 2, 3x + 3 are in G.P., then 5x, 10x + 10, 15x + 15 form
(A) an A.P. (B) a G.P. (C) a constant sequence (D) neither A.P. nor G.P.
14. The sequence -3, -3, -3, ... is
(A) an A.P. only (B) a G.P. only (C) neither A.P. nor G.P. (D) both A.P. and G.P.
15. If the product of the first four consecutive terms of a G.P. is 256 and if the common ratio is 4 and the first term is positive, then its 3rd term is
(A) 8 (B) 1/16 (C) 1/32 (D) 16
16. In a G.P., t2 = 3/5 and t3 = 1/5. Then the common ratio is
(A) 1/5 (B) 1/3 (C) 1 (D) 5
17. If x ≠ 0 then 1 + sec x + sec2x + sec3x + sec4x + sec5x is equal to
(A) (1 + sec x)(sec2x + sec3x + sec4x)
(B) (1 + sec x)(1 + sec2x + sec4x)
(C) (1 - sec x)(sec x + sec3x + sec5x)
(D) (1 + sec x)(1 + sec3x + sec4x)
18. If the nth term of an A.P. is tn = 3 - 5n, then the sum of the first n terms is
(A) n/2 [1 - 5n] (B) n(1 - 5n) (C) n/2 (1 + 5n) (D) n/2 (1 + n)
19. The common ratio of the G.P. am-n, am, am+n is
(A) am (B) a-m (C) an (D) a-n
20. If 1 + 2 + 3 + ... + n = k, then 13 + 23 + ... + n3 is equal to
(A) k2 (B) k3 (C) k(k + 1)/2 (D) (k + 1)3
1. If the system 6x - 2y = 3, kx - y = 2 has a unique solution, then
(A) k = 3 (B) k ≠ 3 (C) k = 4 (D) k ≠ 4
2. A system of two linear equations in two variables is inconsistent, if their graphs
(A) coincide (B) intersect only at a point (C) do not intersect at any point (D) cut the x-axis
3. The system of equations x - 4y = 8, 3x - 12y = 24
(A) has infinitely many solutions (B) has no solution (C) has a unique solution (D) may or may not have a solution
4. If one zero of the polynomial p(x) = (k + 4)x2 + 13x + 3k is reciprocal of the other, then k is equal to
(A) 2 (B) 3 (C) 4 (D) 5
5. The sum of two zeros of the polynomial f(x) = 2x2 + (p + 3)x + 5 is zero, then the value of p is
(A) 3 (B) 4 (C) -3 (D) -4
6. The remainder when x2 - 2x + 7 is divided by x + 4 is
(A) 28 (B) 29 (C) 30 (D) 31
7. The quotient when x3 - 5x2 + 7x - 4 is divided by x - 1 is
(A) x2 + 4x + 3 (B) x2 - 4x + 3 (C) x2 - 4x - 3 (D) x2 + 4x - 3
8. The GCD of (x3 + 1) and x4 - 1 is
(A) x3 - 1 (B) x3 + 1 (C) x + 1 (D) x - 1
9. The GCD of x2 - 2xy + y2 and x4 - y4 is
(A) 1 (B) x + y (C) x - y (D) x2 - y2
10. The LCM of x3 - a3 and (x - a)2 is
(A) (x3 - a3)(x + a) (B) (x3 - a3)(x - a)2
(C) (x - a)2(x2 + ax + a2) (D) (x + a)2(x2 + ax + a2)
11. The LCM of ak, ak+3, ak+5 where k ∈ ℕ is
(A) ak+9 (B) ak (C) ak+6 (D) ak+5
12. The lowest form of the rational expression (x2 + 5x + 6)/(x2 - x - 6) is
(A) (x - 3)/(x + 3) (B) (x + 3)/(x - 3) (C) (x + 2)/(x - 3) (D) (x - 3)/(x + 2)
13. If (a + b)/(a - b) and (a3 - b3)/(a3 + b3) are two rational expressions, then their product is
(A) (a2 + ab + b2)/(a2 - ab + b2) (B) (a2 - ab + b2)/(a2 + ab + b2)
(C) (a2 - ab - b2)/(a2 + ab + b2) (D) (a2 + ab + b2)/(a2 - ab - b2)
14. On dividing (x2 - 25)/(x + 3) by (x + 5)/(x2 - 9) is equal to
(A) (x - 5)(x - 3) (B) (x - 5)(x + 3) (C) (x + 5)(x - 3) (D) (x + 5)(x + 3)
15. If a3/(a - b) is added with b3/(b - a), then the new expression is
(A) a2 + ab + b2 (B) a2 - ab + b2 (C) a3 + b3 (D) a3 - b3
