Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

14.

In Δ ABC, angle BAC space equals space 90 degree and AD space perpendicular space BC, if BD = 3 cm and CD = 4 cm, then the length of AD is

  • 3.5 cm

  • 5 cm

  • 2 square root of 3 space cm
  • 6 cm


C.

2 square root of 3 space cm

BD = 3 cm
CD = 4cm
In Δ ABC
AB2 + AC2 = 72 = 49   ...(i)
In Δ ABD,
AB2 = AD2 + 32 = AD2 + 9  ...(ii)
In Δ ADC,
AC2 = AD2 + 16        ...(iii)
Add equations (ii) and (iii)
AB2 + AC2 = AD2 + 9 + AD2 + 16
⟹  49 = 2AD2 + 25
⟹  2AD2 = 49 - 25 = 24
⟹  AD2 = 12
⟹  AD space equals space square root of 12 space equals space 2 square root of 3 space cm.




281 Views

15.

A and B have their monthly incomes in the ratio 8 : 5, while their monthly expenditures are in the ratio 5 : 3. If they have saved Rs. 12,000 and Rs 10,000 monthly respectively, then the difference in their monthly incomes is

  • Rs 52,000

  • Rs. 42,000

  • Rs. 44,000

  • Rs. 46,000


B.

Rs. 42,000

Let A's monthly income be Rs. 8x
     A's monthly expenditure be Rs. 5y
Let B's monthly income be Rs. 5x
     B's monthly expenditure be Rs. 3y
According to the question,
8x - 5y = 12000          ...(i)
5x - 3y = 10000          ...(ii)
Solving (i) and (ii), we get
⟹   x = 14000
Difference between monthly incomes of A and B
 = 8x - 5x = Rs. 3x = Rs. (3 x 14000)
 = Rs. 42000




650 Views

13.

If tan θ - cot θ = 0 and θ is positive acute angle, then the value of fraction numerator tan space left parenthesis straight theta space plus space 15 degree right parenthesis over denominator tan space left parenthesis straight theta space minus 15 degree right parenthesis end fraction is

  • 3

  • fraction numerator 1 over denominator square root of 3 end fraction
  • 1 third
  • square root of 3

A.

3

tan space straight theta space minus space cot space straight theta space equals space 0
rightwards double arrow space space tan space straight theta space equals space cot space straight theta
rightwards double arrow space space tan space straight theta space equals space tan space left parenthesis 90 degree minus straight theta right parenthesis
rightwards double arrow space space straight theta space equals space 90 degree space minus straight theta
rightwards double arrow space 2 straight theta space equals space 90 degree
rightwards double arrow space space straight theta space equals space 45 degree
therefore space space space space fraction numerator tan left parenthesis straight theta space plus space 15 degree right parenthesis over denominator tan left parenthesis straight theta minus 15 degree right parenthesis end fraction
equals space fraction numerator tan left parenthesis 45 degree space plus 15 degree right parenthesis over denominator tan left parenthesis 45 degree minus 15 degree right parenthesis end fraction space equals fraction numerator tan space 60 degree over denominator tan space 30 degree end fraction
equals space fraction numerator square root of 3 over denominator begin display style fraction numerator 1 over denominator square root of 3 end fraction end style end fraction space equals space square root of 3 space cross times space square root of 3 space equals space 3
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18.

If (3x - 2y) : (2x + 3y) = 5  : 6, then one of the values of open parentheses fraction numerator cube root of straight x space plus space cube root of straight y over denominator cube root of straight x minus cube root of straight y end fraction close parentheses squared is

  • 1 fifth
  • 5

  • 25

  • 1 over 25

C.

25

fraction numerator 3 straight x minus 2 straight y over denominator 2 straight x plus 3 straight y end fraction space equals space 5 over 6
rightwards double arrow space space 18 straight x minus 12 straight y space equals space 10 straight x space plus space 15 straight y
rightwards double arrow space space 18 straight x space minus space 10 straight x space equals space 12 straight y space plus 15 straight y
rightwards double arrow space space space space 8 straight x space equals space 27 straight y
rightwards double arrow space space space straight x over straight y space equals space 27 over 8
Taking cube root both sides
fraction numerator cube root of straight x over denominator cube root of straight y end fraction space equals space cube root of 27 over 8 end root space equals space 3 over 2
By componendo and dividendo,
fraction numerator cube root of straight x space plus space cube root of straight y over denominator cube root of straight x minus cube root of straight y end fraction space equals space fraction numerator 3 plus 2 over denominator 3 minus 2 end fraction space equals space 5 over 1
S.B.S.
open parentheses fraction numerator cube root of straight x space plus space cube root of straight y over denominator cube root of straight x minus cube root of straight y end fraction close parentheses squared space equals space 5 space cross times space 5 space equals space 25

 
200 Views

11.

