**Geometry Questions for RRB Group- D Set- 2 PDF**

Download Top-10 RRB Group-D Geometry Questions set – 2 PDF. RRB GROUP-D questions based on asked questions in previous exam papers very important for the Railway Group-D exam.

Download Geometry Questions for RRB Group- D Set- 2 PDF

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**Question 1: **The ratio of the length and breadth of a rectangle is 4 : 3. What is the ratio of the diagonal of the rectangle to its perimeter?

a) 5 : 12

b) 5 : 14

c) 7 : 12

d) 1 : 2

**Question 2: **What is the internal angle of a regular Decagon?

a) 108

b) 120

c) 135

d) 144

**Question 3: **If the ratio of length and breadth of a rectangle is 7:4, then find the ratio of breadth and perimeter.

a) 11:2

b) 2:11

c) 7:22

d) 22:7

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**Question 4: **If the length is increased by 2 cm and the breadth is decreased by 4 cm, the area of the rectangle decreases by 40 square cms. If the length is decreased by 2 cm and the breadth is increased by 2cm, the area increases by 4 square cms. Find the area of the original rectangle.

a) 90

b) 95

c) 96

d) 100

**Question 5: **How many tangents can be drawn to the circles $x^2+y^2=4$ and $(x-5)^2+y^2=16$??

a) 1

b) 2

c) 3

d) 4

**Question 6: **The diagonal of a rectangle is $\sqrt{130}$ units and its area is 63 sq units. Find the perimeter of the rectangle.

a) 16

b) 20

c) 32

d) 40

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**Question 7: **A sector that makes an angle of 45 degrees at the centre is removed from a circle. What percentage of the area has been removed from the circle?

a) 12.5%

b) 25%

c) 37.5%

d) 50%

**Question 8: **What is the percentage increase/decrease in the area of a rectangle if its length and breadth are increased by 20% and decreased by 20% respectively?

a) 2% decrease

b) 4% decrease

c) 2% increase

d) 4% increase

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**Question 9: **How many squares are present in a 8×8 chessboard?

a) 204

b) 180

c) 160

d) 144

**Question 10: **Difference between the length and breadth of a field is 48 metres and its perimeter is of 160 metres. What would be the length of a side of a square whose area is equal to this field ?

a) 32 metre

b) 16 metre

c) 64 metre

d) 48 metre

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**Answers & Solutions:**

**1) Answer (B)**

Let the length and breadth of the rectangle be 4k and 3k respectively. So, length of the diagonal = $\sqrt{(4k)^2 + (3k)^2}$ = 5k.

Perimeter of the rectangle = 2*(4k + 3k) = 2*7k = 14k

So, required ratio = 5k : 14k = 5 : 14

**2) Answer (D)**

Sum of all external angles = 360 degrees.

There are 10 exterior angles and all are equal.

=> Each exterior angle = 36 degrees.

Interior angle + exterior angle = 180 degrees

=> Interior angle + 36 = 180

=> Interior angle = 144 degrees

**3) Answer (B)**

Let length and breadth be 7x and 4x respectively.

Perimeter = 2(length + breadth) = 2(7x + 4x) = 2 * 11x = 22x

=> Ratio of breadth to perimeter = 4x : 22x = 2:11

**4) Answer (C)**

Let l and b be length and breadth of a rectangle respectively.

(l+2)(b-4) = lb-40 => 2l-b=16

(l-2)(b+2) = lb+4 => l-b = 4

=> l = 12 and b = 80

=> Area = 96

**5) Answer (B)**

Distance between the centers (0,0) and (5,0) = 5

Sum of Radii = 2 + 4 = 6

=> The two circles are intersecting => 2 tangents can be drawn.

**6) Answer (C)**

Let length and breadth of the rectangle be l and b respectively.

lb = 63

$\sqrt{l^2+b^2}$ = $\sqrt{130}$

=> $l^2+b^2$ = 130

$(l+b)^2$ = $l^2+b^2+2lb$

=> $(l+b)^2$ = 256

=> l+b = 16

Perimeter = 2(l+b) = 2*16 = 32

**7) Answer (A)**

Area of a circle = $\pi r^2$

Area of a sector = $\frac{x}{360}*\pi r^2$, where x is the angle it subtends at the center.

= $\frac{45}{360}*\pi r^2$

= $\frac{\pi r^2}{8}$

=> Percentage removed = $\frac{1}{8}*100$ = 12.5%

**8) Answer (B)**

Let the length and breadth of the rectangle be l and b respectively.

Initial area = lb

Changed dimensions: length = 1.2l and breadth = 0.8b

=> New area = 1.2l * 0.8b = 0.96lb

Area decreased by 0.04lb

Percentage decrease = $\frac{0.04lb}{lb}*100$ = 4%

**9) Answer (A)**

There are 8 different types of squares – 1×1, 2×2, 3×3, …., 7×7 and 8×8.

There are 64 1×1 squares, 49 2×2 squares, 36 3×3 squares, 25 4×4 squares, 16 5×5 squares, 9 6×6 squares, 4 7×7 squares and 1 8×8 square.

Sum = $8^2 + 7^2 + …. + 2^2 + 1^2$ = $\frac{8*9*17}{6}$ = 204.

**10) Answer (A)**

l – b = 48

(l+b)*2 = 160

So, l = 64

b = 16

Area of the rectangle = area of the square = 64 x 16

Side of the square = sq root (64 x 16) = 8 x 4 = 32

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