Practice

Question 101

If log₁₀ a = p and log₁₀ b = q, then the value of log₁₀(aᵖbᑫ) is

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Correct answer: (C) p² + q²

1 marks · 2023 · Set A

Question 102

The value of logₑ 2 is

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Correct answer: (C) 1 − 1/2 + 1/3 − 1/4 + …

1 marks · 2023 · Set A

Question 103

The sum of the infinite series 1 − 1/2 + 1/2² − 1/2³ + … is

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Correct answer: (C) 2/3

1 marks · 2023 · Set A

Question 104

The values of a and b in the equation [[2a + b, a − 2b], [5c − d, 4c + 3d]] = [[4, −3], [11, 24]] are

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Correct answer: (E) None of the above

1 marks · 2023 · Set A

Question 105

If A = [[1, 0], [0, 2]] and B = [[3, 0], [0, 4]], then

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Correct answer: (D) More than one of the above

1 marks · 2023 · Set A

Question 106

If A and B are invertible matrices of the same order, then

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Correct answer: (B) (AB)⁻¹ = B⁻¹A⁻¹

1 marks · 2023 · Set A

Question 107

Which of the following statements is not correct?

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Correct answer: (B) A is skew-symmetric if A′ ≠ −A.

1 marks · 2023 · Set A

Question 108

The number of possible 3 × 3 matrices with each entry 1 or 2 is

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Correct answer: (C) 512

1 marks · 2023 · Set A

Question 109

If the area of a triangle with vertices (−3, 0), (3, 0) and (0, k) is 9 square units, then k is

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Correct answer: (A) 3

1 marks · 2023 · Set A

Question 110

Which of the following statements is correct?

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Correct answer: (C) A determinant is a number associated with a square matrix.

1 marks · 2023 · Set A

Question 111

If A is an invertible matrix of order 2, then det(A⁻¹) is equal to

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Correct answer: (B) 1/det(A)

1 marks · 2023 · Set A

Question 112

The value of the determinant |1 1 −2; 3 4 5; −1 2 1| is

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Correct answer: (A) −34

1 marks · 2023 · Set A

Question 113

For which value of x will the matrix [[8, x, 0], [4, 0, 2], [12, 6, 0]] become singular?

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Correct answer: (B) 4

1 marks · 2023 · Set A

Question 114

यदि Δ₁ = |ax x² 1; by y² 1; cz z² 1| तथा Δ₂ = |a b c; x y z; zy zx xy| हों, तो

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Correct answer: (B) Δ₁ − Δ₂ = 0

1 marks · 2023 · Set A

Question 115

If |A| = 7, then the value of |2A| is (where |A| is the determinant of A).

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Correct answer: (C) 56

1 marks · 2023 · Set A

Question 116

यदि sin⁻¹x + sin⁻¹y = π/2 हो, तो cos⁻¹x + cos⁻¹y का मान है

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Correct answer: (A) π/2

1 marks · 2023 · Set A

Question 117

If x ∈ [−π/2, π/2], then the value of sin⁻¹(cos x) is

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Correct answer: (E) None of the above

1 marks · 2023 · Set A

Question 118

If −1/√2 ≤ x ≤ 1/√2, then the value of sin⁻¹(2x√(1 − x²)) is

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Correct answer: (A) 2 sin⁻¹x

1 marks · 2023 · Set A

Question 119

The value of sin 3x is

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Correct answer: (B) 3 sin x − 4 sin³x

1 marks · 2023 · Set A

Question 120

The value of cos(−1710°) is

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Correct answer: (C) 0

1 marks · 2023 · Set A

Question 121

यदि cos x = a/b हो, तो sin x है

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Correct answer: (C) √(b² − a²)/b

1 marks · 2023 · Set A

Question 122

sin⁶θ + cos⁶θ + 3 sin²θ cos²θ का मान है

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Correct answer: (A) 1

1 marks · 2023 · Set A

Question 123

(tan 57° + cot 37°)/(tan 33° + cot 53°) का मान है

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Correct answer: (A) tan 53° × tan 57°

1 marks · 2023 · Set A

Question 124

The equation of the line passing through (1, 5) and (2, 3) is

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Correct answer: (C) 2x + y − 7 = 0

