Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
The parallel sides of a trapezium differ by 4 cm. Its height is 8 cm and the area is 192 cm2. What are the lengths of the parallel sides?
20 cm and 24 cm
21 cm and 25 cm
22 cm and 26 cm
23 cm and 27 cm
Correct answer
20 cm and 24 cm
A right prism has a trapezium-shaped base with parallel sides 6 cm and 10 cm, height of trapezium 5 cm, and prism height 15 cm. Find the volume.
800 cm3
1200 cm3
600 cm3
350 cm3
Correct answer
800 cm3
If the lateral surface area of a right circular cylinder is 440 cm2 and radius is 5 cm, find the height.
12 cm
15 cm
14 cm
21 cm
Correct answer
12 cm
A cylinder is melted and recast into 8 smaller cylinders of the same height. If the original radius was 6 cm and height 10 cm, find the radius of each small one?
3 cm
2.5 cm
2.7 cm
2.12 cm
Correct answer
3 cm
Two circles touch each other externally at P. AB is a direct common tangent to the two circles, A and B are points of contact and ∠PAB = 22°. The measure of ∠ABP is:
72°
68°
70°
44°
Correct answer
72°
Consider the following two statements, labeled Assertion (A) and Reason (R). Evaluate them and choose the appropriate answer from the given options.
Assertion (A): Two non-intersecting and non-touching circles have four common tangents.
Reason (R): Two direct and two transverse tangents can be drawn between such circles.
Both A and R are true, and R is the correct explanation of A
Both A and R are true, but R is not the correct explanation of A
A is true, but R is false
A is false, but R is true
Correct answer
Both A and R are true, and R is the correct explanation of A
If \(\sqrt{x} = 11\), what is the value of \(x + \sqrt{x}\)?
121
132
122
133
Correct answer
121
Which of the following is a perfect square of an even number?
81
144
121
169
Correct answer
81
Two numbers 63527 and 60784 are divided by a certain three-digit number and leave the same remainder. What is the sum of digits of the divisor?
6
3
4
5
Correct answer
6
Which of the following sets is a proper subset of rational numbers?
Irrational number
Natural number
Real number
Imaginary numbers
Correct answer
Irrational number
Match the sets in Column I with their correct descriptions in Column II:
| Column I | Column II |
|---|---|
| A. Rational numbers () | 1. Closed under multiplication but not subtraction |
| B. Whole numbers (W) | 2. All terminating and recurring decimals |
| C. Prime numbers (P) | 3. Include zero and natural numbers |
| D. Irrational numbers () | 4. Non-repeating, non-terminating decimals |
A-2, B-3, C-1, D-4
A-4, B-2, C-1, D-3
A-2, B-4, C-3, D-1
A-3, B-2, C-4, D-1
Correct answer
A-2, B-3, C-1, D-4
A scholarship fund of ₹1200 is to be distributed between two students, A and B, in a ratio 5:3. However, after allocating ₹200 to administrative charges, the remaining amount is first increased by 10% as a bonus before the final division. What amount will student A receive?
₹675
₹687.5
₹750
₹700
Correct answer
₹675
Average score of a batsman in 10 innings is 32. How many runs must he score in the 11th innings to raise his average to 34?
54
60
56
50
Correct answer
54
Average of 11 numbers is 45. Average of first 5 is 42 and last 5 is 46. Find the 6th number.
55
44
43
47
Correct answer
55
A man's salary is increased by 40% and then decreased by 30%. What is the net effect on his salary?
2% decrease
2% increase
5% decrease
5% increase
Correct answer
2% decrease
A bookstore buys 2,000 books for ₹180 each. They offer a "Buy 4, Get 1 Free" scheme but sell at the marked price of ₹225 per book. What is their effective profit percentage per book sold (after adjusting for the free books)?
0%
0.2
0.4
0.37
Correct answer
0%
16 men can complete a work in 15 days. How many men are required to complete the same work in 10 days?
20 men
22 men
24 men
25 men
Correct answer
20 men
A can do a work in 15 days, B in 20 days, and C in 30 days. They all start the work together but C leaves after 5 days. How many more days will A and B take to complete the remaining work?
2 days, 3 hours, 20 minutes
2 days, 3 hours, 26 minutes
2 days, 4 hours, 15 minutes
2 days, 2 hours, 45 minutes
Correct answer
2 days, 3 hours, 20 minutes
A train 150 meters long crosses another train of length 100 meters running in the opposite direction in 12 seconds. If the speed of the first train is 60 km/h, estimate the speed of the second train.
12 km/h
15 km/h
18 km/h
20 km/h
Correct answer
12 km/h
A person lent ₹2,000 at 6% per annum simple interest and ₹3,000 at 5% per annum simple interest. Find his total interest after 3 years.
₹780
₹800
₹810
₹820
Correct answer
₹780
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.