Subject

Quantitative Aptitude

Class

SSCCHSL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

11.

If cos C - cos D = x, then the value of x is

  • 2 space sin space open square brackets fraction numerator left parenthesis straight C plus straight D right parenthesis over denominator 2 end fraction space space COS fraction numerator left parenthesis straight C minus straight D right parenthesis over denominator 2 end fraction close square brackets

  • 2 space cos space open square brackets fraction numerator left parenthesis straight C plus straight D right parenthesis over denominator 2 end fraction close square brackets space sin space open square brackets fraction numerator left parenthesis straight D minus straight C right parenthesis over denominator 2 end fraction close square brackets

  • 2 sin open square brackets fraction numerator open parentheses straight C plus straight D close parentheses over denominator 2 end fraction close square brackets space sin space open square brackets fraction numerator open parentheses straight D minus straight C close parentheses over denominator 2 end fraction close square brackets

  • 2 space cos space open square brackets fraction numerator open parentheses straight C plus straight D close parentheses over denominator 2 end fraction close square brackets space cos space open square brackets fraction numerator open parentheses straight C minus straight D close parentheses over denominator 2 end fraction close square brackets


C.

2 sin open square brackets fraction numerator open parentheses straight C plus straight D close parentheses over denominator 2 end fraction close square brackets space sin space open square brackets fraction numerator open parentheses straight D minus straight C close parentheses over denominator 2 end fraction close square brackets

Shortcut Method:
As, we know that,
rightwards double arrow space space space space space cos space straight C space minus space cos space straight D space equals space minus 2 space sin space open parentheses fraction numerator straight C plus straight D over denominator 2 end fraction close parentheses space sin space open parentheses fraction numerator straight C minus straight D over denominator 2 end fraction close parentheses
therefore space space space space space space cos space straight C space minus space cos space straight D space equals space 2 space sin space open parentheses fraction numerator straight C plus straight D over denominator 2 end fraction close parentheses space sin space open parentheses fraction numerator straight D minus straight C over denominator 2 end fraction close parentheses


12.

In the first 26 overs of a cricket match, the run rate was 5.4 runs per over. What is the required run rate in the remaining 24 overs to reach the target of 294 runs?

  • 7

  • 6.4

  • 7.6

  • 5.8


B.

6.4

Run Rate in 26 overs = 5.4 runs/over
∴  Runs scored in 26 over = 26 x 5.4 = 140.4
 Runs required to score in 24 overs = 294 - 140.4 = 153.6
∴    Required Run Rate
                equals space fraction numerator 153.6 over denominator 24 end fraction space equals space 6.4


13.

Δ DEF and Δ GHI are similar triangles. Length of DE is 4 cm and length of the corresponding side GH is 9 cm. What is the ratio of areas of Δ DEF and Δ GHI?

  • 81 : 16

  • 4 : 9

  • 16 : 81

  • 9 : 4


C.

16 : 81

As we know,
Ratio of similar triangles = Ratio of squares of the corresponding sides.
therefore space space space fraction numerator increment DEF over denominator increment GHI end fraction space equals space open parentheses DE over GH close parentheses squared space equals space open parentheses 4 over 9 close parentheses squared space equals space 16 over 81
increment DEF space space colon space increment GHI space equals space 16 space colon space 81






14.

There is 75% increase in an amount in 5 years at simple interest. What will be the compound interest of ₹ 40,000/- after 2 years at the same rate?

  • ₹ 25,800/-

  • ₹ 32,250/-

  • ₹ 12,900/-

  • ₹ 19,350/-


C.

₹ 12,900/-

Rate of interest  = open parentheses 75 over 5 close parentheses percent sign space equals space 15 percent sign
C.I. = A - P
      equals space 40000 open parentheses 1 plus 15 over 100 close parentheses squared minus 40000
equals space 40000 space cross times space 115 over 100 space cross times space 115 over 100 space minus space 40000
equals space 52900 space minus space 40000 space space equals space ₹ space 12900

 

  


15.

