Math Chapter Wise

EnglishUP PCS (Pre) 2000

Q301.A particle describes a circle under a central force directed to a point on its circumference. The law of force is inversely proportional to:

Athe square of distance Bthe cube of distance Cthe fifth power of distance Dnone of these

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EnglishUP PCS (Pre) 2000

Q302.A particle is dropped under gravity from rest from a height h and it travels a distance 9h 25 in the last second. The height h is (g = 9.8 m/sec2):

A100 meter B122.5 meter C145 meter D167.5 meter

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EnglishUP PCS (Pre) 2001

Q303.The tension at a point P of a common cantenary is 13 units and the tension at the lowest point A is 12 units. The weight of the arc AP is:

A5 units B6 units C7 units D3 units

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EnglishUP PCS (Pre) 2001

Q304.A particle moves along a circle of radius with velocity v and angular acceleration ω then the normal acceleration is given by:

Aav2 Bav Caω D2/aω

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EnglishUP PCS (Pre) 2001

Q305.Two balls are projected respectively from the same point in directions inclined at 60° ° ° and 30° ° to the horizontal. If they attain the same height, the ratio of their velocities of projection is:

A3:1 B1: 3 C1:1 D1:2

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EnglishUP PCS (Pre) 2001

Q306.A particle moves in a straight line with velocity u and constant acceleration f. The distance travelled in 4th second is:

Au+4f Bu+5f Cu+3f D7 2 + u f

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EnglishUP PCS (Pre) 2002

Q307.If the horizontal range of a projectile is 4 3 times its maximum height, then its angles of projection is:

A60° B45° C30° Dnone of the above

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EnglishUP PCS (Pre) 2002

Q308.If f be the tension at any point B of a catenary and T0 that at the lowest point A and W be the weight of the arc AB of the catenary. Then () 2 2 0 T - T is equal to:

A2 1 W 2 BW2 C2W2 Dnone of the above

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EnglishUP PCS (Pre) 2002

Q309.A particle possesses two simple harmonic motion in perpendicular directions, having the same period, but differing in phase and amplitude. The path of the particle is:

Aa circle Ban ellipse Ca cycloid Da catenary

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EnglishUP PCS (Pre) 2002

Q310.The moment of inertia of a rectangular lamina of mass M and sides 2a and 2b about a diagonal is:

A() 2 2 a b M 3 a b + B() 2 2 M 2a b 3 a b + C() 2 2 M 3a b 2 3 a b + DNone of the above

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EnglishUP PCS (Pre) 2002

Q311.The chord of curvature through the pole for the curve p = f(r) is:

Af (r) Bf(r)/f'(r) C2f(r)/f '(r) D2f (r) f '(r)

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EnglishUP PCS (Pre) 2003

Q312.The moment of inertia of the ellipse 2 2 x y 1 a b of mass M about its major axis is–

A2 1 Ma 2 B2 1 Mb 2 C2 1 Mb 4 D2 1 Ma 4

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EnglishUP PCS (Pre) 2003

Q313.The ratio of the range on horizontal plane and the time of flight of a projectile whose angle of projection is 600 is 5:2. Its velocity of projection is–

A5 m/s B10 m/s C15 m/s DNone of the above

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EnglishUP PCS (Pre) 2003

Q314.If a particle describes a curve r = a (1+cosθ) under a central force F, then the law of forces is–

A2 1 F r B4 1 F r C5 1 F r DF r

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EnglishUP PCS (Pre) 2004, 2005

Q315.A heavy uniform string of length 10m is suspended between two points in the same horizontal line so that the sag in the middle is 1m. Its parameter c is–

A24m B25m C6m D12m

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EnglishUP PCS (Pre) 2004

Q316.When a uniform inextensible chain hangs under gravity, the difference in the tensions at two points varies as–

Athe difference of their heights Bthe difference of inclinations of tangents at these points Cthe horizontal distance between them Dnone of the above

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EnglishUP PCS (Pre) 2004

Q317.If a particle moves along the curve r = aeθ such that its radical acceleration is zero, then its angular velocity is–

AProportional to 1 r / 1 r Bproportional to r/ r Cproportional to 2 1 r Da constant

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EnglishUP PCS (Pre) 2004

Q318.In a simple harmonic motion, if the velocities at distance b and c from the centre of force be respectively u and v, then the frequency n of oscillations satisfies:

A2 2 2 2 2/4 n (b c ) v u B2 2 2 2 2 2/4 n (b c ) v u C2 2 2 2 2/4 n(b c ) v u D2 2 2 2/4 n (b c) v u

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EnglishUP PCS (Pre) 2004

Q319.A particle is projected so that its horizontal range is maximum. The ratio of its greatest height to its horizontal range is–

A1/6 B1/4 C1/2 D1

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EnglishUP PCS (Pre) 2004

Q320.If a particle is moving in a parabolic orbit under a central acceleration 2 r, then the square of the velocity at a point is–

Agreater then 2 r Bless than 2 r Cequal to 2 r Dequal to 2 2 r

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