The ratio of simple interest earned on a certain amount at the same rate for 6 years and 9 years is
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Correct answer: (B) 2:3
1 marks · 2023 · Set A
Question 102
The number of years required for ₹12,500 to become ₹17,500 at 10% per annum is
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Correct answer: (A) 4 years
1 marks · 2023 · Set A
Question 103
The compound interest on ₹25,000 after 3 years at 12% per annum is
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Correct answer: (A) ₹10,123.20
1 marks · 2023 · Set A
Question 104
Pipe A can fill a cistern in 36 minutes and pipe B in 48 minutes. Both are opened together and the cistern fills in 24 minutes. After how long is pipe B closed?
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Correct answer: (A) 16 minutes
1 marks · 2023 · Set A
Question 105
A plot is sold for ₹18,700 at a loss of 15%. To gain 15%, it must be sold for
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Correct answer: (C) ₹25,300
1 marks · 2023 · Set A
Question 106
A and B can complete a work in 8 days, B and C in 12 days, and C and A in 24 days. In how many days can they complete the work together?
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Correct answer: (B) 8 days
1 marks · 2023 · Set A
Question 107
A quantity X is 25% more than Y. By what percent is Y less than X?
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Correct answer: (A) 20%
1 marks · 2023 · Set A
Question 108
Three pipes A, B and C can fill a tank in 6 hours. After working together for 2 hours, C is closed, and A and B fill the remainder in 7 hours. C alone can fill the tank in
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Correct answer: (C) 14 hours
1 marks · 2023 · Set A
Question 109
A batsman scores 120 runs, including 3 boundaries and 8 sixes. What percentage of his total score is made by running between the wickets?
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Correct answer: (B) 50
1 marks · 2023 · Set A
Question 110
A test is taken by 1,100 boys and 700 girls. 42% of the boys and 30% of the girls pass. What percentage of the total candidates fail?
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Correct answer: (A) 62⅔
1 marks · 2023 · Set A
Question 111
The area of a rectangle is 460 square metres. If its length is 15% more than its breadth, what is its breadth?
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Correct answer: (A) 20 metres
1 marks · 2023 · Set A
Question 112
The ratio of the outer and inner perimeters of a circular path is 23:22. If the path is 5 metres wide, the diameter of the inner circle is
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Correct answer: (C) 220 metres
1 marks · 2023 · Set A
Question 113
The radius of the circumcircle of an equilateral triangle of side 12 cm is
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Correct answer: (E) None of the above
1 marks · 2023 · Set A
Question 114
The height of a right circular cylinder is 14 cm and its curved surface area is 704 cm². Its volume is
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Correct answer: (B) 2816 cm³
1 marks · 2023 · Set A
Question 115
If the surface areas of two spheres are in the ratio 4:25, the ratio of their volumes is
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Correct answer: (A) 8:125
1 marks · 2023 · Set A
Question 116
Which of the following numbers has a non-terminating repeating decimal expansion?
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Correct answer: (C) 117/(62 × 5³)
1 marks · 2023 · Set A
Question 117
If f(x) = ax² + bx + c has no real zeroes and a + b + c < 0, then
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Correct answer: (C) c < 0
1 marks · 2023 · Set A
Question 118
If α, β, γ are the zeroes of f(x) = x³ − px² + qx − r, then 1/(αβ) + 1/(βγ) + 1/(γα) equals
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Correct answer: (B) p/r
1 marks · 2023 · Set A
Question 119
The zeroes of the quadratic polynomial f(x) = x² + 99x + 127 are
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Correct answer: (B) both negative
1 marks · 2023 · Set A
Question 120
If the pair of linear equations (3k + 1)x + 3y − 5 = 0 and 2x − 3y + 5 = 0 has infinitely many solutions, then k is
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Correct answer: (C) −1
1 marks · 2023 · Set A
Question 121
If 2/x + 3/y = 13 and 5/x − 4/y = −2, then x + y equals
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Correct answer: (C) 5/6
1 marks · 2023 · Set A
Question 122
The pair of linear equations y = 0 and y = −5 has
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Correct answer: (E) None of the above
1 marks · 2023 · Set A
Question 123
If c and d are roots of (x − a)(x − b) − k = 0, then a and b are roots of which equation?