Rahul sells a machine for ₹ 50 lakh at a loss. Had he sold it for ₹ 60 lakh, his gain would have 7 times the earlier loss. What is the cost price of the machine?

  • ₹ 51.25 lakh

  • ₹ 58.75 lakh

  • ₹ 67.14 lakh

  • ₹ 43.75 lakh


A.

₹ 51.25 lakh

Let the cost price of the machine  = ₹ x.
                      Selling price = ₹ 50 lakh.
New selling price of the machine = ₹ 60 lakh
                          Profit = 7(x - 50)
According to the question,
                         7(x - 50) = 60 - x
⟹                       7x - 350 = 60 - x
⟹                             8x = 410
⟹                              x = 51.25 lakh
       


16.

If a merchant offers a discount of 20% on the list price, then she makes a loss of 16%. What percent profit or percent loss will she make if she sells goods at a discount of 10% of the list price?

  • 14% profit

  • 20% profit

  • 50% profit

  • 5.5% loss


D.

5.5% loss

Let the marked price be ₹ 100/-
  ∴   Selling Price
               space equals space 100 space cross times 80 over 100 space equals space ₹ space 80 divided by negative
Loss = 16%(given)
∴  Cost price
           equals space 80 space cross times space fraction numerator 100 over denominator left parenthesis 100 minus 16 right parenthesis end fraction
equals space 80 space cross times space 100 over 84
equals space ₹ space space 2000 over 21
New discount = 10%
∴  New S.P.
      equals space 100 space cross times space 90 over 100 space equals space ₹ space 90 divided by negative
∴   Required loss percentage:
          equals space fraction numerator begin display style 2000 over 21 end style minus 90 over denominator begin display style 2000 over 21 end style end fraction space cross times space 100
equals space fraction numerator 2000 space minus space 1890 over denominator 21 end fraction space cross times space 21 over 2000 space cross times space 100
equals 110 over 20 space equals space 5.5 percent sign



17.

If 2x - 1 < 5x  +2  and 2x + 5 < 6 - 3x, then x can take which of the following values?

  • 1

  • 0

  • 2

  • -2


B.

0

Putting x = 0
I.              2x - 1 < 5x + 2
⟹            2 x 0 - 1 < 5 x 0 + 2
⟹               0 - 1 < 0 + 2
⟹                   -1 < 2

II.             2x + 5 < 6 - 3x
⟹               2 x 0 + 5 < 6 -  x 0
⟹                      0 + 5 < 6 - 0
⟹                          5 < 6

Clearly it satisfies the equation.



18.

The sum of all prime numbers between 30 and 42 is

  • 103

  • 109

  • 105

  • 104


B.

109

All prime numbers between 30 and 42 = 31, 37, 41
The sum of all prime numbers between 30 and 42
                                               = 31 + 37 + 41 = 109


19.

The value of x for which the expressions 12 - 6x and 4x + 2 become equal is:

  • 0

  • 2

  • 1

  • 4


C.

1

According to the question,
12 - 6x = 4x + 2
    6x + 4x = 12 - 2
      10x = 10
          x = 1


20.

Refer the below of data table and answer the following question.

Employee Number of employees Annual Salary (in ₹ lakh) Bonus as percent of annual salary
Manager 1 48 40%
Executive 6 16 20%
Trainee 2 2 20%

What is the average bonus (in ₹)?

  • 3920004

  • 220000

  • 228000

  • 435556


D.

435556

Average bonus:
      equals space fraction numerator begin display style fraction numerator 1 space cross times space 48 space cross times space 40 over denominator 100 end fraction end style space plus space begin display style fraction numerator 6 space cross times space 16 space cross times space 20 over denominator 100 end fraction end style space plus space begin display style fraction numerator 2 space cross times space 2 space cross times space 20 over denominator 100 end fraction end style over denominator left parenthesis 1 plus 6 plus 2 right parenthesis end fraction
equals space fraction numerator 1920 space plus space 1920 space plus space 80 over denominator 900 end fraction
equals space 3920 over 900 space equals space 4.35556 space cross times space 100000
equals space 435556