Math Chapter Wise

EnglishUP PCS (Pre) 1996

Q281.A particle moves in a curve so that its tangential and normal accelerations are equal. If the angular velocity of the tangent is constant, then the curve is:

Aks Ae B Bks Ae B Cks Alog B DNone of these Where k is the angular velocity. A and B are constants.

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EnglishUP PCS (Pre) 1996

Q282.A particle coming from infinity will reach the earth's surface with velocity:

A3gr B5gr Cgr D2gr where r is the radius of the earth.

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EnglishUP PCS (Pre) 1996

Q283.Let a particle of 1kg be projected vertically with velocity U in a resisting medium. If it goes up to a height h and then returns to the point of projection with velocity V, then:

AV U BV U CV U D2 2/V U 2gh

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EnglishUP PCS (Pre) 1996

Q284.When a particle is in motion under a force, f then:

Aits velocity may be in any direction Bits acceleration may be in any direction Cits acceleration is always in the direction of motion Dits acceleration is in the direction of f

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EnglishUP PCS (Pre) 1996

Q285.Two satellites of masses m1 and m2 (m1>m2) are revolving round the earth in circular orbits of radii r1 and r2 (r1>r2) respectively and speeds 1 v and 2 v respectively, then:

A1 2 v v = B1 2 v v > C1 2 v v < DNone of these

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EnglishUP PCS (Pre) 1996

Q286.The effect of the resistance of a medium on the range of a particle, is:

ATo increase it BTo decrease it CNo effect DNone of these

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EnglishUP PCS (Pre) 1996

Q287.Two equal uniform rods AB and AC each of length 2b are freely and rest on a smooth vertical circle of radius a, if 2θ be the angle between them, then:

A3 bsin a cos θ = θ B3/a sin bcos C3 bcos asin θ = θ DNone of these

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EnglishUP PCS (Pre) 1996

Q288.A particle is projected vertically upwards with a velocity u and resistance of the medium is kv2. The velocity V with which the particle will return to the point of projection, is given by:

A2 2 1 1 k g V u B2 2 1 1 k g u V C2 2 1 1 k g V v DNone of these

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EnglishUP PCS (Pre) 1996

Q289.A particle in rests under the attraction of two centres of forces, which attract directly as distance, their intensities being and. The particle is slightly displaced towards one of them, then the time of small oscillation is:

A2 BImage/formula option B (see source) C2 DNone of these

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EnglishUP PCS (Pre) 1996

Q290.The greatest least velocities of a certain planet in its orbit round the sun are 30 km/sec. and 29.2 km/sec respectively. Then the eccentricity of the orbit is–

A1/72 B1/74 C1/75 DNone of these

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EnglishUP PCS (Pre) 1996

Q291.The curves, for which polar subnormal varies as the radius vector, are given by the following:

Ar = k sin (θ + c) Br = k cos cθ Cr = c ekθ DNone of these

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EnglishUP PCS (Pre) 1999

Q292.A particle moves in a straight line under the equation of motion dv v = -x dx where is the velocity at a distance x, the motion is:

Aperiodic with period 2π Bperiodic with period π Cπ periodic with period 2 Dnot periodic

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EnglishUP PCS (Pre) 1999

Q293.A particle is projected in vaccum with the velocity 20 meters per second. The maximum range on the horizontal plane and the corresponding angle of projection are:

A200, g 4 π B200, g 3 π C400, g 4 π D400, g 3 π

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EnglishUP PCS (Pre) 1999

Q294.For motion under a central force, the angular momentum is:

A, B, CImage/formula option C (see source) Dnone of

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EnglishUP PCS (Pre) 1999

Q295.A particle moves in a straight line with initial velocity u and acceleration f in the direction of motion. The distance travelled in the third second is:

Au+4f Bu+2f C7 u f 2 + D5 u f 2 +

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EnglishUP PCS (Pre) 1999

Q296.If a projectile with a given initial velocity attains its maximum range on the horizontal plane, then the greatest height of the projectile is:

A1 the range 2 B1 the range 4 C1 the range 4 Dthe same as the range

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EnglishUP PCS (Pre) 1999

Q297.A uniform string of weight W is suspended from two points at the same level and a weight W' is attached to its lowest point. If the tangents at the highest and lowest points make angles 3 π and 4 π with the horizontal, then W W' equals:

A3 1 B3 1/+ C3 D2

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EnglishUP PCS (Pre) 1999

Q298.The moment of inertia about the x–axis of the ellipse disc given by 2 2 x y + = 1 a b is:

A2 1 Ma 2 B2 1 Ma 4 C2 1 Mb 4 D2 1 Mb 2 were M is the mass of the ellipse.

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EnglishUP PCS (Pre) 2000

Q299.A body is moving in a straight line with uniform acceleration. It covers distances of 10 m and 12 m in third and fourth seconds respectively, then the initial velocity in m/sec is:

A1 B3 C5 D7

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EnglishUP PCS (Pre) 2000

Q300.The equation of the catenary is:

As = c cos Ψ Bs = c sec Ψ Cs = c tan Ψ Dnone of these

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