16. The square root of 49(x2 - 2xy + y2)2 is
(A) 7|x - y| (B) 7(x + y)(x - y) (C) 7(x + y)2 (D) 7(x - y)2
17. The square root of x2 + y2 + z2 - 2xy + 2yz - 2zx is
(A) |x + y - z| (B) |x - y + z| (C) |x + y + z| (D) |x - y - z|
18. The square root of 121x4y8z6(l - m)2 is
(A) 11x2y4z4|l - m| (B) 11x4y4|z3(l - m)|
(C) 11x2y4z6|l - m| (D) 11x2y4|z3(l - m)|
19. If ax2 + bx + c = 0 has equal roots, then c is equal to
(A) b2/(2a) (B) b2/(4a) (C) -b2/(2a) (D) -b2/(4a)
20. If x2 + 5kx + 16 = 0 has no real roots, then
(A) k > 8/5 (B) k > -8/5 (C) -8/5 < k < 8/5 (D) 0 < k < 8/5
21. A quadratic equation whose one root is 3 is
(A) x2 - 6x - 5 = 0 (B) x2 + 6x - 5 = 0 (C) x2 - 5x - 6 = 0 (D) x2 - 5x + 6 = 0
22. The common root of the equations x2 - bx + c = 0 and x2 + bx - a = 0 is
(A) (c + a)/(2b) (B) (c - a)/(2b) (C) (c + b)/(2a) (D) (a + b)/(2c)
23. If α, β are the roots of ax2 + bx + c = 0, a ≠ 0, then the wrong statement is
(A) α2 + β2 = (b2 - 2ac)/a2 (B) αβ = c/a
(C) α + β = b/a (D) 1/α + 1/β = -b/c
24. If α and β are the roots of ax2 + bx + c = 0, then one of the quadratic equations whose roots are 1/α and 1/β is
(A) ax2 + bx + c = 0 (B) bx2 + ax + c = 0 (C) cx2 + bx + a = 0 (D) cx2 + ax + b = 0
25. Let b = a + c. Then the equation ax2 + bx + c = 0 has equal roots, if
(A) a = c (B) a = -c (C) a = 2c (D) a = -2c
1. Which one of the following statements is not true?
(A) A scalar matrix is a square matrix
(B) A diagonal matrix is a square matrix
(C) A scalar matrix is a diagonal matrix
(D) A diagonal matrix is a scalar matrix
3. Matrix A = [aij]m × n is a square matrix if
(A) m < n (B) m > n (C) m = 1 (D) m = n
| 3x + 7 | 5 |
| y + 1 | 2 - 3x |
| 1 | y - 2 |
| 8 | 8 |
(A) -2, 7 (B) -1/3, 7 (C) -1/3, -2/3 (D) 2, -7
| 1 | -2 | 3 |
| -1 |
| 2 |
| -3 |
(A) (0 0 0) (B)
| 0 |
| 0 |
| 0 |
6. If a matrix is of order 2 × 3, then the number of elements in the matrix is
(A) 5 (B) 6 (C) 2 (D) 3
| 8 | 4 |
| x | 8 |
| 2 | 1 |
| 1 | 2 |
(A) 1 (B) 2 (C) 1/4 (D) 4
8. If A is of order 3 × 4 and B is of order 4 × 3, then the order of BA is
(A) 3 × 3 (B) 4 × 4 (C) 4 × 3 (D) not defined
| 1 | 1 |
| 0 | 2 |
(A) 2 × 1 (B) 2 × 2 (C) 1 × 2 (D) 3 × 2
10. If A and B are square matrices such that AB = I and BA = I, then B is
(A) Unit matrix (B) Null matrix (C) Multiplicative inverse matrix of A (D) -A
| 1 | 2 |
| 2 | 1 |
| x |
| y |
| 2 |
| 4 |
(A) 2, 0 (B) 0, 2 (C) 0, -2 (D) 1, 1
| 1 | -2 |
| -3 | 4 |
(A)
| 1 | -2 |
| -3 | 4 |
| -1 | 2 |
| 3 | -4 |
| -1 | -2 |
| -3 | -4 |
| 1 | 0 |
| 0 | 1/2 |
| 4 | -2 |
| 6 | -3 |
(A)
| 16 | 4 |
| 36 | 9 |
| 8 | -4 |
| 12 | -6 |
| -4 | 2 |
| -6 | 3 |
| 4 | -2 |
| 6 | -3 |
14. A is of order m × n and B is of order p × q. Addition of A and B is possible only if
(A) m = p (B) n = q (C) n = p (D) m = p, n = q
| a | 3 |
| 1 | 2 |
| 2 |
| -1 |
| 5 |
| 0 |
(A) 8 (B) 4 (C) 2 (D) 11
| α | β |
| γ | -α |
(A) 1 + α2 + βγ = 0 (B) 1 - α2 + βγ = 0 (C) 1 - α2 - βγ = 0 (D) 1 + α2 - βγ = 0
(A)
| 1 | 2 |
| 3 | 4 |
| 2 | 3 |
| 3 | 4 |
| 2 | 3 |
| 4 | 5 |
| 4 | 5 |
