Q. The height of an equilateral triangle with side ‘a’ is equal to
The correct answer was: √3a/2
Q. A girl walks 200 meters to the east and then 150 meters to the north. What is the girl’s distance from the starting point?
The correct answer was: 250 m
Q. The curved surface area of a cylinder is 264 m² and its volume is 924 m³. The ratio of its diameter to its height is
The correct answer was: 1:2
Q. In the given figure, MN || AB, BC = 7.5 cm, AM = 4 cm, and MC = 2 cm. Find the length of BN.
The correct answer was: 2.5 cm
Q. If tan 30° = sin 45° cos 45° + sin 30°, then θ =
The correct answer was: 15°
Q. What is the value of p for which the system of equations px – y = 2; 6x – 2y = 3 has only one solution (i.e., a unique solution)?
The correct answer was: p ≠ 3
Q. If the cubic polynomial ax³ + bx² + cx + d has two zeros, each of which is a root, what is the third root?
The correct answer was: -b/a
Q. What is the sum of the first 20 odd natural numbers?
The correct answer was: 400
Q. How many rotations are required for a circular wheel with a radius of 0.7 meters to cover a distance of 176 meters?
The correct answer was: 22
Q. If 2 sin²β – cos²β = 2, what is the value of β?
The correct answer was: 90°
Q. If the mode of a distribution is 12 more than its mean, by how much is the mode greater than the median?
The correct answer was: 4
Q. If sin(x – 20°) = cos(3x – 10°), where 3x – 10° is an acute angle, what is the value of x?
The correct answer was: 35°
Q. An alphabet from the English alphabet is randomly selected. What is the probability that it is a letter from the word ‘MATHEMATICS’?
The correct answer was: 9/26
Q. What is the area of the triangle with vertices (a, b + c), (b, c + a), and (c, a + b)?
The correct answer was: 0
Q. The lines x = a and y = b are
The correct answer was: Parallel lines
Q. OBAC is a rectangle with three vertices A(0, 3), O(0, 0), and B(5, 0). What is the length of its diagonal?
The correct answer was: √34 units
Q. If A(4, 2), B(6, 5), and C(1, 4) are the vertices of ΔABC and AD is the median, what are the coordinates of D?
The correct answer was: (5/2, 3)
Q. From a lighthouse, the angle of depression of two ships in opposite directions is 30° and 45°. If the height of the lighthouse is h meters, find the distance between the ships.
The correct answer was: (√3+1)h
Q. The ratio of the LCM and HCF of the smallest composite and smallest prime numbers is
The correct answer was: 1:2
Q. If the sum of the first p terms of an A.P. is ap² + bp, then its common difference is
The correct answer was: 2a
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