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?
उत्तर देखें
सही उत्तर: (A) 60 km/h, 40 km/h
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (A) 6
1 अंक · 2023 · सेट A
प्रश्न 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
उत्तर देखें
सही उत्तर: (B) 30–40
1 अंक · 2023 · सेट A
प्रश्न 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
उत्तर देखें
सही उत्तर: (E) None of the above
1 अंक · 2023 · सेट A
प्रश्न 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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सही उत्तर: (C) 40, 22
1 अंक · 2023 · सेट A
प्रश्न 56
The slope of the line joining (k, 4) and (−3, −2) is 1/2. Find k.
उत्तर देखें
सही उत्तर: (C) 9
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (B) 12 days
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (B) 6 km/h
1 अंक · 2023 · सेट A
प्रश्न 59
Find the centre of the circle passing through (6, −6), (3, −7) and (3, 3).
उत्तर देखें
सही उत्तर: (B) (3, −2)
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (B) 15, 25 hours
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (D) More than one of the above
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (A) 10/21
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (A) ₹2,850
1 अंक · 2023 · सेट A
प्रश्न 64
A square field has area 24,200 m². At 6.6 km/h, how long will a woman take to cross it diagonally?
उत्तर देखें
सही उत्तर: (B) 2 minutes
1 अंक · 2023 · सेट A
प्रश्न 65
What is the sum of all three-digit natural numbers that are multiples of 11?
उत्तर देखें
सही उत्तर: (B) 44,550
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (A) 2
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (C) 4
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (B) 1:5
1 अंक · 2023 · सेट A
प्रश्न 69
In ΔABC, AD bisects ∠A. If AB = 6.4 cm, AC = 8 cm and BD = 5.6 cm, find DC.
उत्तर देखें
सही उत्तर: (A) 7 cm
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (B) 194,400
1 अंक · 2023 · सेट A
प्रश्न 71
If an angle bisector of a triangle bisects the opposite side, the triangle is
उत्तर देखें
सही उत्तर: (C) isosceles
1 अंक · 2023 · सेट A
प्रश्न 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.
उत्तर देखें
सही उत्तर: (A) 6 m
1 अंक · 2023 · सेट A
प्रश्न 73
A rhombus has area 480 cm² and one diagonal is 20 cm. Find the length of each side.
उत्तर देखें
सही उत्तर: (C) 26 cm
1 अंक · 2023 · सेट A
प्रश्न 74
The factors of 2a⁷ − 128a are
उत्तर देखें
सही उत्तर: (C) 2a(a+2)(a−2)(a²+2a+4)(a²−2a+4)
1 अंक · 2023 · सेट A
प्रश्न 75
Which pair of lines in a circle cannot be parallel?
उत्तर देखें
सही उत्तर: (C) Two diameters
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (C) 20
1 अंक · 2023 · सेट A
प्रश्न 77
If sin A + sin² A = 1, then cos² A + cos⁴ A equals
उत्तर देखें
सही उत्तर: (B) 1
1 अंक · 2023 · सेट A
प्रश्न 78
The probability of an event can be
उत्तर देखें
सही उत्तर: (C) 18/23
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (B) 150√3 m
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (B) 48
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (C) 30°
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (A) 0.12, 0.96
1 अंक · 2023 · सेट A
प्रश्न 83
Find the area of a triangle with sides 42 cm, 34 cm and 20 cm.
उत्तर देखें
सही उत्तर: (C) 336 cm²
1 अंक · 2023 · सेट A
प्रश्न 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.
उत्तर देखें
सही उत्तर: (B) 3/5
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (C) 6 m
1 अंक · 2023 · सेट A
प्रश्न 86
If seven times the seventh term of an AP equals eleven times its eleventh term, its eighteenth term is
उत्तर देखें
सही उत्तर: (C) 0
1 अंक · 2023 · सेट A
प्रश्न 87
A wire forming a circle of radius 28 cm is rebent into a square. Find the square’s side length.
उत्तर देखें
सही उत्तर: (A) 44 cm
1 अंक · 2023 · सेट A
प्रश्न 88
Given x = 1/[2 − {1/[2 − (1/(2−x))]}], with x ≠ 2, find x.
उत्तर देखें
सही उत्तर: (A) 1, 1
1 अंक · 2023 · सेट A
प्रश्न 89
The area of a sector of angle θ° in a circle of radius R is
उत्तर देखें
सही उत्तर: (C) πR²θ/360
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (A) ₹18,000 and ₹14,000
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (C) ₹2,250
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (C) (2, 3), (0, 1), (0, 6)
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (C) 363
1 अंक · 2023 · सेट A
प्रश्न 94
If O is any point inside rectangle ABCD, then
उत्तर देखें
सही उत्तर: (A) OB² + OD² = OA² + OC²
1 अंक · 2023 · सेट A
प्रश्न 95
C(1, 1) divides the segment joining A(−2, 7) and B internally in the ratio 3:2. Find the coordinates of B.
उत्तर देखें
सही उत्तर: (B) (3, −3)
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (C) 775
1 अंक · 2023 · सेट A
प्रश्न 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?
उत्तर देखें
सही उत्तर: (E) None of the above
1 अंक · 2023 · सेट A
प्रश्न 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.
उत्तर देखें
सही उत्तर: (B) 750
1 अंक · 2023 · सेट A
प्रश्न 99
The mean of 20 numbers is zero. At most how many of them may be greater than zero?
उत्तर देखें
सही उत्तर: (A) 19
1 अंक · 2023 · सेट A
प्रश्न 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?