Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
A cone is melted and recast into smaller cones with \(\frac{1}{3}\) the radius and \(\frac{1}{3}\) the height. How many cones are formed?
27
30
32
25
Correct answer
27
A cone is cut by a plane that runs parallel to its base, creating a smaller cone that is similar to the original cone. If the height of this smaller cone is one-third that of the original cone, what is the ratio of their volumes?
1 : 3
1 : 9
1 : 27
1 : 6
Correct answer
1 : 3
Expand : (2x - 3)2
4x2 + 12x + 9
4x2 - 12x + 9
4x2 - 14x + 10
4x2 + 10x + 9
Correct answer
4x2 + 12x + 9
A machine processes 2.4 items per second. How many items does it process in 2\(\frac{1}{2}\) minutes?
360
380
300
420
Correct answer
360
The base of a regular right pyramid is a square with the side length of 6 cm. If its volume is 144 cm3, what is its height?
8 cm
10 cm
12 cm
15 cm
Correct answer
8 cm
What is the sum of the exterior angles of a polygon with n sides?
4π
5π
2π
3π
Correct answer
4π
Simplify:
\(\rm (0.625\div 2.5)\left(\frac{5}{8}\times 2\right)=?\)
2.5
2
0.3125
3
Correct answer
2.5
A regular right pyramid has a square base. Its base area is 100 cm2 and its lateral surface area is 260 cm2. What is the height of the pyramid?
10 cm
12 cm
13 cm
15 cm
Correct answer
10 cm
A water pipe supplies water at a constant rate. In 4.5 minutes, it fills \(2\frac{1}{4}\) liters. At this rate, how much time will it take to fill 5.625 liters?
10 minutes
11.25 minutes
12 minutes
12.5 minutes
Correct answer
10 minutes
A farmer uses \(\frac{2}{3}\) of his land for wheat and 0.125 for rice. What fraction remains unused?
\(\frac{1}{6}\)
\(\frac{1}{8}\)
\(\frac{3}{16}\)
\(\frac{5}{24}\)
Correct answer
\(\frac{1}{6}\)
Find the area of a circle that has a circumference of 44 cm.
154 cm2
121 cm2
100 cm2
138 cm2
Correct answer
154 cm2
If the selling price of an item is increased by 25% and the profit also increases from 20% to 30%, what is the percentage increase in the cost price?
4.5%
5.6%
10.28%
15.38%
Correct answer
4.5%
A circular field is surrounded by a path 2 m wide. If the inner radius is 10 m, find the cost to pave the path at Rs. 20 per m2.
₹2765.71
₹2654
₹2356.45
₹3456
Correct answer
₹2765.71
A square sheet is folded in half. What is the ratio of the area of the folded shape to the original square?
1 : 1
1 : 2
2 : 1
3 : 4
Correct answer
1 : 1
A square plot of land is to be expanded such that its area becomes 225% of the original. By what percentage must each side be increased?
50%
100%
25%
50.5%
Correct answer
50%
A square board 20 cm side has a corner triangle removed (right triangle, legs 5 cm each). What percent of the board remains?
93.76 %
92.54%
96.88%
90%
Correct answer
93.76 %
A regular hexagon has an area of 150 cm2. What is the area of one of its equilateral triangular sections?
25 cm2
30 cm2
35 cm2
40 cm2
Correct answer
25 cm2
The average of 20 numbers is 40. If the sum of the first 10 numbers is 380, what is the average of the remaining 10 numbers?
42
40
44
38
Correct answer
42
A line passes through the point (2, -1) (2, -1) and is perpendicular to the line y = (-2/5)x + 3. What is its equation?
y = 2x - 6
y = (3/2)x - 6
y = (5/2)x - 6
y = (5/2)x - 2
Correct answer
y = 2x - 6
From the top of a lighthouse 100 m high, the angle of depression of a boat is 30°. Find the distance of the boat from the base of the lighthouse.
78 m
173.2 m
254 m
189 m
Correct answer
78 m
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.