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Correct answer: (A) (x − c)(x − d) + k = 0
1 marks · 2023 · Set A
Question 124
The number of real roots of (x − 1)² + (x − 2)² + (x − 3)² = 0 is
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Correct answer: (E) None of the above
1 marks · 2023 · Set A
Question 125
The sum of n terms of the series √2 + √8 + √18 + √32 + ⋯ is
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Correct answer: (A) n(n + 1)/√2
1 marks · 2023 · Set A
Question 126
The coordinates of the fourth vertex of the rectangle formed by O(0, 0), A(2, 0) and B(0, 3) are
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Correct answer: (C) (2, 3)
1 marks · 2023 · Set A
Question 127
If D(1, 2), E(4, −3), F(−2, 4) are respectively the midpoints of sides BC, CA, AB of triangle ABC, the coordinates of its centroid are
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Correct answer: (A) (1, 1)
1 marks · 2023 · Set A
Question 128
If A(a², 0), B(0, b²) and C(1, 1) are collinear, then
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Correct answer: (C) 1/a² + 1/b² = 1
1 marks · 2023 · Set A
Question 129
In triangle ABC, AB = 3 cm, BC = 2 cm and CA = 2.5 cm. If triangle ABC is similar to triangle DEF and EF = 4 cm, the perimeter of triangle DEF is
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Correct answer: (B) 15 cm
1 marks · 2023 · Set A
Question 130
In triangle ABC, ∠B = 90° and BD ⟂ AC. If AC = 9 cm and AD = 3 cm, then BD is
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Correct answer: (C) 3√2 cm
1 marks · 2023 · Set A
Question 131
In triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E. Which of the following is not true?
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Correct answer: (A) DE/PQ = EF/RP
1 marks · 2023 · Set A
Question 132
If PA and PB are two tangents to a circle with centre O and ∠AOB = 110°, then ∠APB is
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Correct answer: (B) 70°
1 marks · 2023 · Set A
Question 133
The length of tangent AP from an external point A is 24 cm. If the distance from A to the centre O is 25 cm, the diameter of the circle is
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Correct answer: (B) 14 cm
1 marks · 2023 · Set A
Question 134
PT is a tangent to a circle at T and PAB is a secant. If PA = 9 cm and AB = 7 cm, then PT is
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Correct answer: (A) 12 cm
1 marks · 2023 · Set A
Question 135
From point P, 13 cm from the centre O of a circle of radius 5 cm, tangents PQ and PR are drawn. The area of quadrilateral PQOR is
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Correct answer: (A) 60 cm²
1 marks · 2023 · Set A
Question 136
If 0 ≤ A, B ≤ 90° such that sin A = 1/2 and cos B = 1/2, then A + B is
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Correct answer: (C) 90°
1 marks · 2023 · Set A
Question 137
If tan 2A = cot(A + 60°), where 2A is an acute angle, then A is
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Correct answer: (A) 10°
1 marks · 2023 · Set A
Question 138
If sin θ + cos θ = √2 cos θ, θ ≠ 90°, then tan θ is
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Correct answer: (C) √2 − 1
1 marks · 2023 · Set A
Question 139
The value of cos² θ + 1/(1 + cot² θ) is
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Correct answer: (B) 1
1 marks · 2023 · Set A
Question 140
यदि sin θ + cos θ = √2 है, तो tan θ + cot θ है
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Correct answer: (B) 2
1 marks · 2023 · Set A
Question 141
यदि [cos²20° + cos²70°]/[2(sin²59° + sin²31°)] = 2/k है, तो k बराबर है
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Correct answer: (C) 4
1 marks · 2023 · Set A
Question 142
The radius of a circle whose circumference equals the sum of the circumferences of two circles with diameters 36 cm and 20 cm is
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Correct answer: (C) 28 cm
1 marks · 2023 · Set A
Question 143
A solid sphere of total surface area 48 cm² is bisected into two hemispheres. The total surface area of either hemisphere is
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Correct answer: (B) 36 cm²
1 marks · 2023 · Set A
Question 144
A solid consists of a circular cylinder surmounted by a right circular cone of height h. If the total volume is 3 times the volume of the cone, the height of the cylinder is
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Correct answer: (A) 2h/3
1 marks · 2023 · Set A
Question 145
If the arithmetic mean of the first n natural numbers is 15, then n is
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Correct answer: (C) 29
1 marks · 2023 · Set A
Question 146
If the difference between the mode and median of a data set is 24, then the difference between the median and mean is
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Correct answer: (A) 12
1 marks · 2023 · Set A
Question 147
If a variable takes the discrete values x + 4, x − 7/2, x − 5/2, x − 3, x − 2, x + 1/2, x − 1/2, x + 5, where x > 0, then the median of the data is
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Correct answer: (C) x − 5/4
1 marks · 2023 · Set A
Question 148
Radha deposits ₹800 in a short-term bank deposit for 73 days at 7½% per annum. How much interest will she get?
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Correct answer: (C) ₹12
1 marks · 2023 · Set A
Question 149
On a sum of money, simple interest for 2 years is ₹660, while compound interest is ₹696.30, at the same rate in both cases. The rate of interest is
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Correct answer: (E) None of the above
1 marks · 2023 · Set A
Question 150
Find the discount equivalent to successive discounts of 20%, 10% and 5% on an invoice.