Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

61.

ABCD is a cyclic trapezium in which AD || BC. If angle ABC space equals space 70 degree, then angle BCD is

  • 110°

  • 80°

  • 70°

  • 90°


C.

70°

ABCD is a cyclic trapezium in which AD || BC. If , then &nbs

angle ABC space equals space 70 degree space left parenthesis given right parenthesis
angle ADC space equals space 180 degree space minus space 70 degree space equals space 110 degree space space left square bracket Sum space of space opposite space angles space of space cyclic space quadrilateral right square bracket
angle BCD space equals space 180 degree minus 110 degree space equals space 70 degree space space left square bracket Adjacent space angles space of space straight a space parallelogram right square bracket
137 Views

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)

115 Views

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

47 Views

62.

If cos 27° = x, then value of 63° is

  • fraction numerator straight x over denominator square root of 1 minus straight x squared end root end fraction
  • fraction numerator straight x over denominator square root of 1 plus straight x squared end root end fraction
  • fraction numerator square root of 1 minus straight x squared end root over denominator straight x end fraction
  • fraction numerator square root of 1 plus straight x squared end root over denominator straight x end fraction

A.

fraction numerator straight x over denominator square root of 1 minus straight x squared end root end fraction
cos space 27 degree space equals space straight B over straight H space equals space straight x over 1
straight P squared space equals space straight H squared space minus space straight B squared space equals space 1 squared space minus space straight x squared
straight P space equals space square root of 1 minus straight x squared end root space space space
tan space 63 degree space equals space tan space left parenthesis 90 degree space minus space 27 degree right parenthesis space equals space cot space 27 degree space equals space straight B over straight P space equals space fraction numerator straight x over denominator square root of 1 minus straight x squared end root end fraction
82 Views

67.

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

  • 45°

  • 60°

  • 90°

  • 120°


C.

90°

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

rightwards double arrow space space angle GBC space plus space angle BGC space plus space angle GCB space equals space 180 degree
rightwards double arrow space space angle GBC space plus space left parenthesis angle BGD space plus space angle CGD right parenthesis space space plus space space angle GCB space equals space 180 degree
rightwards double arrow space left parenthesis angle GBC plus space angle GBD right parenthesis plus left parenthesis angle GCD plus space angle GCB right parenthesis space equals space 180 degree space space
space rightwards double arrow space space space 2 angle GBC space plus space 2 angle GCB space equals space 180 degree
rightwards double arrow space space space space angle GBC space plus space angle GCB space equals space 90 degree
therefore space space space space angle BGC space equals space 90 degree
389 Views

68.

In a circle, a chord 5 square root of 2 space cm 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

In a circle, a chord  long, makes a right angle at the centr
AB = 5 square root of 2 (Chord of a circle)
OA = OB =r =  (radius of a circle)
Now,
In ΔOAB,
left parenthesis AB right parenthesis squared space equals space left parenthesis AO right parenthesis squared space plus space left parenthesis OB right parenthesis squared
left parenthesis 5 square root of 2 right parenthesis squared space equals space straight r squared space plus space straight r squared
25 space cross times space 2 space equals space 2 straight r squared
25 space equals space straight r squared
straight r space equals space 5 space cm
96 Views

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

  • 600 open parentheses square root of 3 plus 1 close parentheses
  • 600 square root of 3
  • 600 open parentheses square root of 3 minus 1 close parentheses

D.

600 open parentheses square root of 3 minus 1 close parentheses
The angle of elevation of aeroplane from a point on the ground is
In ΔABC,
     tan space 45 degree space equals space AC over BC

rightwards double arrow space 1 space equals space 2500 over BC
rightwards double arrow space BC space equals space 2500

In ΔBED,
tan space 30 degree space equals space ED over BD
fraction numerator 1 over denominator square root of 3 end fraction space equals space fraction numerator 2500 over denominator BC plus CD end fraction
2500 space plus space CD space equals space 2500 square root of 3
CD space equals space 2500 square root of 3 space minus space 2500
CD space equals space 2500 space left parenthesis square root of 3 minus 1 right parenthesis

∴  Speed of the aeroplane
            equals space fraction numerator 2500 left parenthesis square root of 3 minus 1 right parenthesis over denominator 15 end fraction space cross times space 18 over 5
equals space 600 space left parenthesis square root of 3 minus 1 right parenthesis space km divided by straight h
281 Views

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
cos squared straight x space equals space fraction numerator sin squared straight x over denominator cos squared straight x end fraction
cos squared straight x space equals space tan squared straight x
cos to the power of 4 straight x space equals space tan to the power of 4 straight x
therefore space space space tan squared straight x space plus space tan to the power of 4 straight x space equals space cos squared straight x space plus space cos to the power of 4 straight x space equals space 1     



199 Views

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

114 Views

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

62 Views