Places A and B are 100 km apart. Cars start simultaneously from A and B. Travelling in the same direction at different speeds, they meet in 5 hours; travelling towards each other, they meet in 1 hour. What are their speeds?
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Correct answer: (A) 60 km/h, 40 km/h
1 marks · 2023 · Set A
Question 52
The sum of the squares of two positive integers is 306. The square of the larger integer is 25 times the smaller integer. What is the difference between the integers?
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Correct answer: (A) 6
1 marks · 2023 · Set A
Question 53
For the frequency distribution 0–10: 3, 10–20: 9, 20–30: 15, 30–40: 30, 40–50: 18, 50–60: 5, the modal class is
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Correct answer: (B) 30–40
1 marks · 2023 · Set A
Question 54
The diagonals AC and DB of quadrilateral ABCD intersect at E, with AE:EC = 1:2 and BE:ED = 3:6. Then ABCD is
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Correct answer: (E) None of the above
1 marks · 2023 · Set A
Question 55
Find two numbers such that three times the first plus the second is 142, and four times the first exceeds the second by 138.
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Correct answer: (C) 40, 22
1 marks · 2023 · Set A
Question 56
The slope of the line joining (k, 4) and (−3, −2) is 1/2. Find k.
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Correct answer: (C) 9
1 marks · 2023 · Set A
Question 57
A person has ₹4,200 for a tour. If the tour is extended by 3 days, daily expenses must be reduced by ₹70. What was the original duration of the tour?
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Correct answer: (B) 12 days
1 marks · 2023 · Set A
Question 58
A motorboat travels at 18 km/h in still water. It takes one hour longer to travel 24 km upstream than to return downstream. What is the speed of the stream?
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Correct answer: (B) 6 km/h
1 marks · 2023 · Set A
Question 59
Find the centre of the circle passing through (6, −6), (3, −7) and (3, 3).
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Correct answer: (B) (3, −2)
1 marks · 2023 · Set A
Question 60
Two taps together fill a tank in 9⅜ hours. The larger-diameter tap takes 10 hours less than the smaller one to fill the tank alone. How long does each take separately?
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Correct answer: (B) 15, 25 hours
1 marks · 2023 · Set A
Question 61
Kamal’s Mathematics and English marks total 40. If he had scored 3 more in Mathematics and 4 fewer in English, their product would have been 360. What were his marks in the two subjects?
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Correct answer: (D) More than one of the above
1 marks · 2023 · Set A
Question 62
A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that neither is blue?
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Correct answer: (A) 10/21
1 marks · 2023 · Set A
Question 63
A man saved ₹33,000 in 10 months. From the second month onward, he saved ₹100 more each month than in the preceding month. How much did he save in the first month?
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Correct answer: (A) ₹2,850
1 marks · 2023 · Set A
Question 64
A square field has area 24,200 m². At 6.6 km/h, how long will a woman take to cross it diagonally?
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Correct answer: (B) 2 minutes
1 marks · 2023 · Set A
Question 65
What is the sum of all three-digit natural numbers that are multiples of 11?
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Correct answer: (B) 44,550
1 marks · 2023 · Set A
Question 66
For what value of k do the equations 3(k−1)x + 4y = 24 and 15x + 20y = 8(k+13) have infinitely many solutions?
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Correct answer: (A) 2
1 marks · 2023 · Set A
Question 67
For what value of p are A(4, 7), B(p, 3), and C(7, 3) the vertices of a right-angled triangle with the right angle at B?
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Correct answer: (C) 4
1 marks · 2023 · Set A
Question 68
A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the large cube’s surface area to the sum of the small cubes’ surface areas?
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Correct answer: (B) 1:5
1 marks · 2023 · Set A
Question 69
In ΔABC, AD bisects ∠A. If AB = 6.4 cm, AC = 8 cm and BD = 5.6 cm, find DC.
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Correct answer: (A) 7 cm
1 marks · 2023 · Set A
Question 70
The sum of the LCM and HCF of two numbers is 1,260. Their LCM is 900 greater than their HCF. What is the product of the numbers?
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Correct answer: (B) 194,400
1 marks · 2023 · Set A
Question 71
If an angle bisector of a triangle bisects the opposite side, the triangle is
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Correct answer: (C) isosceles
1 marks · 2023 · Set A
Question 72
Angles of elevation to the top of a tower from points 4 m and 9 m from its base, on the same straight line, are complementary. Find the tower’s height.
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Correct answer: (A) 6 m
1 marks · 2023 · Set A
Question 73
A rhombus has area 480 cm² and one diagonal is 20 cm. Find the length of each side.
Which pair of lines in a circle cannot be parallel?
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Correct answer: (C) Two diameters
1 marks · 2023 · Set A
Question 76
A bag contains 5 red balls and some blue balls. The probability of drawing a blue ball is four times that of drawing a red ball. How many blue balls are in the bag?