In triangle ABC, DE || BC where D is a point on AB and E is a point on AC. DE divides the area of Δ ABC into two equal parts. Then DB : AB is equal to

  • square root of 2 space colon thin space open parentheses square root of 2 space plus space 1 close parentheses
  • square root of 2 space colon thin space left parenthesis square root of 2 minus 1 right parenthesis
  • left parenthesis square root of 2 minus 1 right parenthesis space colon space square root of 2
  • left parenthesis square root of 2 plus 1 right parenthesis thin space colon thin space square root of 2


C.

left parenthesis square root of 2 minus 1 right parenthesis space colon space square root of 2

DE || BC
As DE divides the area of Δ ABC into two equal parts
∴  D and E is the midpoint of AB and AC
As increment ADE space tilde space space increment ABC  
therefore space space space space space fraction numerator Area space of space increment ABC over denominator Area space of space increment ADE end fraction space equals space AB squared over AD squared
rightwards double arrow space space space space space AB squared over AD squared space equals space 2 space space space rightwards double arrow space space space AB space equals space square root of 2 AD
rightwards double arrow space space space space space AB space equals space square root of 2 left parenthesis AB space minus space DB right parenthesis
rightwards double arrow space space space space square root of 2 AB space minus space AB space equals space square root of 2 DB
rightwards double arrow space space space AB thin space left parenthesis square root of 2 minus 1 right parenthesis space equals space square root of 2 space DB
rightwards double arrow space space space space space DB over AB space equals space fraction numerator square root of 2 minus 1 over denominator square root of 2 end fraction

476 Views

20.

The portion of a ditch 48m long, 16.5m wide and 4 m deep that can be filled with stones and earth available during excavation of a tunnel, cylindrical in shape, of diameter 4 m and length 56 m is open parentheses Take space straight pi space equals space 22 over 7 close parentheses

  • 1 fourth Part
  • 1 half Part
  • 2 over 9 Part
  • 1 over 9 Part

C.

2 over 9 Part

Volume of ditch  = (48 x 16.5 x 4) m3 = 3168 m3
Volume of earth and stones taken out from the tunnel equals space πr squared straight h
             equals space open parentheses 22 over 7 cross times 2 cross times 2 cross times 56 close parentheses straight m cubed
equals space 704 space straight m cubed
∴  Part of the ditch filled
     equals space 704 over 3168 space equals space 2 over 9 parts


380 Views

16.

Pipe A can fill an empty tank in 6 hours and pipe B in 8 hours. If both the pipes are opened and after 2 hours pipe. A is closed, how much time B will take to fill the remaining tank?

  • 7 1 half space hours
  • 2 2 over 5 space hours
  • 2 1 third space hours
  • 3 1 third space hours

D.

3 1 third space hours

Part filled by A and B together in first 2 hours
 equals space 2 space open parentheses 1 over 6 space plus space 1 over 8 close parentheses
equals space 2 open parentheses fraction numerator 4 plus 3 over denominator 24 end fraction close parentheses space equals space 7 over 12
Remaining part = 1 minus 7 over 12 space equals space 5 over 12
This part shall be filled by pipe B
∴ Required time to fill the remaining tank by B
 equals space 5 over 12 space cross times space 8 space equals space 10 over 3 space hours space equals space 3 1 third space hours


188 Views

12.

Ram sold two horses at the same price. In one he gets a profit of 10% and in the other he gets a loss of 10%. Then Ram gets

  • 2% loss

  • No loss or profit

  • 1% loss

  • 1% profit


C.

1% loss

Shortcut Method:
In such a question there is always a loss, use the formula:
equals space fraction numerator straight A space cross times space straight B over denominator 100 end fraction space equals space fraction numerator 10 space cross times space 10 over denominator 100 end fraction space equals space 1 percent sign space Loss

285 Views

19.

Articles are marked at a price which gives a profit of 25%. After allowing a certain discount the profit reduces to 12 1 half percent sign. The discount percent is

  • 11.1%

  • 10%

  • 12 1 half percent sign
  • 12%


B.

10%

Let the C.P. of each article be Rs. 100
Profit  = 25%
∴   Marked Price = Rs 125
As profit reduces to 12.5%
∴  New Marked price = Rs 112.5
∴   Discount = Rs (125 - 112.5) = Rs 12.5
Let the discount be x%
     rightwards double arrow space space space space 125 space cross times space straight x over 100 space equals space 12.5
rightwards double arrow space space space space space space space straight x space equals space fraction numerator 12.5 space cross times space 100 over denominator 125 end fraction space equals space 10 percent sign
       


 

507 Views

17.

A right prism has a triangular base, whose sides are 13 cm, 20 cm and 21 cm. If the altitude of the prism is 9 cm, then its volume is

  • 1314 cm3

  • 1134 cm3

  • 1413 cm3

  • 1143 cm3


B.

1134 cm3

In the triangle,  a = 13 cm,   b  = 20 cm,   c = 21 cm
straight s space equals space fraction numerator straight a plus straight b plus straight c over denominator 2 end fraction space equals space fraction numerator 13 plus 20 plus 21 over denominator 2 end fraction space equals space 54 over 2 space equals space 27 space cm
Area of base = Area of triangle
                 equals space square root of straight s left parenthesis straight s minus straight a right parenthesis thin space left parenthesis straight s minus straight b right parenthesis thin space left parenthesis straight s minus straight c right parenthesis end root
equals space square root of 27 left parenthesis 27 minus 13 right parenthesis thin space left parenthesis 27 minus 20 right parenthesis thin space left parenthesis 27 minus 21 right parenthesis end root
equals space square root of 27 space cross times space 14 space cross times space 7 space cross times space 6 end root
equals space 126 space cm squared
Height  = 9 cm
∴ Volume of prism = Area of base x height
                            = 126 x 9 = 1134 cm3.



208 Views