Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

58.

If x = at2 and y = 2at then

  • x2 = 4ay

  • y2 = 4ax

  • x2 + y2 = a2

  • x2 - y2 = a2


B.

y2 = 4ax

x = at2
straight t squared space equals space straight x over straight a space space space space space space... left parenthesis straight i right parenthesis
y = 2at
y2 = 4a2t2
straight t squared space equals space fraction numerator straight y squared over denominator 4 straight a squared end fraction space space space space space space... left parenthesis ii right parenthesis
From (i) and (ii),
straight x over straight a space space equals space fraction numerator straight y squared over denominator 4 straight a squared end fraction
therefore space space space straight y squared space equals space 4 ax

46 Views

57.

A train 110 m long is running with a speed of 60 km/h. In what time will it pass a man who is running at 6 km/h in the direction opposite to that in which the train is going?

  • 5 sec

  • 6 sec

  • 7 sec

  • 10 sec


B.

6 sec

Distance  = 110 m
Relative speed  = (60 + 6) km/h = 66 km/h = equals space 66 space cross times space 5 over 18 straight m divided by sec
Required Time:
                     equals space space Distance over Speed
space equals space fraction numerator 110 space cross times space 18 over denominator 66 space cross times space 5 end fraction
space equals space 6 space sec

55 Views

56.

After selling 5% of a quantity of sugar, 5 kg of sugar remains. Find the total quantity of sugar?

  • 19 kg

  • 5 5 over 19 space kg

  • 100 kg

  • 95 kg


B.

5 5 over 19 space kg

5kg =95%
∴  Total quantity of sugar
    rightwards double arrow space space open parentheses 5 space equals space 95 over 100 close parentheses
rightwards double arrow space space space fraction numerator 5 space cross times space 100 over denominator 95 end fraction space equals space 100 over 19 space equals space 5 5 over 19 kg

69 Views

51.

24 men can do a piece of work in 17 days. How many men will be able to do it in 51 days?

  • 8

  • 10

  • 12

  • 6


A.

8

M1D1 = M2D2
 24 x 17 = M2 x 51
       M2 = 8

86 Views

55.

By selling cloth at Rs 9 per metre, a shopkeeper loses 10%. Find the rate at which it should be sold so as to earn profit of 15%

  • Rs. 11.20

  • Rs. 11.30

  • Rs. 11.40

  • Rs. 11.50


D.

Rs. 11.50

Shortcut Method:
rightwards double arrow space space open parentheses fraction numerator what space is space expected over denominator What space happened end fraction space cross times space Given space value close parentheses
rightwards double arrow space space open parentheses fraction numerator left parenthesis 100 plus 15 right parenthesis over denominator left parenthesis 100 minus 10 right parenthesis end fraction space cross times 9 close parentheses
rightwards double arrow space space 115 over 90 space cross times space 9 space equals space Rs space 11.50

53 Views

53.

The marked price is 10% higher than the cost price. A discount of 10% is given to the marked price. In this kind of sale, the seller

  • bears no gain, no loss

  • gains

  • loses 1%

  • None of these


C.

loses 1%

Net percentage effect:
  equals space open parentheses straight x space plus space straight y space plus space fraction numerator straight x. straight y over denominator 100 end fraction close parentheses percent sign
equals space open parentheses 10 space minus space 10 space plus space fraction numerator left parenthesis 10 right parenthesis thin space left parenthesis negative 10 right parenthesis over denominator 100 end fraction close parentheses percent sign
equals space minus 1 percent sign

56 Views

52.

In a cyclic quadrilateral ABCD, the side AB is extended to a point X. If angle XBC space equals space 82 degree and angle ADB space equals space 47 degree, then the value of angle BDC is:

  • 40°

  • 35°

  • 30°

  • 25°


B.

35°


As we know, Exterior angle of a cyclic quadrilateral is equal to its opposite interior angle.
space space space angle XBC space equals space 82 degree space left parenthesis given right parenthesis
therefore space space angle ADC space equals space angle XBC space equals space 82 degree
space space space space space angle ADB space equals space 47 degree
therefore space space angle BDC space equals space 82 degree space minus space 47 degree
therefore space space angle BDC space equals space 35 degree

101 Views

59.

If xy + yz + zx = 1,   then the value of fraction numerator 1 plus straight y squared over denominator left parenthesis straight x plus straight y right parenthesis thin space left parenthesis straight y plus straight z right parenthesis end fraction is

  • 2

  • 3

  • 4

  • 1


D.

1

xy + yz + zx = 1 (given)
fraction numerator 1 plus straight y squared over denominator left parenthesis straight x plus straight y right parenthesis thin space left parenthesis straight y plus straight z right parenthesis end fraction
rightwards double arrow space space fraction numerator 1 plus straight y squared over denominator left parenthesis xy space plus space xz space plus space yz space plus straight y squared right parenthesis space end fraction
equals space fraction numerator 1 plus straight y squared over denominator 1 plus straight y squared end fraction space equals space 1

44 Views

54.

Two numbers whose sum is 84, can do be in the ratio:

  • 5 : 7

  • 13 : 8

  • 1 : 3

  • 3 : 2


D.

3 : 2

59 Views

60.

If PQ and PR be the two tangents to a circle with centre O such that angle QPR space equals space 120 degree then angle POQ is:

  • 90°

  • 45°

  • 30°

  • 60°


C.

30°



angle QPR space equals space 120 degree space space left parenthesis given right parenthesis
angle OQP space equals space angle QRP space equals space 90 degree space space space space left square bracket Angle space to space the space point space of space contact space of space tangent space is space 90 degree right square bracket
Now, in quadr OQPR,
rightwards double arrow space space space angle OQP space plus space angle ORP space plus space angle QPR space plus space angle QOR space equals space 360 degree
rightwards double arrow space space space space space 90 degree space plus space 90 degree space plus space 120 degree space plus space angle QOR space equals space 360 degree
rightwards double arrow space space space space space space space space angle QOR space equals space 360 degree space minus space 300 degree space equals space 60 degree
therefore space space angle POQ space equals space fraction numerator 60 degree over denominator 2 end fraction space equals space 30 degree

71 Views