Math Chapter Wise

EnglishUP PCS (Pre) 2004

Q321.A particle describes the curve p2 = ar under a force F to the pole; the law of force is–

A4 1 F r ∝ B3 1 F r ∝ C2 1 F r ∝ D1 F r ∝

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EnglishUP PCS (Pre) 2004

Q322.The moment of inertia of a solid sphere of mass M and radius ‘a’ about a diameter is:

A2 1 Ma 5 B2 Ma 5 C2 3 Ma 5 D2 4 Ma 5

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EnglishUP PCS (Pre) 2004

Q323.If the pedal equation of a curve is pr=a2, then the radius of curvature is–

A3 2 r a B2 r a C2 r a D3 r a

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EnglishUP PCS (Pre) 2005

Q324.If a body of mass m kg is carried by a lift moving with upward acceleration f, then the pressure on the plane of the lift is:

Amg–mf Bmf–mg Cmg+mf D(mg)–(mf)

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EnglishUP PCS (Pre) 2005

Q325.If a particle moves under a central force F along the curve r = aemθ, then the law of force is:

AF ∝ r3 BF ∝ r –5 CF ∝ r –3 DF ∝ r5

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EnglishUP PCS (Pre) 2005

Q326.A particle moves along a parabola y = ax2 in such a way that its x-component of velocity is constant. If y is the acceleration in the y- direction, then:

A2 y x ∝ By x/∝ Cy y/∝ Dy constan t =

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EnglishUP PCS (Pre) 2005

Q327.Certesian formula for radius of curvature P for the curve y =f(x), is:

A2 d y dx ρ = B3/2 dy 1 dx ρ = + C3/ 2 2 dy 1 dx d y dx + ρ = D3/ 2 2 dy 1 dx d y dx + ρ =

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EnglishUP PCS (Pre) 2006

Q328.A particle is at rest at the origin. It moves along the X-axis with an acceleration x–x2, where x is the distance of the particle from the origin at time t. The particle next comes to rest after it has covered a distance

A1 B1/2 C3/2 D2

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EnglishUP PCS (Pre) 2006

Q329.If a body is projected at such an angle that the horizontal range is four times the greatest height, then the angle of projection is:

A1 1 tan 4 − B1 1 tan 2 − C() 1 tan 1 − D() 1 tan 2 −

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EnglishUP PCS (Pre) 2006

Q330.A particle is attracted by a force to a fixed point varying as (distance)–n. If the velocity acquired in falling from infinity to a distance a from the fixed point be equal to the velocity acquired in falling distance a to distance a 4, then n is equal to:

A3 B5/2 C3/2 D2

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EnglishUP PCS (Pre) 2006

Q331.If the equation of path of a projectile is given by y=x–x2, then the velocity of projection is:

Ag/2 Bg/4 C2g Dg

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EnglishUP PCS (Pre) 2006

Q332.If a particle describes the cardioid r=a(1+cosθ) under a central force to the pole, then the central acceleration is proportional to:

A1/r B2 1 r C3 1 r D4 1 r

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EnglishUP PCS (Pre) 2006

Q333.For common catenary, the tension at any point is proportional to:

Adistance of the point from the axis Bdepth of the point from the line of span Cthe height of the point above the vertex Dthe height of the point above the directrix

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EnglishUP PCS (Pre) 2006

Q334.Equations forming the parametric equation of a common catenary are:

Ax csec,y clog(sec tan) = ψ = ψ + ψ Bx ctan,y clog(sec tan) = ψ = ψ + ψ Cx clog(sec tan),y csec = ψ + ψ = ψ Dx clog(sec tan),y ctan = ψ + ψ = ψ

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EnglishUP PCS (Pre) 2006

Q335.Moment of inertia of a rod of length 2a and mass M about an axis through an end perpendicular to the rod, is:

A2 4 Ma 3 B2 3 Ma 2 CMa2 D2 Ma 3

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EnglishUP PCS (Pre) 2007

Q336.The product of the two times of height from a point P to another point Q with a given velocity of projections is–

APQ/g B2PQ/g CPQ/2g D3PQ/g

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EnglishUP PCS (Pre) 2007

Q337.If the equation of a particle executing a simple harmonic motion is 2 d x dt + 16x = 0 then the frequency will be–

A2 B2 C8 D8

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EnglishUP PCS (Pre) 2007

Q338.Forces 3P, 7P and 5P act along the sides AB, BC and CA respectively of an equilateral triangle ABC of side 20 units. The resultant force a A makes an angle with side AB.

A1500 B300 C900 D600

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EnglishtUP PCS (Pre) 2007

Q339.Motion of a particle in a plane due to a acceleration P directed towards a fixed point in the plane is given (in usual notation) by–

A2 2 2 d u P u d h u B2 2 2 3 d u P u d h u C2 2 2 du P u d h u D2 2 2 2 d u P u d h u

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EnglishUP PCS (Pre) 2007

Q340.A weight W is attached to an endless string of length l which hangs over two smooth parts distant 1 3 l apart in a horizontal line. The pressure on each parts is–

A2W B1 W 3 CW D1 W 2

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