Basic Mathematics

Number System LCM & HCF Percentage Ratio & Proportion Average Simple Interest

Business Mathematics

Profit & Loss Compound Interest Partnership Discount Stocks & Shares Banking

Time, Work & Motion

Time & Work Pipes & Cisterns Time, Speed & Distance Trains Boats & Streams Races

Advanced Mathematics

Algebra Geometry Mensuration Trigonometry Logarithms & Indices Coordinate Geometry

Statistics & Probability

Statistics Probability Permutation Combination Set Theory Data Interpretation

Mensuration Aptitude Questions & Formulas with answer


Ques 1 GATE 2023 SET-1

In the given figure, PQRSTV is a regular hexagon with each side of length 5 cm. A circle is drawn with its centre at V such that it passes through P. What is the area (in cm2) of the shaded region? (The diagram is representative)

A

25π⁄3

B

20π⁄3

C

6π

D

7π

(a) is the correct answer.

Ques 2 GATE 2023 SET-1

A square of side length 4 cm is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom, each of radius 2 cm, as shown. The area of the shaded region is _______ cm2.

A

8

B

4

C

12

D

10

(a) is the correct answer.

Ques 3 GATE 2023

A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown. The area of the shaded region is _______ cm2.

A

6π

B

18

C

20

D

9π

(b) 18) is the correct answer.

Ques 4 GATE 2022

A sphere of radius 𝑟 cm is packed in a box of cubical shape. What should be the minimum volume (in cm3 ) of the box that can enclose the sphere?

A

r³/8

B

r³

C

2r³

D

8r³

(d) is the correct answer.

Ques 5 GATE 2021

We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm x 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is

A

π/2

B

3/π

C

9/π

D

3π

(c) is the correct answer.

Ques 6 GATE 2021

In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in $cm^{2}$ is:

A

12.50

B

6.25

C

3.125

D

1.5625

(b) is the correct answer.

Ques 7 GATE 2021

We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm x 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is ___________.

A

π/2

B

3/π

C

9/π

D

3π

(c) is the correct answer.

Ques 8 GATE 2019

The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is _______.

A

17.1

B

21.0

C

33.1

D

72.8

(c) is the correct answer.

Ques 9 GATE 2018

The area of an equilateral triangle is √3. What is the perimeter of the triangle?

A

2

B

4

C

6

D

8

(c) is the correct answer.

Ques 10 GATE 2018

Arrange the following three-dimensional objects in the descending order of their volumes:
(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm
(ii) A cube of side 8 cm
(iii) A cylinder with base radius 7 cm and height 7 cm
(iv) A sphere of radius 7 cm

A

(i), (ii), (iii), (iv)

B

(ii), (i), (iv), (iii)

C

(iii), (ii), (i), (iv)

D

(iv), (iii), (ii), (i)

(d) is the correct answer.

Ques 11 GATE 2016 SET-1

A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the body (in square units) after the removal is

A

56

B

64

C

72

D

96

(d) is the correct answer.


Question Options

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