Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

131.

The diagonals of AC and BD of a cyclic quadrilateral ABCD intersect each other at the point P. Then, it is always true that

  • AP . CP = BP. DP

  • AP. BP = CP. DP

  • AP. CD = AB. CP

  • BP. AB = CD. CP

49 Views

132.

N is the foot of the perpendicular from a point P of a circle with radius 7 cm, on a diameter AB of the circle. If the length of the chord PB is 12 cm, the distance of the point N from the point B is

37 Views

133.

If O be the circumcentre of a Δ PQR and ∠QOR = 110°, ∠OPR = 25° then the measure of ∠PRQ is

  • 50°

  • 55°

  • 60°

  • 65°

32 Views

134.

A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40 m long on the ground. The height of the tower is

  • 60 m

  • 65 m

  • 70 m

  • 72 m

51 Views

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135.

A, B, C, D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Then, ∠BAC is

  • 90°

  • 100°

  • 110°

  • 120°

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136.

In a triangle, if three altitudes are equal, then the triangle is

  • equilateral

  • right

  • isosceles

  • obtuse

40 Views

137.

The tops of two poles of height 24 m and 36 m are connected by wire. If the wire makes an angle of 60° with the horizontal, then the length of the wire is

  • 8√3 m

  • 8 m

  • 6√3 m

  • 6 m

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138.

The value of fraction numerator 1 over denominator cosec space straight theta space minus space cot space straight theta end fraction space minus space fraction numerator 1 over denominator sin begin display style space end style begin display style straight theta end style end fraction is

  • cot θ

  • cosec θ

  • tan θ

  • 1


A.

cot θ

fraction numerator 1 over denominator cosec space straight theta space minus space cot space straight theta end fraction space minus space fraction numerator 1 over denominator sin begin display style space end style begin display style straight theta end style end fraction
rightwards double arrow space space fraction numerator 1 over denominator begin display style fraction numerator 1 over denominator sin space straight theta end fraction minus fraction numerator cos begin display style space end style begin display style straight theta end style over denominator sin begin display style space end style begin display style straight theta end style end fraction end style end fraction space minus space fraction numerator 1 over denominator sin begin display style space end style begin display style straight theta end style end fraction
equals space space space fraction numerator sin begin display style space end style begin display style straight theta end style over denominator 1 minus cos space straight theta end fraction minus fraction numerator 1 over denominator sin begin display style space end style begin display style straight theta end style end fraction
equals space fraction numerator begin display style sin squared end style begin display style straight theta end style begin display style minus end style begin display style left parenthesis end style begin display style 1 end style begin display style minus end style begin display style cosθ end style begin display style right parenthesis end style over denominator left parenthesis 1 minus cosθ right parenthesis thin space sinθ end fraction
equals space fraction numerator 1 minus cos squared straight theta space minus space 1 space plus space cosθ over denominator left parenthesis 1 minus cosθ right parenthesis space sinθ end fraction
equals space fraction numerator cos space straight theta space left parenthesis 1 minus cos space straight theta right parenthesis over denominator left parenthesis 1 minus cos space straight theta right parenthesis thin space sin space straight theta end fraction space equals space cot space straight theta

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139.

If cos space straight theta space plus space sin space straight theta space equals space square root of 2 space cos space straight theta comma then cos θ - sin θ is

  • negative square root of 2 space cos space straight theta

  • negative square root of 2 space sin space straight theta

  • square root of 2 space sin space straight theta

  • square root of 2 space tan space straight theta

30 Views

140.

If tan space straight alpha space equals space straight n space space tan space straight beta space space and space sin space αθ space equals space straight m space sin space straight beta comma space space then cos squared straight alpha is

  • straight m squared over straight n squared

  • fraction numerator straight m squared minus 1 over denominator straight n squared minus 1 end fraction

  • fraction numerator straight m squared plus 1 over denominator straight n squared plus 1 end fraction

  • fraction numerator straight m squared over denominator straight n squared plus 1 end fraction

30 Views

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