Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

53.

At what percentage above the cost price must an article be marked so as to gain 33% after allowing a customer a discount of 5%?

  • 40%

  • 45%

  • 35%

  • 47%


A.

40%

Shortcut Method:
space equals space fraction numerator left parenthesis 100 space plus space profit space divided by loss percent sign right parenthesis over denominator left parenthesis 100 minus discount percent sign right parenthesis end fraction space cross times space 100 space minus space 100
equals space fraction numerator left parenthesis 100 space plus space 33 right parenthesis over denominator left parenthesis 100 minus 5 right parenthesis end fraction space cross times space 100 space minus space 100
equals space 133 over 95 space cross times space 100 space minus space 100
equals space space 140 space minus space 100
equals space 40 percent sign

62 Views

60.

The point equidistant from the sides of a triangle is called:

  • Circumcenter

  • Incentre

  • Orthocentre

  • Centroid


B.

Incentre

71 Views

52.

A spherical lead ball of radius 6 cm is melted and small lead balls of radius 3 mm are made. The total number of possible small lead balls is:

  • 4250

  • 4000

  • 8005

  • 8000


D.

8000

Total number of possible small lead balls:
            equals space fraction numerator begin display style 4 over 3 end style straight pi left parenthesis 6 right parenthesis cubed over denominator begin display style 4 over 3 end style straight pi open parentheses begin display style 3 over 10 end style close parentheses cubed end fraction
equals space fraction numerator 6 space cross times space 6 space cross times space 6 space cross times space 10000 over denominator 3 space cross times space 3 space cross times space 3 end fraction
equals space 8000

80 Views

51.

A can do a piece of work in 20 days and B in 15 days. With help of C, they finish the work in 5 days. C can alone do the work in

  • 5 days

  • 6 days

  • 10 days

  • 12 days


D.

12 days

Let C alone can do the work in x days.
According to the question,
    1 fifth minus open parentheses 1 over 20 space plus space 1 over 15 close parentheses space equals space 1 over straight x
rightwards double arrow space space fraction numerator 12 minus 3 minus 4 over denominator 60 end fraction space equals space 1 over straight x
rightwards double arrow space 5 over 60 space equals space 1 over straight x
rightwards double arrow space space space straight x space equals space 12 space days
    

92 Views

55.

Kamal has some apples. He sold 40% more than he ate. If he sold 70 apples, how many did he eat?

  • 18

  • 42

  • 50

  • 90


C.

50

According to the question,
70 = 140%
rightwards double arrow space space open parentheses 70 space equals space 140 over 100 close parentheses
rightwards double arrow space space open parentheses fraction numerator 70 space cross times space 100 over denominator 140 end fraction close parentheses
space equals space space space 50

104 Views

57.

If x2 + 5x + 6 =  0,   then the value of fraction numerator 2 straight x over denominator straight x squared minus 7 straight x plus 6 end fraction is:

  • 1 over 6

  • 1 third

  • negative 1 over 6

  • negative 1 third


C.

negative 1 over 6

x2 + 5x+ 6 
Divide the whole equation by x:
  rightwards double arrow space space straight x space space plus space 5 space plus space 6 over straight x space equals space 0
rightwards double arrow space space space straight x space plus space 6 over straight x space equals space minus 5 space space space space space space space space space... left parenthesis straight i right parenthesis

fraction numerator 2 straight x over denominator straight x squared minus 7 straight x plus 6 end fraction
Again divide the whole equation by x:
rightwards double arrow space space fraction numerator 2 over denominator straight x minus 7 plus begin display style 6 over straight x end style end fraction
space equals space fraction numerator 2 over denominator straight x plus begin display style 6 over straight x end style minus 7 end fraction
equals space fraction numerator 2 over denominator negative 5 minus 7 end fraction space equals space fraction numerator negative 2 over denominator 12 end fraction space equals space minus 1 over 6 space space space left square bracket Using space left parenthesis straight i right parenthesis right square bracket



55 Views

56.

A train 100 m long is running at a speed of 120 km/hr. The time taken to pass a person standing near the lines is

  • 1 sec

  • 3 sec

  • 5 sec

  • 7 sec


B.

3 sec

Distance  = 100 m
Speed  = 120 km/hr = 120 space cross times space 5 over 18 straight m divided by sec
Time space equals space Distance over Speed
Time space equals space 100 over 120 cross times space 18 over 5 space equals space 3 space sec

52 Views

59.

A 8 cm long perpendicular is drawn from the centre of a circle to a 12cm long chord. The diameter of the circle is

  • 10 cm

  • 12 cm

  • 16 cm

  • 20 cm


D.

20 cm

In ΔAOB, 
  (AO)2 = (AB)2 + (OB)2
  (AO)2 = (6)2 + (8)2
  (AO)2 = 36 + 64
  (AO)2 = 100
    AO = 10 cm
∴    Diameter of circle  = 2 x 10 = 20 cm

  

  

55 Views

54.

The four sides of a quadrilateral are in the  ratio of 2 : 3 : 4 : 5 and its perimeter is 280 m. The length of the longest side is:

  • 100 m

  • 150 m

  • 175 m

  • 180 m


A.

100 m

Let the four sides of quadrilateral be 2x, 3x, 4x and 5x respectively.
According to the question,
    2x + 3x + 4x + 5x = 280
                           14x = 280
                               x = 20 m
∴   Length of the longest side = 5 x 20 = 100 m

79 Views

58.

If a + b = 5   and   a - b = 3, then the value of (a2 + b2) is

  • 17

  • 18

  • 19

  • 20


A.

17

a + b = 5  and a - b = 3
(a + b)2 = (a - b)2 + 4ab
(5)2 = (3)2 + 4ab
4ab = 25 - 9
   ab = 4
(a + b)2 = a2 + b2 + 2ab
    (5)2  = a2 + b2 + 2 x 4
      25   = a2 + b2 + 8
      a2 + b2 = 25 - 8
      a2 + b2 = 17
       

    



 

54 Views