﻿ ABCD is a cyclic trapezium in which AD || BC. If , then  is from Quantitative Aptitude SSC - CGL Year 2016 Free Solved Previous Year Papers

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# 61.ABCD is a cyclic trapezium in which AD || BC. If , then  is 110° 80° 70° 90°

C.

70°

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63.

The sum of 10 terms of the arithmetic series is 390. If the third term of the series is 19, find the first term:

• 3

• 5

• 7

• 8

A.

3

According to the question,
a + a+d + a+ 2d + a+3d + a+4d + a+5d + a+6d + a+7d + a+8d + a+9d = 390
10a + 45d = 390.....(i)
a + 2d = 19
or
10a + 20d = 190 ....(ii)
Solve (i) and (ii),
25d = 200
d = 8
Put the value of d  = 8 in equation (i)
a = 19 - 2 x8 = 19 - 16 = 3,  a = 3.(the first term)

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66.

If (x - 4) (x2 + 4x + 16) = x3 - p, then p is equal to

• 27

• 8

• 64

• 0

C.

64

(x - 4) (x2 + 4x + 16) = x3 - p
x3 + 4x2 + 16x - 4x2 - 16x - 64 = x3 - p
-64 = -p
p = 64

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62.

If cos 27° = x, then value of 63° is

A.

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67.

G is the centroid of  ΔABC. If AG = BC, then measure of  is

• 45°

• 60°

• 90°

• 120°

C.

90°

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68.

In a circle, a chord  long, makes a right angle at the centre. Then the length of the radius of the circle will be

• 2.5 cm

• 5 cm

• 7.5 cm

• 10 cm

B.

5 cm

AB =  (Chord of a circle)
OA = OB =r =  (radius of a circle)
Now,
In ΔOAB,

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70.

The angle of elevation of aeroplane from a point on the ground is 45°. After flying 15 sec, the elevation changes to 30°. If the aeroplane is flying at a height of 2500 m, then the speed of the aeroplane in km/hr is

• 600

D.

In ΔABC,

In ΔBED,

∴  Speed of the aeroplane

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69.

If cos2x + cos4x = 1, then tan2x + tan4x = ?

• 0

• 1

• 2tan2x

• 2tan4x

B.

1

Given,
cos2x + cos4x = 1
cos4x = 1 - cos2x
cos4x = sin2x
cos2x. cos2x=  sin2x

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64.

The average of marks obtained by 100 candidates in a certain examination is 30. If the average marks of passed candidates is 35 and that of failed candidates is 10, what is the number of candidates who passed the examination?

• 60

• 70

• 80

• 90

C.

80

Let the number of passed candidates be x.
∴   Failed candidates  = (100 - x)
According to the question,
x x 35 + (100 - x) x 10 = 100 x 30
35x + 1000 - 10x = 3000
25x = 2000
x = 80

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65.

If a + b = 10 and ab = 21, then the value of (a - b)2 is

• 15

• 16

• 17

• 18

B.

16

a + b = 10 and ab = 21
(a + b)2 = a2 + b2 + 2ab
(10)2 = a2 + b2 + 2 x 21
100 = a2 + b2 + 42
a2 + b2 = 58
(a - b)2 = a2 + b2 - 2ab
= 58 - 2 x 21 = 58 - 42 = 16

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