Math Chapter Wise

EnglishPGT 2013

Q161.A particle is projected with a velocity 'u' in a direction at an angle of 45o to the horizontal. It will move perpendicular to the direction of projection after the following time–

A2u/g B2 u g Cu/g D2u/g

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EnglishPGT 2010

Q162.The range of a projectile on horizontal plane is four times of its maximum height. Then angle of projection is

A30o B45o C60o D90o

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EnglishPGT 2010

Q163.If two equal and perfect elastic spheres impinge then their velocities in the direction of centre of line are

AInterchangeable Bequal Cdoubled DNone of these

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EnglishPGT 2010

Q164.A particle is in equilibrium under three forces, two of the forces act at right angles to one another, one being double the other. Third force has a magnitude of 10 N. Other two have magnitude

A10,2 10 B20,2 20 C10, 20 DNone of these

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EnglishPGT 2010

Q165.For the catenary y = c cos x h c

As2 =c2 +y2 By = c tanψ Csin x s c h c = Ds=c secψ

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EnglishPGT 2010

Q166.The frequencies of the values 0, 1, 2, 3, …,n of a variable are given by n n n 1 n n 2 2 n 1 2 q, C q.p, C q.p,...,p − − then the mean of the variable will be (where p+q = 1)

Anq Bnp Cn(p+1) Dn(q–1)

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EnglishPGT 2010

Q167.A ship moving at a velocity of 12 km/hour towards north observes, another ship which is 10 km east of this ship and moving with velocity of 16km/hour towards west. After some time they are at the minimum distance from each other. What is the minimum distance between them at this time?

A2 61km B8km C6km D4km

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EnglishPGT 2010

Q168.The horsepower of an engine which lifts 300 kg water per second from the depth of 100 metre is

A300 B350 C380 DNone of these

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EnglishPGT 2010

Q169.A stone falls from the rest from some height and reaches the earth in 5 seconds. If after 3 seconds of fall the stone is stopped and again allowed to fall, then how much time will it take to reach the ground?

A3sec B4sec C4.5 sec DNone of these

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EnglishPGT 2010

Q170.The extremities of a heavy string of length 2l and weight 2lw, are attached to two small rings which can slide on a fixed wire. Each of these rings is acted on by a horizontal force equal to lw. The distance between the rings is

A() 2 log 1 2 l − B() 2 log 1 2 l + C() log 1 2 l + D() log 1 2 l −

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EnglishPGT 2010

Q171.The reverse effective forces acting on each particle of a body and the external forces of the system are

Ainfinite Bin equilibrium Cequal to each other DNone of these

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EnglishPGT 2010

Q172.Moment of inertia of an elliptic area of mass M and semi-axes a and b about diameter of length 2r is

A2 2 2 1 a b M 4 r B2 1 ab M 2 r C2 1 ab M 4 r D2 2 2 1 a b M 2 r

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EnglishPGT 2010

Q173.The centre of gravity (C.G.) of a solid figure formed by revolving a quadrant of ellipse about its minor axis is

A3b x 0,y 8 = B3a x, y 0 8 = C3a 3b x, y 8 8 = Dx a,y b =

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EnglishPGT 2010

Q174.Three forces, P, Q and R act along the sides BC, CA and AB of a triangle ABC taken in order. If their resultant passes through the centroid of the triangle ABC, then

AP Q R 0 a b c + + = BR P Q c a b = + CP Q R a b c = DNone of these

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EnglishPGT 2009

Q175.Moment of inertia of a solid sphere of mass 'm' and radius 'a' about its tangent is

A7 5 ma2 B2 5 ma2 C2 3 ma2 D5 3 ma2

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EnglishPGT 2009

Q176.If there forces P, Q and R act along the sides BC, AC and AB respectively of the triangle ABC and their resultant passes through the orthocenter of triangle, then

A0 cos cos cos + + = P Q R A B C B1 cos cos cos + + = P Q R A B C Ccos cos cos = P Q R A B C DNone fo these

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EnglishPGT 2009

Q177.A particle is projected with a velocity u so that its range on a horizontal plane is twice the greatest height attained then the range is

A2 u g B2 3 u g C2 4 5 u g D2 g u

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EnglishPGT 2009

Q178.A ball is dropped from a height h on a horizontal plane, bounces up and down and finally comes to rest. The total distance described is

A∞ B2h C2 (1) + h e D2 1 + − e h e

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EnglishPGT 2009

Q179.A uniform chain of length l is suspended from two points A and B in the same horizontal line. If the tension at A is twice that at the lowest point of the chain, then the span AB is

A1 log(1 2) 2 + B1 log(2 3) 3 + C1 log(2 3) 2 − D1 log(1 2) 3 −

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EnglishPGT 2009

Q180.The moment of inertia of any triangular area ABC about a perpendicular to its plane through A is

A2 2 2 (3 3) 12 + − M b c a B2 2 2 () 12 + + M a b c C2 2 2 [ ] 12 − − M a b c D2 2 2 [3 3 2 ] 12 + + M a b c

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