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SSCCGL Quantitative Aptitude Solved Question Paper 2016

Multiple Choice Questions

71.

If x⁴ + 2x³ + ax² + bx + 9 is a perfect square, where a and b are positive real numbers, then the values of a and b are

a = 5, b = 6
a = 6, b = 7
a = 7, b = 6
a = 7, b = 6

1312 Views

72.
If a² + b² + c² = 16, x² + y² + z² = 25 and ax + by + cz = 20, then the value of $fraction numerator straight a plus straight b plus straight c over denominator straight x plus straight y plus straight z end fraction$ is

$3 over 5$
$5 over 3$
$4 over 5$
$4 over 5$

4 over 5

left parenthesis ax plus by plus cz right parenthesis squared space equals space left parenthesis 20 right parenthesis squared space equals space 400 space space space... left parenthesis straight i right parenthesis left parenthesis straight a squared plus straight b squared plus straight c squared right parenthesis thin space left parenthesis straight x squared plus straight y squared plus straight z squared right parenthesis space equals space 25 space cross times space 16 space equals space 400 space... left parenthesis ii right parenthesis

From (i) and (ii)

left parenthesis ax plus by plus cz right parenthesis squared space equals space left parenthesis straight a squared plus straight b squared plus straight c squared right parenthesis space left parenthesis straight x squared space plus space straight y squared space plus space straight z squared right parenthesis

straight a squared straight x squared space plus space straight b squared straight y squared space plus space straight c squared straight z squared space plus space 2 abxy space plus space 2 bcyz space plus space 2 acxz

equals space straight a squared straight x squared space plus space straight a squared straight y squared space plus space straight a squared straight z squared space plus space straight b squared straight x squared space plus space straight b squared straight y squared space plus space straight b squared straight z squared space plus space straight c squared straight x squared space plus space straight c squared straight y squared space plus straight c squared straight z squared

⟹ a²y² + a²z² + b²x² + b²z² + c²x² + c²y² = 2abx + 2bcyz + 2acxz
⟹ a²y² - 2abxy + b²x² + a²z² + c²x² - 2acxz + b²z² + c²y² - 2bcyz = 0
⟹ (ay - bx)² + (az - cx)² + (bz - cy)² = 0
⟹ ay - bx = 0 ⟹ ay = bx ⟹

straight a over straight b space equals space straight x over straight y

az - cx = 0

rightwards double arrow space space space az space equals space cx space space rightwards double arrow space space straight a over straight c space equals space straight x over straight z

therefore space space space straight a space equals space kx semicolon space space straight b space equals space ky semicolon space space straight c space equals space kz therefore space space space straight a squared space plus space straight b squared space plus space straight c squared space equals space 16 rightwards double arrow space space space space space straight k squared left parenthesis straight x squared space plus space straight y squared space plus space straight z squared right parenthesis space equals space 16 rightwards double arrow space space space space space straight k squared space cross times space 25 space equals space 16 rightwards double arrow space space space space space straight k squared space equals space 16 over 25 space rightwards double arrow space space space straight k space equals space 4 over 5

therefore space space space fraction numerator straight a plus straight b plus straight c over denominator straight x plus straight y plus straight z end fraction space equals space straight k space equals 4 over 5

1136 Views

73.

The value of x which satisfies the equation $fraction numerator straight x plus straight a squared plus 2 straight c squared over denominator straight b plus straight c end fraction plus fraction numerator straight x plus straight b squared space plus 2 straight a squared over denominator straight c plus straight a end fraction plus fraction numerator straight x plus straight c squared plus 2 straight b squared over denominator straight a plus straight b end fraction space equals space 0$
is

(a² + b² + c²)
- (a² + b² + c²)
(a² + 2b² + c²)
(a² + 2b² + c²)

394 Views

74.

If a³ = 117 + b³ and a = 3 + b, then the value of (a + b) is

$plus-or-minus space 7$
$plus-or-minus space 49$
$plus-or-minus space 13$
$plus-or-minus space 13$

420 Views

75.

If $open parentheses straight a plus 1 over straight a close parentheses space equals space minus 2 comma$ then the value of $straight a to the power of 1000 plus space straight a to the power of negative 1000 end exponent$ is

262 Views

76.

Δ ABC is similar to ΔDEF. If the area of ΔABC is 9 sq. cm. and the area of ΔDEF is 16 sq. cm. and BC = 2.1 cm, then the length of EF will be

5.6 cm
2.8 cm.
3.7 cm.
3.7 cm.

323 Views

77.

A chord of a circle is equal to its radius. The angle subtended by this chord at a point on the circumference is

80°
60°
30°
90°

355 Views

78.

Let two chords AB and AC of the larger circle touch the smaller circle having same centre at X and Y. Then XY = ?

BC
1/2 BC
1/3 BC
2/3 BC

985 Views

79.

Let G be the centroid of the equilateral triangle ABC of perimeter 24 cm. Then the length of AG is

2√3 cm
8⁄√3 cm
8√3 cm
3√8 cm

458 Views

80.

A and B are the centres of two circles with radii 11 cm and 6 cm respectively. A common tangent touches these circles at P and Q respectively. If AB = 13 cm, then the length of PQ is