Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
A rhombus whose diagonals are 12 cm and 15 cm. Find the area of the rhombus.
90 cm²
48 cm²
72 cm²
64 cm²
Correct answer
90 cm²
What is the width of a rectangle which has a 60 cm perimeter and length of 20 cm?
10 cm
5 cm
15 cm
20 cm
Correct answer
10 cm
A solid cone with a radius of 6 cm and a height of 8 cm is melted and recast into small spheres, each having a radius of 2 cm. How many such spheres can be formed?
8
9
10
11
Correct answer
8
If a customer gets a discount of Rs. 144 on a product originally priced at Rs. 960, and is later charged 18% GST on the discounted price, what is the final bill amount?
Rs. 742.88
Rs. 834.88
Rs. 882.88
Rs. 962.88
Correct answer
Rs. 742.88
If the sides of a parallelogram are in the ratio 3:4 and its perimeter is 84 cm, the longer side is:
24 cm
35 cm
26 cm
25 cm
Correct answer
24 cm
A store advertises, "Buy items worth Rs. 3000, get Rs. 500 off instantly." What is the effective discount percentage?
16.67%
15.67%
14.67%
13.67%
Correct answer
16.67%
Convert 60° to radians.
π/4
π/3
π/2
π/6
Correct answer
π/4
Convert 150° to radians.
5π
5π/6
5π4
π
Correct answer
5π
The radii of two right circular cylinders are in the ratio 2:5, and their heights are in the ratio 3:2. What is the ratio of their curved surface areas?
1:2
3:5
4:25
9:4
Correct answer
1:2
A right prism with a rectangular base has a perimeter of 28 cm and height 12 cm. What is its lateral surface area?
312 cm²
288 cm²
360 cm²
336 cm²
Correct answer
312 cm²
20 girls can complete a work in 16 days. 16 boys can complete the same work in 15 days. What is the ratio between the capacity of a boy and a girl?
2:3
3:2
4:3
3:4
Correct answer
2:3
How much space does a hemisphere with a 7 cm radius occupy?
618.66 cm³
912.66cm³
716.66cm³
718.66 cm³
Correct answer
618.66 cm³
If a cone has a base radius of 5 cm and a perpendicular height of 12 cm, what is the volume?
250π cm²
120π cm²
90π cm²
100π cm²
Correct answer
250π cm²
Find the radius of the circle if the length of the chord is 8 cm and the perpendicular distance from the center of the circle is 3 cm
4 cm
5 cm
6 cm
7 cm
Correct answer
4 cm
In a right-angled triangle, where is the orthocenter located?
Outside the triangle
Midpoint of the hypotenuse
At the centroid
At the right-angled vertex
Correct answer
Outside the triangle
A cone is cut parallel to its base at half its height. What is the ratio of volumes of the two parts?
1:7
1:3
1:4
1:5
Correct answer
1:7
What is the ratio of the volume of a cone to that of a cylinder having the same base radius and height?
2:3
3:5
1:3
1:4
Correct answer
2:3
The radius of a circle is 12 cm. The length of a tangent drawn to this circle from a point at a distance of 15 cm from its center is
15 cm
12 cm
9 cm
6 cm
Correct answer
15 cm
How many distinct triangles can be formed by selecting any three vertices of a hexagon?
20
30
60
120
Correct answer
20
If cosθ = 3/5, find the value of tanθ.
4 /3
2/3
2/5
5/2
Correct answer
4 /3
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.