| 6 | 7 |
| -1 | 0 |
| 0 | 1 |
| a | b |
| c | d |
| 1 | 0 |
| 0 | -1 |
(A) -1, 0, 0, -1 (B) 1, 0, 0, 1 (C) -1, 0, 1, 0 (D) 1, 0, 0, 0
| 7 | 2 |
| 1 | 3 |
| -1 | 0 |
| 2 | -4 |
(A)
| 1 | 0 |
| 0 | 1 |
| 6 | 2 |
| 3 | -1 |
| -8 | -2 |
| 1 | -7 |
| 8 | 2 |
| -1 | 7 |
| 2 |
| -1 |
| 3 |
(A) 7 (B) -7 (C) 1/7 (D) 0
21. Which one of the following is true for any two square matrices A and B of same order?
(A) (AB)T = ATBT (B) (ATB)T = ATBT (C) (AB)T = BA (D) (AB)T = BTAT
1. The midpoint of the line joining (a, -b) and (3a, 5b) is
(A) (-a, 2b) (B) (2a, 4b) (C) (2a, 2b) (D) (-a, -3b)
2. The point P which divides the line segment joining the points A(1, -3) and B(-3, 9) internally in the ratio 1 : 3 is
(A) (2, 1) (B) (0, 0) (C) (5/3, 2) (D) (1, -2)
3. If the line segment joining the points A(3, 4) and B(14, -3) meets the x-axis at P, then the ratio in which P divides the segment AB is
(A) 4 : 3 (B) 3 : 4 (C) 2 : 3 (D) 4 : 1
4. The centroid of the triangle with vertices at (-2, -5), (-2, 12) and (10, -1) is
(A) (6, 6) (B) (4, 4) (C) (3, 3) (D) (2, 2)
5. If (1, 2), (4, 6), (x, 6) and (3, 2) are the vertices of a parallelogram taken in order, then the value of x is
(A) 6 (B) 2 (C) 1 (D) 3
6. Area of the triangle formed by the points (0, 0), (2, 0) and (0, 2) is
(A) 1 sq. units (B) 2 sq. units (C) 4 sq. units (D) 8 sq. units
7. Area of the quadrilateral formed by the points (1, 1), (0, 1), (0, 0) and (1, 0) is
(A) 3 sq. units (B) 2 sq. units (C) 4 sq. units (D) 1 sq. units
8. The angle of inclination of a straight line parallel to x-axis is equal to
(A) 0° (B) 60° (C) 45° (D) 90°
9. Slope of the line joining the points (3, -2) and (-1, a) is -3/2, then the value of a is equal to
(A) 1 (B) 2 (C) 3 (D) 4
10. Slope of the straight line which is perpendicular to the straight line joining the points (-2, 6) and (4, 8) is equal to
(A) 1/3 (B) 3 (C) -3 (D) -1/3
11. The point of intersection of the straight lines 9x - y - 2 = 0 and 2x + y - 9 = 0 is
(A) (-1, 7) (B) (7, 1) (C) (1, 7) (D) (-1, -7)
12. The straight line 4x + 3y - 12 = 0 intersects the y-axis at
(A) (3, 0) (B) (0, 4) (C) (3, 4) (D) (0, -4)
13. The slope of the straight line 7y - 2x = 11 is equal to
(A) -7/2 (B) 7/2 (C) 2/7 (D) -2/7
14. The equation of a straight line passing through the point (2, -7) and parallel to x-axis is
(A) x = 2 (B) x = -7 (C) y = -7 (D) y = 2
15. The x and y-intercepts of the line 2x - 3y + 6 = 0, respectively are
(A) 2, 3 (B) 3, 2 (C) -3, 2 (D) 3, -2
16. The centre of a circle is (-6, 4). If one end of the diameter of the circle is at (-12, 8), then the other end is at
(A) (-18, 12) (B) (-9, 6) (C) (-3, 2) (D) (0, 0)
17. The equation of the straight line passing through the origin and perpendicular to the straight line 2x + 3y - 7 = 0 is
(A) 2x + 3y = 0 (B) 3x - 2y = 0 (C) y + 5 = 0 (D) y - 5 = 0
18. The equation of a straight line parallel to y-axis and passing through the point (-2, 5) is
(A) x - 2 = 0 (B) x + 2 = 0 (C) y + 5 = 0 (D) y - 5 = 0
19. If the points (2, 5), (4, 6) and (a, a) are collinear, then the value of a is equal to
