Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
A solid hemisphere of radius R is sliced horizontally at 1/3 rd of its height from the base. Find the volume of the smaller (top) segment.
\( \frac{8\pi R^3}{81} \)
\( \frac{28\pi R^3}{81} \)
\( \frac{11\pi R^3}{81} \)
\( \frac{7\pi R^3}{81} \)
Correct answer
\( \frac{8\pi R^3}{81} \)
A circular fountain of radius 10 m is at the center of a square park of side 24 m. If grass covers the remaining area, what percentage of the park is grass?
45.47%
57.2%
70.5%
72.1%
Correct answer
45.47%
If an angle is equal to its complement, what is the angle?
145°
415°
45°
5°
Correct answer
145°
If sinA = 5/13, find the value of (1 + tan2A)/sec2A.
1
2
3
4
Correct answer
1
Find the inter quartile range for the following series.
3, 5, 6, 8, 10, 12, 14, 16, 18, 20, 22
10
12
14
16
Correct answer
10
In triangle ABC, the orthocenter is at (0,0), centroid at (2,4). Find the circumcenter.
(3, 6)
(4, 8)
(6, 12)
(1, 2)
Correct answer
(3, 6)
Compute the quartile deviation for the data given here 27, 3, 28, 40, 28, 30, 36, 27, 25, 27?
2
2.5
3
3.5
Correct answer
2
PQ is the diameter of the circle with center O and R, S, T are three points on the semi-circle in a given figure. Which of the following statements is true?
\(\angle PRQ = 90^\circ\)
\(\angle PTQ = 90^\circ\)
\(\angle RPS = \angle RTS\)
Both 1 and 2
Correct answer
\(\angle PRQ = 90^\circ\)
What is the y-intercept of the line that passes through the points (3, 6) and (-1, -5)?
10/3
2/3
-9/4
9/4
Correct answer
10/3
Two circles with a common center (concentric circles) have radii of 5 cm and 12 cm. A tangent to the inner circle forms a chord of the outer circle. What is the length of this chord?
21.8 cm
13 cm
17.5 cm
24 cm
Correct answer
21.8 cm
Simplify \( (3\sqrt{5} + 2\sqrt{20}) - (\sqrt{45} + 4\sqrt{5}) .\)
0
\( 3\sqrt{5} \)
\( 5\sqrt{5} \)
\( -3\sqrt{5} \)
Correct answer
0
What is the sum of all three-digit numbers divisible by 7?
70336
70707
72000
71407
Correct answer
70336
\( 62 \frac{1}{2} % \) of a number exceeds 25% of the same number by 15. What is the number?
40
50
60
70
Correct answer
40
A, B, and C invest ₹40,000, ₹60,000, and ₹80,000, respectively. A invests for 12 months, B for 10 months, and C for 6 months. The total profit is ₹60,000. What is A's share of the profit?
₹20,461.54.
₹15,461.54.
₹18,461.54.
₹12,461.54.
Correct answer
₹20,461.54.
The average of ten numbers is 42. The average of the first four numbers is 38, while the average of the last three numbers is 48. What is the average of the remaining three numbers?
41.33
51.33
61.33
71.33
Correct answer
41.33
A student scores 75% marks in an exam. If he scored 450 marks and the remaining 25% of the marks were for practicals, what were the total marks for the exam (including practicals)?
500
550
600
650
Correct answer
500
The difference between the compound and simple interest on a sum of ₹12,000 for 2 years is ₹216. Find the rate of interest per annum.
15.42%
17.42%
12.42%
13.42%
Correct answer
15.42%
A shopkeeper finds that the profit from selling a watch for ₹1100 is equal to the loss incurred when selling it for ₹900. What will be the percentage loss if the watch is sold for ₹850?
15%
16%
17%
18%
Correct answer
15%
A mixture contains juice and water in the ratio 5:2. If 10 litres of water are added to this mixture, the ratio of juice to water becomes 2:1. What was the initial quantity of the mixture (in litres)?
60 litres
70 litres
140 litres
190 litres
Correct answer
60 litres
A can complete a task by himself in 6 days, while B can do it alone in 8 days. Together with C's assistance, they've agreed to finish the work for Rs. 3200. They successfully completed the task in 3 days. What amount should be given to C?
₹ 400
₹ 500
₹ 800
₹ 900
Correct answer
₹ 400
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.