Math Chapter Wise

EnglishPGT 2009

Q181.Time period for compound pendulum is

A= h T g B2 = k T gh π C2 = k T gh π DNone of these

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EnglishPGT 2009

Q182.If two equal and perfectly elastic spheres impacting at 900, their directions after impact will still be at?

Aright angles Bat the same line Cat an angle of 1800 DNone of these

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EnglishPGT 2009

Q183.Two forces P and Q have a resultant R and the resolved part of R in the direction of P is of magnitude Q. The angle between the forces is

A1 2sin 2 − P Q B1 2sin− P Q C1 2sin 2 − Q P D1 2sin− Q P

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EnglishPGT 2005

Q184.Two equal rods of weight W each and length 2a, are attached to each other with free joint, and are placed symmetrically on a fixed smooth sphere of radius r. If the inclination of each rod with the horizon is θ, then

Ar tan2 θ–r tan θ = a Br tan2 θ + r tan θ = a Cr tan3 θ + r tan θ = a Dr tan3 θ – r tan θ = a

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EnglishPGT 2005

Q185.If (x,y) be a point of catenary whose intrinsic equation is s = ctanφ, then the value of secφ– tanφ is

Aex/c Be–x/c Cey/c De–y/c

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EnglishPGT 2005

Q186.The x-coordinate of the centre of gravity of an arc bounded by x=a and x= b is given by

Ax b x a x b x a ydx x dx = ∫ Bx b x a x b x a ydx x ds = ∫ Cx b x a x b x a yds x ds = ∫ DNone of these

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EnglishPGT 2005

Q187.A spacecraft of mass M is moving with velocity v in free space when it explodes and breaks in two parts. After the explosion a mass m of the spacecraft is left stationary. The velocity of the other part is -

A−Mv/M m BMv M m + C−mv/M m Dmv M m +

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EnglishPGT 2005

Q188.A particle is projected with velocity 'u'at an angle with the horizontal. The maximum height, it attains, will be

A2 2 sin 2 u g α Bsin 2 2 u g α C2 2 sin u g α D2 sin 2 2 u g α

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EnglishPGT 2005

Q189.A ball is dropped from a height of 40m and rebounds to a height 20m. The loss of K.E. is

A50% B25% C50% D75%

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EnglishPGT 2005

Q190.Moment of inertia of a uniform circular ring of radius 2a about an axis through the centre perpendicular to its plane (where m is its mass) is

Ama2 B2ma2 C3ma2 D4ma2

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EnglishPGT 2005

Q191.If particles are projected from the same point and in the same vertical plane so as to describe equal parabolas, then their vertices lie on

Aan ellipse Ba hyperbola Ca circle Da parabola

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EnglishPGT 2005

Q192.If the petrol burnt in driving a motor boat varies with the cube of its velocity, what will be the most economical speed when going against the current of 6km/hour?

A8km/hour B9km/hour C12km/hour D16km/hour

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EnglishPGT 2004

Q193.The equation of catenary is

As = c sec ψ Bs = c sinh x/2 Cs = c cosh x/2 DNone of these

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EnglishPGT 2004

Q194.The moment of inertia of a solid sphere of mass M and radius r about any diameter is

A2 5 Mr B2 5 Mr C3 2 5 Mr D2 1 5 Mr

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EnglishPGT 2004

Q195.A stone with a velocity of 9.8 metre/sec is projected vertically upwards. At which height will the potential energy and kinetic energy of the stone be equal?

A2.43 metres B2.40 metres C2.45 metres DNone of these

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EnglishPGT 2004

Q196.Particles each of equal weight are placed at (n - 1) corners of a regular polygon of n sides. If the radius of the circumcircle of the regular polygon is r units, then the distance of the centre of gravity of these particles from the centre of the circumcircle of regular polygon will be-

A2(1) r n − B1 r n + C1 r n − D2(1) r n +

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EnglishPGT 2004

Q197.The statement, ''if three concurrent force in a plane are in equilibrium, then each force is proportional to the sine of the angle between the other two,'' is known as-

Alaw of triangle of forces Blaw of parallelogram of forces CConverse of Lami's theorem DNone of the above

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EnglishPGT 2004

Q198.A uniform cubical box of edge a is placed on the top of a fixed sphere, the centre of the face of the cube being in contact with the highest point of the sphere. The least radius of the sphere, for which the equilibrium will be stable, is

Aa Ba / 2 C2a D3a / 2

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EnglishPGT 2003

Q199.A train of mass 200 tons, including the engine, is drawn up an incline of 3 in 500 at the rate of 40 km per hour by an engine of 600 H.P. The resistance per ton due to friction etc is

A24.685 pounds–weight B20.236 pounds–weight C16.685 pounds–weight D14.685 pounds–weight

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EnglishPGT 2003

Q200.At what angle a smooth ball strike a horizontal plane so that after impact its direction may be right angle to its former path

A−1/tan c B−1/tan c C−1/sin c D−1/sin c

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