Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
If one angle is 15° less than twice its complement, find the angle.Â
25°
30°
55°
40°
Correct answer
25°
The angle of elevation of a tower from a point 120 m away is 45°. Find the height of the tower.
100 m
150 m
120 m
10 m
Correct answer
100 m
The complement of an angle is one-fourth the angle. Find the angleÂ
72°
7°
42°
87°
Correct answer
72°
From a point 20 m above ground level on a vertical tower, the angle of depression of a point on the ground is 30°. Find the distance from the base of the tower to that point.
10 mÂ
34.64 mÂ
110 mÂ
90 m
Correct answer
10 mÂ
A cylinder is inscribed inside a cube of side 10 cm. What percentage of the cube's volume is occupied by the cylinder?
78.5%
60.5%
50%Â
90.5%
Correct answer
78.5%
Consider a jar formed by a cylinder and a hemispherical lid, both having the same radius 'r'. If the cylinder's height is also 'r', what is the ratio of the hemisphere's volume to the total volume of the jar?
1 ∶ 6
1 ∶ 3
1 ∶ 4
2 ∶ 5
Correct answer
1 ∶ 6
The base of a right prism is an equilateral triangle with each side measuring 8 cm. Given that the height of the prism is 10 cm, what is its volume?
320√3 cm3
676.6 cm3
240 cm3
160√3 cm3
Correct answer
320√3 cm3
A glass trough is in the shape of a right prism with trapezium base (parallel sides 10 cm & 6 cm, height = 4 cm). If prism height = 20 cm, find volume.
660 cm3
540 cm3
550 cm3
640 cm3Â
Correct answer
660 cm3
If the circumradius of a triangle is 7 cm, what is the distance from the circumcenter to a vertex?Â
5 cm
7 cm
3.5 cmÂ
14 cmÂ
Correct answer
5 cm
Given a hollow hemisphere with an inner radius of 7 cm and an outer radius of 8 cm, what is its entire surface area?
248Ï€ cm2
441Ï€ cm2
231Ï€ cm2
241Ï€ cm2
Correct answer
248Ï€ cm2
A cone has a base diameter of 70 cm and a height of 12 cm. Calculate its volume.Â
15800 cm3
15400 cm3
16800 cm3
14800 cm3
Correct answer
15800 cm3
The x-intercept of the line 6x - 2y = 10 is:Â
5/3
3/5
-1/2
-2/3
Correct answer
5/3
If cot A = 1, find the value of sin2Â A - cos2Â A.
0
1
2
3
Correct answer
0
If tan2θ + cot2θ = 50, then find sec4θ + cosec4θ.
2600
2800
3200
3000
Correct answer
2600
Find the coordinates of the centroid for a triangle with vertices located at the points (2, 1), (5, 4), and (8, 1).Â
(5, 2)
(6, 2)
(5, 3)
(6, 3)
Correct answer
(5, 2)
In ΔABC, ∠A = 90° AD is the altitude to BC. If AB = 15 cm and AC = 20 cm, what is the length of AD?
9 cm
12 cm
15 cm
25 cm
Correct answer
9 cm
Simplify:
72 +Â \(\sqrt{32}\)Â -Â \(\sqrt{18}\)
72 + √2
63 + √2
51 + √5
47 + √9
Correct answer
72 + √2
In a circle, chords AB and AC are equal in length. If chord AB subtends an angle of 50° at the center, what is the angle subtended by chord AC at the center?
50°
100°Â
25°
130°
Correct answer
50°
In a circle, two tangents PA and PB are drawn from an external point P. If the angle between the tangents ∠APB = 120°, if the radius is 10 cm, what is the length of the segment OP? (use √3 = 1.732)
10√2 cm
10.2 cm
10√3 cmÂ
11.5 cm
Correct answer
10√2 cm
​Ravi borrowed $ 5,000 from a bank at an interest rate of 6% per annum for 4 years. Calculate the simple interest and the
the total amount he has to repay after 4 years$.
SI = $ 1,000; Total = $ 6,000
SI = $ 1,200; Total = $ 6,200
SI = $ 1,400; Total = $ 6,400
SI = $ 1,500; Total = $ 6,500
Correct answer
SI = $ 1,000; Total = $ 6,000
Solving previous year questions by topic helps identify recurring concepts, question patterns, and frequently asked sub-topics. Attempt each question, review the step-by-step explanation, and note down key formulas or facts for quick revision before the exam.