(A) -8 (B) 4 (C) -4 (D) 8
20. If a straight line y = 2x + k passes through the point (1, 2), then the value of k is equal to
(A) 0 (B) 4 (C) 5 (D) -3
21. The equation of a straight line having slope 3 and y-intercept -4 is
(A) 3x - y - 4 = 0 (B) 3x + y - 4 = 0 (C) 3x - y + 4 = 0 (D) 3x + y + 4 = 0
22. The point of intersection of the straight lines y = 0 and x = -4 is
(A) (0, -4) (B) (-4, 0) (C) (0, 4) (D) (4, 0)
23. The value of k if the straight lines 3x + 6y + 7 = 0 and 2x + ky = 5 are perpendicular is
(A) 1 (B) -1 (C) 2 (D) 1/2
1. (1 - sin2θ) sec2θ =
(A) 0 (B) 1 (C) tan2θ (D) cos2θ
2. (1 + tan2θ) sin2θ =
(A) sin2θ (B) cos2θ (C) tan2θ (D) cot2θ
3. (1 - cos2θ)(1 + cot2θ) =
(A) sin2θ (B) 0 (C) 1 (D) tan2θ
4. sin(90° - θ) cos θ + cos(90° - θ) sin θ =
(A) 1 (B) 0 (C) 2 (D) -1
5. 1 - sin2θ/(1 + cos θ) =
(A) cos θ (B) tan θ (C) cot θ (D) cosec θ
6. cos4x - sin4x =
(A) 2 sin2x - 1 (B) 2 cos2x - 1 (C) 1 + 2 sin2x (D) 1 - 2 cos2x
7. If tan θ = a/x, then the value of x/√(a2 + x2) =
(A) cos θ (B) sin θ (C) cosec θ (D) sec θ
8. If x = a sec θ, y = b tan θ, then the value of x2/a2 - y2/b2 =
(A) 1 (B) -1 (C) tan2θ (D) cosec2θ
9. sec θ/(cot θ + tan θ) =
(A) cot θ (B) tan θ (C) sin θ (D) -cot θ
10. [sin(90° - θ) sin θ]/tan θ + [cos(90° - θ) cos θ]/cot θ =
(A) tan θ (B) 1 (C) -1 (D) sin θ
11. In the adjoining figure, with right angle at B, base AB = 25 m and ∠C = 60°, AC =
(A) 25 m (B) 25√3 m (C) 25/√3 m (D) 25√2 m
12. In the adjoining figure, with right angle at A, vertical side AC = 100√3 m and base AB = 100 m, ∠ABC =
(A) 45° (B) 30° (C) 60° (D) 50°
13. A man is 28.5 m away from a tower. His eye level above the ground is 1.5 m. The angle of elevation of the tower from his eyes is 45°. Then the height of the tower is
(A) 30 m (B) 27.5 m (C) 28.5 m (D) 27 m
14. In the adjoining figure, with right angle at B, hypotenuse AC = 85 m and sin θ = 15/17. Then BC =
(A) 85 m (B) 65 m (C) 95 m (D) 75 m
15. (1 + tan2θ)(1 - sin θ)(1 + sin θ) =
(A) cos2θ - sin2θ (B) sin2θ - cos2θ (C) sin2θ + cos2θ (D) 0
16. (1 + cot2θ)(1 - cos θ)(1 + cos θ) =
(A) tan2θ - sec2θ (B) sin2θ - cos2θ (C) 1 (D) cos2θ - sin2θ
17. (cos2θ - 1)(cot2θ + 1) + 1 =
(A) 1 (B) -1 (C) 2 (D) 0
18. (1 + tan2θ)/(1 + cot2θ) =
(A) cos2θ (B) tan2θ (C) sin2θ (D) cot2θ
19. sin2θ + 1/(1 + tan2θ) =
(A) cosec2θ + cot2θ (B) cosec2θ - cot2θ (C) cot2θ - cosec2θ (D) sin2θ - cos2θ
20. 9 tan2θ - 9 sec2θ =
(A) 1 (B) 0 (C) 9 (D) -9
1. The curved surface area of a right circular cylinder of radius 1 cm and height 1 cm is equal to
(A) π cm2 (B) 2π cm2 (C) 3π cm3 (D) 2 cm2
2. The total surface area of a solid right circular cylinder whose radius is half of its height h is equal to
(A) 3/2 πh sq.units (B) 2/3 πh2 sq.units (C) 3/2 πh2 sq.units (D) 2/3 πh sq.units
4. Base area of a right circular cylinder is 80 cm2. If its height is 5 cm, then the volume is equal to
(A) 400 cm3 (B) 16 cm3 (C) 200 cm3 (D) 400/3 cm3
6. If the total surface area of a solid right circular cylinder is 200π cm2 and its radius is 5 cm, then the sum of its height and radius is
