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

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## 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.

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

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

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

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

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

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

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

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

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.

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

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%

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%

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.

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

We hope this Geometry Questions set – 2 PDF for RRB Group-D Exam will be highly useful for your preparation.