1 marks · 2023 · Set A

Question 125

The difference between the slopes of two parallel lines is

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Correct answer: (B) 0

1 marks · 2023 · Set A

Question 126

The centre of the circle x² + y² − 4x − 10y + 4 = 0 is

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Correct answer: (A) (2, 5)

1 marks · 2023 · Set A

Question 127

The equation of the parabola with vertex at the origin and directrix x − 2 = 0 is

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Correct answer: (B) y² = −8x

1 marks · 2023 · Set A

Question 128

The perpendicular distance from (3, −4) to the line 3x − 4y + 10 = 0 is

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Correct answer: (C) 7

1 marks · 2023 · Set A

Question 129

The equation of a hyperbola with foci on the x-axis and centre (0, 0) is

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Correct answer: (B) x²/a² − y²/b² = 1

1 marks · 2023 · Set A

Question 130

lim(x→0) x sin(1/x) का मान है

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Correct answer: (B) 0

1 marks · 2023 · Set A

Question 131

lim(x→0) [(1 − cos x)/x²] का मान है

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Correct answer: (B) 1/2

1 marks · 2023 · Set A

Question 132

The function f(x) = x|x| is

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Correct answer: (C) differentiable at the origin

1 marks · 2023 · Set A

Question 133

The value of lim(x→3) [(x³ − 7x² + 15x − 9)/(x⁴ − 5x³ + 27x − 27)] is

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Correct answer: (C) 1/9

1 marks · 2023 · Set A

Question 134

If f(x) = |sin x|, then

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Correct answer: (B) f(x) is everywhere continuous but not differentiable at x = nπ, n ∈ Z

1 marks · 2023 · Set A

Question 135

If E₁ and E₂ are independent events, then

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Correct answer: (B) P(E₁ ∩ E₂) = P(E₁) × P(E₂)

1 marks · 2023 · Set A

Question 136

The probability of getting exactly three tails when three coins are tossed simultaneously is

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Correct answer: (B) 1/8

1 marks · 2023 · Set A

Question 137

If E₁ and E₂ are events such that P(E₁) ≠ 0 and P(E₂|E₁) = 1, then

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Correct answer: (A) E₁ ⊂ E₂

1 marks · 2023 · Set A

Question 138

The mode of the data 4, 6, 5, 9, 3, 2, 7, 7, 6, 5, 4, 9, 10, 3, 4, 7, 6, 9, 9, 10 is

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Correct answer: (B) 9

1 marks · 2023 · Set A

Question 139

Which of the following is a measure of central tendency?

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Correct answer: (D) More than one of the above

1 marks · 2023 · Set A

Question 140

∫[((log|x|)²/x)] dx का मान है

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Correct answer: (B) [log|x|]³/3 + C

1 marks · 2023 · Set A

Question 141

∫ cot x log(sin x) dx का मान है

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Correct answer: (B) (1/2)(log sin x)² + C

1 marks · 2023 · Set A

Question 142

The value of ∫₀¹ tan⁻¹((2x − 1)/(1 + x − x²)) dx is

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Correct answer: (B) 0

1 marks · 2023 · Set A

Question 143

The function f(x) = xˣ, x > 0, has

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Correct answer: (B) only one extremum point

1 marks · 2023 · Set A

Question 144

The area of the ellipse x²/a² + y²/b² = 1 is

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Correct answer: (B) πab

1 marks · 2023 · Set A

Question 145

The length of the vector represented by the directed line segment with initial point P(2, −3, 4) and terminal point Q(−2, 1, 1) is

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Correct answer: (A) √41

1 marks · 2023 · Set A

Question 146

The value of (a⃗ − b⃗) × (a⃗ + b⃗) is

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Correct answer: (A) 2(a⃗ × b⃗)

1 marks · 2023 · Set A

Question 147

Time period is a

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Correct answer: (B) scalar quantity

1 marks · 2023 · Set A

Question 148

The pair of equations 3x − 5y = 7 and −6x + 10y = 7 has

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Correct answer: (C) no solution

1 marks · 2023 · Set A

Question 149

The optimal value of the objective function is attained at the points

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Correct answer: (C) at the corner points of the feasible region

1 marks · 2023 · Set A

Question 150

The point which does not lie in the half-plane 2x + 3y − 12 < 0 is

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Correct answer: (A) (2, 3)

1 marks · 2023 · Set A

TRE2 — Language General Studies And Mathematics