Math Chapter Wise

EnglishTGT 2011

Q261.Three forces are acting at a point in a plane, The angle between P and Q is 150o and the angle between Q and R is 120o. In equilibrium, the ratio of force P,Q, R will be–

A1: 2: 3 B1: 2: 3 C3: 2: 1 D3: 2: 1

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EnglishTGT 2011

Q262.The resultant of two equal forces is equal to either of them. The angle between the forces is–

A45o B60o C90o D120o

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EnglishTGT 2011

Q263.The resultant of the forces acting on the side BC, CA and AB of a triangle ABC Passes through the center of circumference of the triangle is–

AP sinA +QsinB+RsinC= 0 BP cosA +QcosB+RcosC= 0 CP secA +QsecB+RsecC= 0 DP tanA +QtanB+RtanC= 0

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EnglishTGT 2011

Q264.The two identical spheres made of same materials of radius 6 cm and 3 cm respectively joined together. At what distance will the center of gravity of the whole system be from the center of the larger sphere?

A1 cm B3 cm C2 cm D4 cm

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EnglishTGT 2011

Q265.If the interior center of ∆ ∆ ∆ABC is 'I', and the lengths of sides BC, CA and AB area a, b, c respectively then the value of aIA bIB cIC + + Will be–

A0 BAB CAC DAD

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EnglishUP PCS (Pre) 1998

Q266.A body is free to slide on a smooth vertical circular wire and is connected by a string, equal in length to the radius of the circle, to the highest point of the circle. The tension T of the string equals:

Athe weight of the body Bone-third of the weight of the body Chalf of the weight of the body Ddouble of the weight of the body

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EnglishUP PCS (Pre) 1998

Q267.If a central orbit is the lemniscate of Bernoulli r2 = a2 cos 2θ, then the law of force is:

A4 1 F r ∝ B5 1 F r ∝ C7 1 F r ∝ D9 1 F r ∝

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EnglishUP PCS (Pre) 1998

Q268.A particle possesses two simple harmonic motions in perpendicular directions, having the same period, but differing in phase and amplitude. The particle describes:

Aa circle Ba parabola Can ellipse Da hyperbola

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EnglishUP PCS (Pre) 1994

Q269.The chord of curvature, through the pole of the equiangular spiral r = aemθ is–

A2r Br C4r D3r

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EnglishUP PCS (Pre) 1994

Q270.The equations of the inverted cycloid is–

Ax a( cos )/y a(1 cos ) Bx a( sin )/y a(1 cos ) Cx a( sin )/y a(1 cos ) Dx a( sin )/y a(1 cos )

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EnglishUP PCS (Pre) 1994

Q271.A particle is projected with velocity u making an angle α with the horizontal. The maximum horizontal is–

A2g α 2 u sin B2g/u Cg/2u Dg 2 u

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EnglishUP PCS (Pre) 1994

Q272.The coefficient of friction is equal to–

Asine of the angle of friction Bcosine of the angle of friction Ctangent of the angle of friction Dcotangent of the angle of friction

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EnglishUP PCS (Pre) 1994

Q273.The resultant of two forces P and Q is R, if Q is doubled, R is doubled; and if Q is reversed, R is again doubled. If the ratio 2 2 2 P: Q: R 2: 3: x, then x is equal to–

A5 B4 C3 D2

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EnglishUP PCS (Pre) 1994

Q274.The equation of the line of action of the single resultant of a system of coplanar forces is–

AxY yX G BxY yX G CyX xY G DNone of these Where all symbols have their usual meanings.

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EnglishUP PCS (Pre) 1995

Q275.The distance from the base, of the central of gravity, of a solid right circular cone of uniform density and height 12cm is–

A2 cm B3 cm C4 cm D6 cm

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EnglishUP PCS (Pre) 1995

Q276.If the reaction R = 5 Newton and the forced friction 5 3 R 3 Newton then the angle of frictions is–

A2 B3 C4 D6

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EnglishUP PCS (Pre) 1995

Q277.The product of mass and acceleration is called:

AMomentum BWork CForce DMoment

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EnglishUP PCS (Pre) 1995

Q278.If a particle moves in a plance curve r = f (θ) then the radial acceleration is equal to–

A2 d r d r dt B2 d r d r dt C2 d r d r dt D2 2 d r d r dt dt

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EnglishUP PCS (Pre) 1995

Q279.The moment of inertia of a hollow sphere about a diameter is:

AMa2 B1 3 Ma2 C2 4 Ma 3 Dnone of these

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EnglishUP PCS (Pre) 1995

Q280.The maximum range, in a horizontal plane, of a projectile with a given velocity of projection is obtained if the angle of projection is–

A4 B3 C6 DNone of these

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