Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
A solid cylinder is reduced in radius by 20% and increased in height by 50%. What net percentage change occurs in its volume?
20% increase
10% decrease
7% increase
4% decrease
Correct answer
20% increase
A triangular prism has a base formed by a triangle with side lengths 9cm, 12 cm, and 15 cm. If the height of the prism (perpendicular to the base) is 10 cm, calculate its lateral surface area.
360 cm2
420 cm2
480 cm2
540 cm2
Correct answer
360 cm2
The volume of a solid hemisphere is \(\frac{396}{7}\) cm3 Find the total surface area of hemisphere
74.85 cm2
64.76 cm2
84.75 cm2
84.85 cm2
Correct answer
74.85 cm2
If the total surface area of a hemisphere is 462 cm2, calculate its radius.
7 cm
8 cm
9 cm
10 cm
Correct answer
7 cm
If the area of the circular base of a hemisphere is 308 cm2, find the volume of the hemisphere
1235.33√2 cm3
1658.33√2 cm3
1537.33√2 cm3
1437.33√2 cm3
Correct answer
1235.33√2 cm3
The area of a sector is 18 π cm2, and its radius is 6 cm. What is the central angle (in radians)?
π
\(\frac{\pi}{2}\)
2π
\(\frac{3\pi}{2}\)
Correct answer
π
A chord of length 24 cm subtends a right angle at the center of the circle. What is the radius of the circle?
10√2 cm
12√2 cm
8√3 cm
24√3 cm
Correct answer
10√2 cm
A circle is inscribed in a right-angled triangle with legs of length 5 and 12. What is the area of the quadrilateral formed by the two legs and the two radii to the tangent points on the legs?
4 square units
14 square units
23 square units
24 square units
Correct answer
4 square units
Anita took a loan of Rs. 8,000 at a simple interest rate of 7% per annum for 3 years. What will be the simple interest and the total amount she has to repay after 3 years?
SI = Rs. 1,680; Total = Rs. 9,680
SI = Rs. 1,600; Total = Rs. 9,600
SI = Rs. 1,700; Total = Rs. 9,700
SI = Rs. 1,800; Total = Rs. 9,800
Correct answer
SI = Rs. 1,680; Total = Rs. 9,680
Aman invested Rs. 6,000 in a scheme that gives 5% simple interest per annum. What will be the interest earned and the total amount after 5 years?
SI = Rs. 1,200; Total = Rs. 7,200
SI = Rs. 1,500; Total = Rs. 7,500
SI = Rs. 1,000; Total = Rs. 7,000
SI = Rs. 1,400; Total = Rs. 7,400
Correct answer
SI = Rs. 1,200; Total = Rs. 7,200
Solve:(56.75)2 - 3220
0.5625
2.5625
Correct answer
A sum of money invested at compound interest amounts to Rs. 1,000 in 3 years and 1,200 in 4 years. Find the rate of interest.
20%
30%
35%
42%
Correct answer
20%
A sum becomes Rs. 11,650 in 5 years and Rs. 12,076 in 6 years at simple interest. What is the sum?
9,230
9,340
9,420
9,520
Correct answer
9,230
Given: \(\rm x+\frac{1}{x}=2\), find the value of \(\rm x^6+\frac{1}{x^6}-3\left(x^3-\frac{1}{x^3}\right)+5\left(x^2+\frac{1}{x^2}\right) \)
2
4
12
8
Correct answer
2
From the summit of a 90-meter-high building, the angles of depression to the top and bottom of a tower are measured at 30° and 60°, respectively. What is the height of the tower in meters?
50 m
60 m
70 m
75 m
Correct answer
50 m
If the space diagonal of a cuboid is 13 cm, and two of its edges are 3 cm and 4 cm, what is the third edge?
11 cm
12 cm
13 cm
14 cm
Correct answer
11 cm
A solid metal sphere that has a radius of 12 centimeters is melted down and reshaped into smaller spheres, each with a radius of 2 centimeters. How many smaller spheres can be created from this material?
216
6
36
1728
Correct answer
216
A solid metallic sphere of diameter 14 cm is melted and recast into smaller hemispheres each of diameter 7 cm. How many hemispheres can be made?
16
17
18
19
Correct answer
16
The proportions of the dimensions of a rectangular parallelepiped are 2 : 3 : 4. If its volume is 768 cm3 what is its smallest dimension?
6.34 cm
8.45 cm
12.25 cm
16.89 cm
Correct answer
6.34 cm
A rectangular tank has a length of 1 meter, a width of 80 cm, and a height of 50 cm. If the tank needs to be covered completely with square tiles of side 20 cm, how many tiles will be required?
42
85
57
34
Correct answer
42
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.