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SSCCGL Quantitative Aptitude Solved Question Paper 2014

Multiple Choice Questions

11.
A ball of lead 4 cm in diameter is covered with gold. If the volume of the gold and lead are equal, then the thickness of gold [given $cube root of 2 space equals space 1.259$ ] is approximately.

5.038 m

5.190 cm

1.038 cm

1.038 cm

1.038 cm

Diameter of lead = 4 cm
Radius of lead = 2 cm
Volume of lead = $4 over 3 πr cubed space space equals space 4 over 3 straight pi cross times 2 cubed$
Let the thickness of gold be x cm, then
Volume of gold = $4 over 3 straight pi open parentheses left parenthesis 2 plus straight x right parenthesis cubed minus 2 cubed close parentheses space cu. space cm$
   $therefore space space 4 over 3 straight pi open parentheses open parentheses 2 plus straight x close parentheses cubed minus 2 cubed close parentheses space equals space 4 over 3 straight pi space cross times space 2 cubed$
$rightwards double arrow space space left parenthesis 2 plus straight x right parenthesis cubed space minus space 2 cubed space equals space 2 cubed rightwards double arrow space space left parenthesis 2 plus straight x right parenthesis cubed space space equals space 8 space plus space 8 space equals space 16 rightwards double arrow space space left parenthesis 2 plus straight x right parenthesis cubed space equals space 2 cubed. space 2$
   $rightwards double arrow space space 2 space plus space straight x space equals space 2 space cross times space cube root of 2 rightwards double arrow space space 2 space space plus space straight x space equals space 2 space cross times space 1.259 space equals space 2.518 therefore space space space space straight x space equals space 2.518 space minus space 2 space equals space 0.518 space cm$

551 Views

12.

A large solid sphere is melted and moulded to form identical right circular cones with base radius and height same as the radius of the sphere. One of these cones is melted and moulded to form a smaller solid sphere. Then the ratio of the surface area of the smaller to the surface area of the larger sphere is

$1 space colon space 3 to the power of 4 over 3 end exponent$
$1 space colon space 2 to the power of 3 over 2 end exponent$
$1 space colon space 3 to the power of 2 over 3 end exponent$
$1 space colon space 3 to the power of 2 over 3 end exponent$

463 Views

13.

Two sides of a plot measuring 32 m and 24 m and the angle between them is a perfect right angle. The other two sides measure 25 m each and the other three angles are not right angles. The area of the plot in m² is

768
534
696.5
696.5

587 Views

14.

a and b are two sides of adjacent to the right angle of a right-angled and p is the perpendicular drawn to the hypotenuse from the opposite vertex. Then p² is equal to

$straight a squared plus straight b squared$
$1 over straight a squared plus 1 over straight b squared$
$fraction numerator straight a squared straight b squared over denominator straight a squared plus straight b squared end fraction$
$fraction numerator straight a squared straight b squared over denominator straight a squared plus straight b squared end fraction$

479 Views

15.

A conical cup is filled with ice cream. The ice-cream forms a hemispherical shape on its open top. The height of the hemispherical part is 7 cm. The radius of the hemispherical part equals the height of the cone. Then the volume of the ice-cream is $open square brackets straight pi space equals space 22 over 7 close square brackets$

1078 cubic cm
1708 cubic cm
7108 cubic cm
7108 cubic cm

323 Views

16.

A is the centre of a circle whose radius is 8 and B is the centre of a circle whose diameter is 8. If these two two circles touch externally, then the area of the circle with diameter AB is

$36 straight pi$
$64 straight pi$
$144 straight pi$
$144 straight pi$

333 Views

17.

If $straight a squared plus straight b squared plus straight c squared space equals space ab space plus bc plus space ac$ then the value of $fraction numerator straight a plus straight c over denominator straight b end fraction$ is

162 Views

18.

If ab + bc + ca = 0, then the value of $open parentheses fraction numerator 1 over denominator straight a squared minus bc end fraction space plus space fraction numerator 1 over denominator straight b squared minus ca end fraction plus fraction numerator 1 over denominator straight c squared minus ab end fraction close parentheses$ is

182 Views

19.

If $left parenthesis 2 plus square root of 3 right parenthesis straight a space equals space left parenthesis 2 minus square root of 3 right parenthesis straight b space equals space 1$ then the value of $1 over straight a plus 1 over straight b$ is