﻿ SSC - CGL Quantitative Aptitude Solved Question Paper 2013 | Previous Year Papers | Zigya

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Quantitative Aptitude

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# SSCCGL Quantitative Aptitude Solved Question Paper 2013

#### Multiple Choice Questions

108.

ABCD is a cyclic trapezium with AB || DC and AB a diameter of the circle. If then is

• 60°

• 120°

• 150°

• 30°

B.

120°  Now, in Δ ACB, As ABCD is a cyclic trapezium, 44 Views

105.

Two circles touch each other internally, Their radii are 2cm and 3 cm. The biggest chord of the greater circle which is outside the inner circle is of length

• • • • D.  From the figure,
MN is the diameter fo the smaller circle and PQ is the biggest chord of the greater circle. O is the centre of the greater circle and O' is the centre of the inner circle.
Now,
OM = MN - ON = 4 - 3 = 1 cm
Now,
In Δ PMO,  35 Views

102.

If x + y + z = 6  and x2 + y2 + z2 = 20,  then the value of x3 + y3 + z3 - 3xyz is

• 64

• 70

• 72

• 76

C.

72

x + y  + z = 6
S.B.S.
(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)
⟹      (6)2 = 20 + 2(xy + yz + zx)
⟹        36 = 20 + 2(xy + yz + zx)
⟹         36 - 20 = 2(xy + yz + zx)
⟹               16 = 2(xy + yz + zx)
⟹             (xy + yz + zx) = 8
∴        x3 + y3 + z3 - 3xyz
= (x + y + z) (x2 + y2 + z2 - (xy + yz + zx)
=  6 (20 - 8) = 6 x 12 = 72

38 Views

110.

AB is the chord of a circle with centre O and DOC is a line segment originating from a point D on the circle and intersecting AB produced at C such that BC = OD. If then is equal to

• 20°

• 30°

• 40°

• 60°

D.

60° Given that, OD = BC   ...(i)
and OD = OB  ...(ii) [Radii of a circle]
From (i) and (ii),
OB  =  BC Then,  As,  OB = OA  (Radii of a circle) Now,  44 Views

101.

The minimum value of (x - 2) (x - 9) is

• • • 0

• D. (x - 2) (x - 9)
= (x2 - 2x - 9x + 18) = (x2 - 11x + 18)
As the co-efficient of x2 is greater than 0,
∴ Minimum value of (x - 2) (x - 9) is given by,
= (-D/4a)
=  - (b2 - 4ac)/4a
= - (121 - 4*1*18)/4*1
= - (121 - 72)/4
=   - 49/4

75 Views

109.

ABC is a triangle. The bisectors of the internal angle and external angle intersect at D. If ,  then is

• 100°

• 90°

• 120°

• 60°

A.

100° In Δ BDC,
y + 180° - 2x + x + 50° = 180°
y - x + 50° = 0
y - x = -50°    ...(i)
In Δ ABC, 38 Views

106.

ABCD is a cyclic quadrilateral. AB and DC are produced to meet at P. If then the is

• 130°

• 150°

• 155°

• 180°

A.

130° As ABCD is a cyclic quadrilateral, Now, 40 Views

103.

The third proportional to is

• xy

• • • A.

xy

Third proportion is given by,  35 Views

104.

In a ΔABC, the side BC is extended upto D. Such that CD = AC, if and then the value of is

• 35°

• 60°

• 40°

• 45°

A.

35°  As AC = CD  (given),  Now, in Δ BAC, 35 Views

107.

From a point P which is at a distance of 13 cm from centre O of a circle of radius 5 cm, in the same plane, a pair of tangents PQ and PR are drawn to the circle. Area of quadrilateral PQOR is

• 65 cm2

• 60 cm2

• 30 cm2

• 90 cm2

B.

60 cm2  Now,
In Δ OQP, ∴  Area of Δ OQP ∴  Area of PQOR
= 2 x 30 = 60 cm2

43 Views