SSC CGL Tier 1 Quantitative Aptitude Questions and Answers Free Online Mock Test 14

1 .

A. a

B. b

C. c

D. d

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2 .

Find the value of cot θ tan(90°– θ )– sec(90°– θ )cosec θ + sin 2 25°+ sin 2 65° + $\sqrt3$ (tan 5°tan 15°tan 30°tan 75°tan 85°)

A. 1

B. -1

C. 2

D. 0

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3 .

If (1 + sin α )(1 + sin β )(1 + sin γ ) = (1 – sin α ) (1 – sin β )(1 – sin γ ), then each side is equal to

A. ± cos α cos β cos γ

B. ± sin α sin β sin γ

C. ± sin α cos β cos γ

D. ± sin α sin β cos γ

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4 .

There are two vertical posts, one on each side of a road, just opposite to each other. One post is 108 metre high. From the top of this post, the angles of depression of the top and foot of the other post are 30° and 60° respectively. The height of the other post is –

A. 36 m

B. 72 m

C. 108 m

D. 110 m

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5 .

If ABC is an equilateral triangle and D is a point on BC such that AD ┴BC, then

A. AB : BD = 1 : 1

B. AB : BD = 1 : 2

C. AB : BD = 2 : 1

D. AB : BD = 3 : 2

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6 .

ABC is a right angled triangle, right angled at C and pis the length of the perpendicular from C on AB. If a, band care the lengths of the sides BC, CA and AB respectively, then
A. $1\over p^2$= $1\over b^2$-$1\over a^2$

B. $1\over p^2$= $1\over a^2$+$1\over b^2$

C. $1\over p^2$+ $1\over a^2$+$1\over b^2$ = 0

D. $1\over p^2$= $1\over a^2$-$1\over b^2$

A. a

B. b

C. c

D. d

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7 .

Each edge of a regular tetrahedron is 3 cm, then its volume is –

A.$9\sqrt3\over4$ $cm^3$

B.$27\sqrt3$ $cm^3$

C.$4\sqrt3\over9$ $cm^3$

D.$9\sqrt3$ $cm^3$

A. a

B. b

C. c

D. d

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8 .

Three circles of radii 4 cm, 6 cm and 8 cm touch each other pair wise externally. The area of the triangle formed, by the line segments joining the centers of the three circles is –

A.$144\sqrt3$ sq.cm

B.$12\sqrt105$ sq.cm

C.$6\sqrt6$ sq.cm

D.$24\sqrt6$ sq.cm

A. a

B. b

C. c

D. d

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9 .

Let C be a point on a straight line AB, Circles are drawn with diameters AC and AB. Let P be any point on the circumference of the circle with diameter AB. If AP meets other circle at Q, then –

A.QC ║ PB

B. QC is never parallel to PB

C.QC = $1\over 2$ PB

D. QC ║ PB and QC =$1\over 2$ PB

A. a

B. b

C. c

D. d

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10 .

A prism has as the base a right-angled triangle whose sides adjacent to the right angles are 10 cm and 12 cm long. The height of the prism is 20 cm. The density of the material of the prism is 6 gm/cubic cm. The weight of the prism is –

A. 6.4 kg

B. 7.2 kg

C. 3.4 kg

D. 4.8 kg

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