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Correct answer: (C) 20
1 marks · 2023 · Set A
Question 77
If sin A + sin² A = 1, then cos² A + cos⁴ A equals
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Correct answer: (B) 1
1 marks · 2023 · Set A
Question 78
The probability of an event can be
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Correct answer: (C) 18/23
1 marks · 2023 · Set A
Question 79
The angle of depression of a car from the top of a 150 m tower is 30°. What is the car’s distance from the tower?
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Correct answer: (B) 150√3 m
1 marks · 2023 · Set A
Question 80
A hemispherical bowl of internal diameter 36 cm is full of liquid. The liquid is poured into cylindrical bottles of radius 3 cm and height 9 cm. How many bottles are needed?
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Correct answer: (B) 48
1 marks · 2023 · Set A
Question 81
A kite is 30 m above the ground, and its taut string is 60 m long. What is the angle of elevation of the kite from the ground?
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Correct answer: (C) 30°
1 marks · 2023 · Set A
Question 82
A carton contains 100 shirts: 88 good, 8 with minor defects and 4 with major defects. Jimmy accepts only good shirts; Sujata rejects only shirts with major defects. For one randomly drawn shirt, what are the probabilities that it is unacceptable to Jimmy and acceptable to Sujata, respectively?
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Correct answer: (A) 0.12, 0.96
1 marks · 2023 · Set A
Question 83
Find the area of a triangle with sides 42 cm, 34 cm and 20 cm.
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Correct answer: (C) 336 cm²
1 marks · 2023 · Set A
Question 84
The denominator of a fraction is 2 more than its numerator. The sum of the fraction and its reciprocal is 2 4/15. Find the fraction.
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Correct answer: (B) 3/5
1 marks · 2023 · Set A
Question 85
Carpeting a 15 m long room with carpet 75 cm wide at ₹70 per metre costs ₹8,400. What is the room’s width?
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Correct answer: (C) 6 m
1 marks · 2023 · Set A
Question 86
If seven times the seventh term of an AP equals eleven times its eleventh term, its eighteenth term is
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Correct answer: (C) 0
1 marks · 2023 · Set A
Question 87
A wire forming a circle of radius 28 cm is rebent into a square. Find the square’s side length.
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Correct answer: (A) 44 cm
1 marks · 2023 · Set A
Question 88
Given x = 1/[2 − {1/[2 − (1/(2−x))]}], with x ≠ 2, find x.
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Correct answer: (A) 1, 1
1 marks · 2023 · Set A
Question 89
The area of a sector of angle θ° in a circle of radius R is
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Correct answer: (C) πR²θ/360
1 marks · 2023 · Set A
Question 90
Two people’s incomes are in the ratio 9:7 and their expenditures in the ratio 4:3. If each saves ₹2,000 per month, what are their monthly incomes?
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Correct answer: (A) ₹18,000 and ₹14,000
1 marks · 2023 · Set A
Question 91
A factory makes 120,000 cylindrical pencils daily. Each is 25 cm long and has base circumference 1.5 cm. What is the cost of colouring their curved surfaces at ₹0.05 per dm²?
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Correct answer: (C) ₹2,250
1 marks · 2023 · Set A
Question 92
Consider x − y + 1 = 0 and 3x + 2y − 12 = 0. What are the vertices of the triangle formed by these lines and the y-axis?
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Correct answer: (C) (2, 3), (0, 1), (0, 6)
1 marks · 2023 · Set A
Question 93
A cubical ice-cream bar has edge 22 cm. It is distributed by filling cones of radius 2 cm and height 7 cm to the brim. How many children can receive a cone?
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Correct answer: (C) 363
1 marks · 2023 · Set A
Question 94
If O is any point inside rectangle ABCD, then
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Correct answer: (A) OB² + OD² = OA² + OC²
1 marks · 2023 · Set A
Question 95
C(1, 1) divides the segment joining A(−2, 7) and B internally in the ratio 3:2. Find the coordinates of B.
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Correct answer: (B) (3, −3)
1 marks · 2023 · Set A
Question 96
A TV manufacturer produced 600 sets in year 3 and 700 sets in year 7. If annual production increases uniformly by a fixed amount, how many sets are produced in year 10?
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Correct answer: (C) 775
1 marks · 2023 · Set A
Question 97
Rajveer saves ₹32 in month 1, ₹36 in month 2 and ₹40 in month 3, continuing in this pattern. In how many months will she save ₹2,000?
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Correct answer: (E) None of the above
1 marks · 2023 · Set A
Question 98
In an examination, one student scored 30% and failed by 45 marks. Another scored 42%, which was 45 marks above the minimum passing mark. Find the total marks.
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Correct answer: (B) 750
1 marks · 2023 · Set A
Question 99
The mean of 20 numbers is zero. At most how many of them may be greater than zero?
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Correct answer: (A) 19
1 marks · 2023 · Set A
Question 100
Suhit borrowed ₹6,300 from Vikas at 14% simple interest for 3 years. He lent a larger principal to Mohit at 16% simple interest for the same period and earned ₹618 in the transaction. How much did he lend to Mohit?