(A) 20 cm (B) 25 cm (C) 30 cm (D) 15 cm
8. The curved surface area of a right circular cylinder whose radius is a units and height is b units, is equal to
(A) πa2b sq.cm (B) 2πab sq.cm (C) 2π sq.cm (D) 2 sq.cm
10. Radius and height of a right circular cone and that of a right circular cylinder are respectively equal. If the volume of the cylinder is 120 cm3, then the volume of the cone is equal to
(A) 1200 cm3 (B) 360 cm3 (C) 40 cm3 (D) 90 cm3
12. If the diameter and height of a right circular cone are 12 cm and 8 cm respectively, then the slant height is
(A) 10 cm (B) 20 cm (C) 30 cm (D) 96 cm
13. If the circumference at the base of a right circular cone and the slant height are 120 cm and 10 cm respectively, then the curved surface area of the cone is equal to
(A) 1200π cm2 (B) 600π cm2 (C) 300π cm2 (D) 600 cm2
14. If the volume and the base area of a right circular cone are 48π cm3 and 12π cm2 respectively, then the height of the cone is equal to
(A) 6 cm (B) 8 cm (C) 10 cm (D) 12 cm
15. If the height and the base area of a right circular cone are 5 cm and 48 sq. cm respectively, then the volume of the cone is equal to
(A) 240 cm3 (B) 120 cm3 (C) 80 cm3 (D) 480 cm3
16. The ratios of the respective heights and the respective radii of two cylinders are 1:2 and 2:1 respectively. Then their respective volumes are in the ratio
(A) 4:1 (B) 1:4 (C) 2:1 (D) 1:2
17. If the radius of a sphere is 2 cm, then the curved surface area of the sphere is equal to
(A) 8π cm2 (B) 16 cm2 (C) 12π cm2 (D) 16π cm2
18. The total surface area of a solid hemisphere of diameter 2 cm is equal to
(A) 12 cm2 (B) 12π cm2 (C) 4π cm2 (D) 3π cm2
19. If the volume of a sphere is 9/16π cu.cm, then its radius is
(A) 4/3 cm (B) 3/4 cm (C) 3/2 cm (D) 2/3 cm
20. The surface areas of two spheres are in the ratio of 9 : 25. Then their volumes are in the ratio
(A) 81 : 625 (B) 729 : 15625 (C) 27 : 75 (D) 27 : 125
21. The total surface area of a solid hemisphere whose radius is a units, is equal to
(A) 2πa2 sq.units (B) 3πa2 sq.units (C) 3πa sq.units (D) 3a2 sq.units
22. If the surface area of a sphere is 100π cm2, then its radius is equal to
(A) 25 cm (B) 100 cm (C) 5 cm (D) 10 cm
23. If the surface area of a sphere is 36π cm2, then the volume of the sphere is equal to
(A) 12π cm3 (B) 36π cm3 (C) 72π cm3 (D) 108π cm3
24. If the total surface area of a solid hemisphere is 12π cm2, then its curved surface area is equal to
(A) 6π cm2 (B) 24π cm2 (C) 36π cm2 (D) 8π cm2
25. If the radius of a sphere is half of the radius of another sphere, then their respective volumes are in the ratio
(A) 1 : 8 (B) 2 : 1 (C) 1 : 2 (D) 8 : 1
26. Curved surface area of solid sphere is 24 cm2. If the sphere is divided into two hemispheres, then the total surface area of one of the hemispheres is
(A) 12 cm2 (B) 8 cm2 (C) 16 cm2 (D) 18 cm2
27. Two right circular cones have equal radii. If their slant heights are in the ratio 4 : 3, then their respective curved surface areas are in the ratio
