Math Chapter Wise

EnglishUP PCS (Pre) 2007

Q341.At 6, the slope of the tangent to the cardioids r a(1 cos) with the initial line is–

A1/2 B1 C2 DImage/formula option D (see source)

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EnglishUP PCS (Pre) 2008, 2007

Q342.If a particle moving along a curve r = aeθ with constant speed, then its acceleration will be proportional to

A1/r Br Cr2 D2 1 r

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EnglishUP PCS (Pre) 2008

Q343.A force P acting on a particle of mass 10 gm acting for 3 sec, generates a velocity of 9m/sec. The magnitude of P is

A0.3 N B300 dynes C3000 dynes D3 N

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EnglishUP PCS (Pre) 2008

Q344.A particle is moving under the influence of a central force along the curve r = aeθ cotα, then the force is proportional to

Ar3 Br2 C3 1 r D2 1 r

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EnglishUP PCS (Pre) 2008

Q345.Three equal and like forces act at the vertices of a triangle, then their resultant passes through

Acentroid of the triangle Bincentre of the triangle Ccircumcentre of the triangle Dorthocentre of the triangle

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EnglishUP PCS (Pre) 2008

Q346.If a system of coplanar forces be in equilibrium, the algebraic sum of their moments about any point in their plane, is

Anon-zero Bzero Ca constant other than zero Dnone of the above

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EnglishUP PCS (Pre) 2008

Q347.For the common catenary y = c cosh x c the following relation holds:

Ay = c tan Ψ Bs = c secΨ Cy2 = c2 +s2 Dw T y =

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EnglishUP PCS (Pre) 2008

Q348.Consider a disc in the form of an ellipse 2 2 x y + = 1. a b Then 4 2 a M = whose M is the total mass of the disc, is the moment of inertia about the

Ay–axis Bx–axis Cz–axis Dgiven line

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EnglishUP PCS (Pre) 2009

Q349.If µ is the coefficient of friction and λ is the angle of friction, then the relation between µ and λ is

Aµ = sin λ Bµ = cos λ Cµ = tan λ Dµ = cot λ

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EnglishUP PCS (Pre) 2009

Q350.A body is in equilibrium on a rough inclined plane of which the coefficient of friction is 1 3. The angle of inclination of the plane is gradually increased. The body will be on the point of sliding downward, when the inclination of the plane reaches

A15° B30° C45° D60°

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EnglishUP PCS (Pre) 2009

Q351.The intrinsic equation of a common catenary is

As = c sin Ψ Bs = c cot Ψ Cs = c sec Ψ DNone of the above

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EnglishUP PCS (Pre) 2009

Q352.The centre of gravity of a circular arc of a unit circle subtending an angle 60° ° ° at the centre, is at a distance from the centre

A3/π B2/π C6/π D3 3/π

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EnglishUP PCS (Pre) 2009

Q353.The number of loops in r = a sin 5θ is

A1 B3 C4 D5

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English(GIC) Lecturer Exam, 2015

Q354.The path of a projectile in vacuum is a

ACircle BStraight line CParabola DEllipse

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English(GIC) Lecturer Exam, 2015

Q355.The Cartesian equation of the common catenary is

Ay cosh x = Bx y cosh c = Cx y = c cosh c DNone of the above

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English(GIC) Lecturer Exam, 2015

Q356.Two projectiles A and B are projected with same initial velocity making an angle α and 90º–α with the horizontal. The ratio of their ranges is

A1:1 Btan2 α:1 C1:tan2 α D1: 2

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English(GIC) Lecturer Exam, 2015

Q357.A plane is inclined at an angle 1 3 tan 4 to the horizon, A horizontal force of w 2 is required just to support a weight w on the plane. The coefficient of friction is–

A3/11 B4/11 C5/11 D2/11

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English(GIC) Lecturer Exam,2015

Q358.If a particle is at point (r,θ) at time t, then its transverse acceleration will be–

A2 d r d r dt B2 1 d d r r dt dt C2 dr d d r dt dt dt D2 1 d d r 2r dt dt

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English(GIC) Lecturer Exam,2015

Q359.The centre of gravity of a uniform circular arc subtending an angle 2α at the centre is–

Asin,0 a Bsin 0, a Casin,0 Dsin 0, a

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English(GIC) Lecturer Exam, 2015

Q360.A particle describes a curve with uniform speed v. If acceleration at any point s be 2 2 2 v c s c and 0, when s 0, then the intrinsic equation of the curve is–

A2 2 2/s c Bs csin Cs c tan Dc s tan

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