Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
A cylinder is half-filled with liquid. If radius doubles and height halves, what's the new filled depth percentage-wise?
25%
50%
75%
100%
Correct answer
25%
A composite solid is formed by placing a cone, which has a radius of 2 cm and a height of 6 cm, on top of a right circular cylinder. The cylinder's radius is twice that of the cone, and its height is also double that of the cone. What is the ratio of the volume of the cone to that of the cylinder?
1 :24
1 : 12
1 : 18
1 : 26
Correct answer
1 :24
The volume of a right prism is 600 cm3 and its base area is 30 cm2. Find its height.
10 cm
15 cm
20 cm
25 cm
Correct answer
10 cm
A triangular prism has side lengths of 5 cm, 6 cm, and 7 cm. If its height is 8 cm, what is the lateral surface area?
144 cm2
120 cm2
136 cm2
152 cm2
Correct answer
144 cm2
If the orthocenter and centroid coincide, the triangle must be:
Scalene
Right-angled
Equilateral
Isosceles
Correct answer
Scalene
If the radius of a sphere is increased by 30%, by what percentage does its surface area increase?
57%
58%
69%
67%
Correct answer
57%
If \(\rm \tanθ=\frac{3}{4}\), what is sec θ?
\(\frac{5}{4}\)
\(\frac{11}{5}\)
\(\frac{6}{5}\)
\(\frac{7}{4}\)
Correct answer
\(\frac{5}{4}\)
If \(\rm \sin A=\frac{3}{5}\) and \(\rm \cos B=\frac{4}{5}\), and both A, B in first quadrant, then sin(A + B) = ?
\(\frac{12}{25}\)
\(\frac{7}{10}\)
\(\frac{24}{25}\)
\(\frac{4}{25}\)
Correct answer
\(\frac{12}{25}\)
Find the equation of the line passing through (0,0) and (5,10)
y = 5x
y = 3x
y = 4x
y = 2x
Correct answer
y = 5x
If y = mx + c passes through (2, 5) and (4, 9), find m
4
2
3
5
Correct answer
4
If \(\rm \sec A=\frac{13}{12}\) and A is acute, find sin(90° - A).
\(\frac{5}{13}\)
\(\frac{12}{13}\)
\(\frac{1}{13}\)
\(\frac{3}{13}\)
Correct answer
\(\frac{5}{13}\)
A triangle has vertices at A(0, 0), B(6, 0), and C(0, 8). What are the coordinates of its Circumcenter?
(4, 3)
(3, 5)
(3, 4)
(4, 5)
Correct answer
(4, 3)
In triangle XYZ, a line is drawn parallel to YZ intersecting XZ at A and XY at B. If XA = 2 cm, AZ = 6 cm, and XB = 3 cm, find BY.
7 cm
19 cm
9 cm
6 cm
Correct answer
7 cm
553 + 173 - 723 + 201960 is equal to:
0
1
2
3
Correct answer
0
If tan x = 2, find the value of cot(90° - x) + tan(90° - x).
\(\frac{5}{2}\)
\(\frac{7}{2}\)
\(\frac{2}{3}\)
\(\frac{1}{4}\)
Correct answer
\(\frac{5}{2}\)
In a circle, chord AB subtends an angle of 80° at the center. What is the measure of the angle subtended by the same chord at any point C on the circumference, on the same side as the arc?
20°
30°
40°
50°
Correct answer
20°
From a point 13 cm away from the center of a circle, a tangent of length 12 cm is drawn. Find the radius of the circle?
5 cm
13 cm
7 cm
12 cm
Correct answer
5 cm
Which of the following is least?
\(\frac{1}{2}, 0.25, 0.3, \frac{3}{4}\)
\(\frac{1}{2}\)
0.25
0.3
\(\frac{3}{4}\)
Correct answer
\(\frac{1}{2}\)
A sum doubles in 10 years at Sl. find its Rate of interest
15%
20%
25%
10%
Correct answer
15%
If A works twice as fast as B, and A can complete a task in 10 days, how many days will it take for B to complete the task?
50 days
40 days
30 days
20 days
Correct answer
50 days
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.