(A) 16 : 9 (B) 2 : 3 (C) 4 : 3 (D) 3 : 4
1. The range of the first 10 prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 is
(A) 28 (B) 26 (C) 29 (D) 27
2. The least value in a collection of data is 14.1. If the range of the collection is 28.4, then the greatest value of the collection is
(A) 42.5 (B) 43.5 (C) 42.4 (D) 42.1
3. The greatest value of a collection of data is 72 and the least value is 28. Then the coefficient of range is
(A) 44 (B) 0.72 (C) 0.44 (D) 0.28
4. For a collection of 11 items, Σx = 132, then the arithmetic mean is
(A) 11 (B) 12 (C) 14 (D) 13
5. For any collection of n items, Σ(x - x̄) =
(A) Σx (B) x̄ (C) nx̄ (D) 0
6. For any collection of n items, (Σx) - x̄ =
(A) nx̄ (B) (n - 2)x̄ (C) (n - 1)x̄ (D) 0
7. If t is the standard deviation of x, y, z, then the standard deviation of x + 5, y + 5, z + 5 is
(A) t/3 (B) t + 5 (C) t (D) xyz
8. If the standard deviation of a set of data is 1.6, then the variance is
(A) 0.4 (B) 2.56 (C) 1.96 (D) 0.04
9. If the variance of a data is 12.25, then the S.D is
(A) 3.5 (B) 3 (C) 2.5 (D) 3.25
10. Variance of the first 11 natural numbers is
(A) √5 (B) √10 (C) 5√2 (D) 10
11. The variance of 10, 10, 10, 10, 10 is
(A) 10 (B) √10 (C) 5 (D) 0
12. If the variance of 14, 18, 22, 26, 30 is 32, then the variance of 28, 36, 44, 52, 60 is
(A) 64 (B) 128 (C) 32√2 (D) 32
13. Standard deviation of a collection of data is 2√2. If each value is multiplied by 3, then the standard deviation of the new data is
(A) √12 (B) 4√2 (C) 6√2 (D) 9√2
14. Given Σ(x - x̄)2 = 48, x̄ = 20 and n = 12. The coefficient of variation is
(A) 25 (B) 20 (C) 30 (D) 10
15. Mean and standard deviation of a data are 48 and 12 respectively. The coefficient of variation is
(A) 42 (B) 25 (C) 28 (D) 48
1. If φ is an impossible event, then P(φ) =
(A) 1 (B) 1/4 (C) 0 (D) 1/2
2. If S is the sample space of a random experiment, then P(S) =
(A) 0 (B) 1/8 (C) 1/2 (D) 1
3. If p is the probability of an event A, then p satisfies
(A) 0 < p < 1 (B) 0 ≤ p ≤ 1 (C) 0 ≤ p < 1 (D) 0 < p ≤ 1
4. Let A and B be any two events and S be the corresponding sample space. Then P(Ā ∩ B̄) =
(A) P(B) - P(A ∩ B) (B) P(A ∩ B) - P(B) (C) P(S) (D) P[(A ∪ B)′]
5. The probability that a student will score centum in mathematics is 4/5. The probability that he will not score centum is
(A) 1/5 (B) 2/5 (C) 3/5 (D) 4/5
6. If A and B are two events such that P(A) = 0.25, P(B) = 0.05 and P(A ∩ B) = 0.14, then P(A ∪ B) =
(A) 0.61 (B) 0.16 (C) 0.14 (D) 0.6
7. There are 6 defective items in a sample of 20 items. One item is drawn at random. The probability that it is a non-defective item is
(A) 7/10 (B) 0 (C) 3/10 (D) 2/3
8. If A and B are mutually exclusive events and S is the sample space such that P(A) = 1/3 P(B) and S = A ∪ B, then P(A) =
(A) 1/4 (B) 1/2 (C) 3/4 (D) 3/8
9. The probabilities of three mutually exclusive events A, B and C are given by 1/3, 1/4 and 5/12. Then P(A ∪ B ∪ C) is
(A) 19/12 (B) 11/12 (C) 7/12 (D) 1
11. If P(A) = 0.25, P(B) = 0.50, P(A ∩ B) = 0.14 then P(neither A nor B) =
