# TCS NQT Questions on Geometry with Answers Quiz 1

Question 1 Time: 00:00:00
An oblong piece of ground measures 19m 2.5 dm by 12m5dm. From center of each side of the ground, a path 2m wide goes across to the center of the opposite side. What is the area of the path? 59.5 $m^{2}$

59.5 $m^{2}$

54 $m^{2}$

54 $m^{2}$

78.65 $m^{2}$

78.65 $m^{2}$

34 $m^{2}$

34 $m^{2}$

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Question 2 Time: 00:00:00
In triangle PQR, PQ=6 cm, PR=8 cm, and QR=12 cm. Calculate the area of the triangle PQR 23.33 $cm^{2}$

23.33 $cm^{2}$

17.5 $cm^{2}$

17.5 $cm^{2}$

21.33 $cm^{2}$

21.33 $cm^{2}$

28.67 $cm^{2}$

28.67 $cm^{2}$

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we can use formula s=1/2(6+8+12)=13cm area=? 13(13-6)(13-12)(13-8) => ?13*35=?455=21.33

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Question 3 Time: 00:00:00
If the perimeter and the diagonal of a rectangle is 18 cm and $\sqrt{41}$ cm respectively. Calculate the area of the rectangular field. 25 $cm^{2}$

25 $cm^{2}$

29 $cm^{2}$

29 $cm^{2}$

18 $cm^{2}$

18 $cm^{2}$

20 $cm^{2}$

20 $cm^{2}$

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Question 4 Time: 00:00:00
Find the area of Rhombus one of whose diagonals measures 8 cm and the other 10 cm. 47 $cm^{2}$

47 $cm^{2}$

34 $cm^{2}$

34 $cm^{2}$

40 $cm^{2}$

40 $cm^{2}$

64 $cm^{2}$

64 $cm^{2}$

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area of rhombus=1/2(product of diagnoals) 1/2(8*10) 80/2=40cm^2

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Question 5 Time: 00:00:00
The diagonal of square is $18\sqrt{2}$ cm. Find Area of that square. 81

81

289

289

324

324

144

144

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Question 6 Time: 00:00:00
What is the radius of the circular plate of thickness 1 cm made by melting a sphere of radius 3 cm? 6 cm

6 cm

5 cm

5 cm

4 cm

4 cm

7 cm

7 cm

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Question 7 Time: 00:00:00
A polygon has 77 diagonals.Determine the number of sides? 15

15

12

12

17

17

14

14

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A polygon having n sides has n(n-3)/2 diagonals. n(n-3)/2=77 n^2-3n-155=0 n=14

A complete graph with n nodes will have n(n-1)/2 edges Out of which n are non diagnal edges Diagonal edges=total- non diagnal Given diagonals=77 77=n(n-1)/2 - n n=14

diagonal D= n(n-1)/2 - n 77=(n^2-3*n)/2 n^2-3*n-154=0 (n-14)(n+11)=0 n=14 Ans

diagonal D= n(n-1)/2 - n ; 77=(n^2-3*n)/2 ; n^2-3*n-154=0 ; (n-14)(n+11)=0 ; n=14 Ans

the number of diagonals of polygon being n(n-3)/2, where n is the number of sides. So n(n-3)/2 = 77 n(n-3) = 77*2 = 154 n^2 - 3n = 154 n^2 - 3n - 154 = 0 Using the quadratic formula, n = [3 ± ?(9 - 4*(-154))]/2 = [3 ± ?(9 + 616)]/2 = [3 ± ?(625)]/2 = [3 ± 25]/2. Since we can’t have a negative number of sides, n = 28/2 = 14.

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Question 8 Time: 00:00:00
A square field of area 31684 meter square is to be enclosed with the wire placed at height 1 m, 2 m, 3 m, 4 m above the ground. What length of the wire will be required if its length required for each circuit is 5% greater than the perimeter of the field? 6456 m

6456 m

27666 m

27666 m

2990.4 m

2990.4 m

4666.5 m

4666.5 m

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Question 9 Time: 00:00:00
Determine the metal required to make a 21 m long pipe if its inner and outer diameter is 12 m and 10 m respectively 726 $m^{3}$

726 $m^{3}$

2534 $m^{3}$

2534 $m^{3}$

2843 $m^{3}$

2843 $m^{3}$

2647 $m^{3}$

2647 $m^{3}$

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Question 10 Time: 00:00:00
A rectangular grassy plot is 112 m by 78 m. It has a gravel path 2.5 m m wide all around it on the inside. Find the area of the path? 952 $m^{2}$

952 $m^{2}$

925 $m^{2}$

925 $m^{2}$

912 $m^{2}$

912 $m^{2}$

950 $m^{2}$

950 $m^{2}$

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