(A) 0.39 (B) 0.25 (C) 0.11 (D) 0.24
12. A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected at random, the probability that it is not red is
(A) 5/12 (B) 4/12 (C) 3/12 (D) 3/4
13. Two dice are thrown simultaneously. The probability of getting a doublet is
(A) 1/36 (B) 1/3 (C) 1/6 (D) 2/3
14. A fair die is thrown once. The probability of getting a prime or composite number is
(A) 1 (B) 0 (C) 5/6 (D) 1/6
15. Probability of getting 3 heads or 3 tails in tossing a coin 3 times is
(A) 1/8 (B) 1/4 (C) 3/8 (D) 1/2
16. A card is drawn from a pack of 52 cards at random. The probability of getting neither an ace nor a king card is
(A) 2/13 (B) 11/13 (C) 4/13 (D) 8/13
17. The probability that a leap year will have 53 Fridays or 53 Saturdays is
(A) 2/7 (B) 1/7 (C) 4/7 (D) 3/7
18. The probability that a non-leap year will have 53 Sundays and 53 Mondays is
(A) 1/7 (B) 2/7 (C) 3/7 (D) 0
19. The probability of selecting a queen of hearts when a card is drawn from a pack of 52 playing cards is
(A) 1/52 (B) 16/52 (C) 1/13 (D) 1/26
20. Probability of sure event is
(A) 1 (B) 0 (C) 100 (D) 0.1
21. The outcome of a random experiment results in either success or failure. If the probability of success is twice the probability of failure, then the probability of success is
(A) 1/3 (B) 2/3 (C) 1 (D) 0
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| A | C | C | A | A | B | B | B | B | C |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| B | D | C | D | D | A | B | B | B | B |
| 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| B | A | B | D | A | B | B | A | C | A |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| B | C | A | A | C | D | B | C | C | C | D | B | A |
| 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | - |
| A | A | D | D | D | B | C | D | A | C | C | A | - |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| D | D | A | D | B | D | B | C | C | A |
| 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| B | D | D | B | C | B | A | C | B | D |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| C | B | A | D | A | B | D | A | D | C | C | B |
| 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | - |
| C | C | C | D | B | B | D | A | A | B | B | - |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| B | C | C | A | A | B | A | A | C | B |
| 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| B | C | A | D | C | C | D | B | B | D |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| B | C | A | A | B | C | A | B | D | C | C |
| 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
| D | D | B | D | B | C | B | D | A | D | C |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| D | A | C | B | D | C | - | B | A | D |
| 11 | 12 | 13 | 14 | 15 | - | - | - | - | - |
| D | B | C | D | B | - | - | - | - | - |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| C | D | B | A | A | B | A | A | D | A |
| 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| D | C | C | B | B | D | D | A | A | B |
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