Math Chapter Wise

EnglishUPPSC Polytechnic Lecturer 2021(II)

Q81.Equation of continuity in cartesian coordinates is -

AD u v w 0 Dt x y z ρ ∂ ∂ ∂ + ρ + + = ∂ ∂ ∂ Bu v w 0 t x y z ∂ρ ∂ ∂ ∂ + ρ − − = ∂ ∂ ∂ ∂ Cu v w 0 t x y z ∂ρ ∂ ∂ ∂ − ρ − − = ∂ ∂ ∂ ∂ DNone of these Where D u v w Dt t x y z ∂ ∂ ∂ ∂ ≡ + + + ∂ ∂ ∂ ∂

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q82.If φ = A (x2 – y2) represents a possible flow phenomenon, then the stream function is-

Aψ = Ax + C Bψ = 2Axy + C Cψ = A x y + C Dψ = Ax2 y2 + C

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q83.If the speed of fluid is everywhere the same, the streamlines are –

ACircular BParabolic CStraight lines DNone of these

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EnglishUP PGT 2021

Q84.If a normal at any point P of a common catenary meets the directrix at Q & ρ is the radius of curvature of catenary at P then PQ is equal to–

Aρ Bc sec ψ Cc tan ψ Dc 2 sec ψ

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EnglishUP PGT 2021

Q85.A sphere after collision with a plane vertically downwards with velocity 20 cm per second returns upwards with velocity 4 cm/second then the value of the coefficient of restitution e is–

A1/2 B1/3 C1/4 D1/5

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EnglishUP PGT 2021

Q86.A hemisphere rests in equilibrium on a sphere of equal radius. If the flat surface of the hemisphere rests on the sphere then this equilibrium is –

AStable BUnstable CNeutral DNone of the above

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EnglishUP PGT 2021

Q87.Two uniform solid spheres composed of the same material and having their radii 6 cm and 3 cm respectively are firmly united. The distance of the centre of gravity of the whole body from the centre of the larger sphere is –

A4 cm B3 cm C2 cm D1 cm

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EnglishUP PGT 2021

Q88.A stone just clears a wall of height 75 meters situated at a distance 150 meter and goes in horizontal direction, then the angle of projection is-

A30º B60º C45º D75º

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EnglishUP PGT 2021

Q89.The work done by the force () () ∧ ∧ 2 2 F = – y + i– 2 y + y j x x x, displacing a particle in the xy plane from (0, 0) to (1, 1) along the parabola y2 = x, is

A2 B3 C1/2 Dnone of these

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EnglishUP PGT 2021

Q90.The moment of inertia of a circular ring of radius a and mass M about an axis through the centre perpendicular to its plane is–

A2 1 Ma 2 BMa2 C2 Ma 3 D2 4 Ma 3

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EnglishUP PGT 2021

Q91.The Cartesian equation of the common catenary is -

Ay2 = c2 + x2 By = c cosh c x Cy = c secx Dy = c tan hx

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EnglishUP PGT 2021

Q92.The area lying between line y = x, x axis and ordinates x = 0 and x = 2 is revolved about x axis. The centre of gravity of the solid thus generated is at the following point.

A1,0 2 B3,0 2 C3,0 4 D1,0 4

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EnglishUP PGT 2021

Q93.Moment of inertia of a hollow sphere about a diameter whose mass is M and radius a, is

AM. 2 2a 3 BM. 2 2a 5 CM. 2 a 4 DM. 2 a 3

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EnglishUP PGT 2021

Q94.A particle moves along the curve x = t3 –2, y = t2 + t, z = 2t + 1. The component of its acceleration at t =1 in the direction i– j k ∧ ∧ ∧ + is-

A4 B4 3 C4/3 D2

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EnglishUP PGT 2021

Q95.If the horizontal range of a projectile is equal to its gained maximum height then its angle of projection is –

A4/π Btan–1/2 Ctan–1/4 D3/π

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EnglishUPPSC GIC 2021

Q96.A particle is moving along a plane curve with uniform speed v. Its angular velocity θ ɺ about a point O in the plane, when it is at some point P of its path, is

AInversely proportional to OP2 BProportional to OP2 CProportional to OP DInversely proportional to OP

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q97.If the radial and transverse velocities of a particle are always proportional to each other, then the particle will describe-

Aa straight line Ba parabola Ca hyperbola Dan equiangular spiral

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EnglishUPPSC GIC 2021

Q98.If the horizontal range of a projectile is four times of its maximum height, then the angle of projection will be

A30º B45º C60º DNone of these

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EnglishUPPSC GIC 2021

Q99.A body of mass m falls from rest through a height 1 km under gravitational acceleration 10 m/s2 and is then brought to rest by penetrating through a depth 200 m into sand. The average deceleration of the body during penetration into sand is-

A50 m/s2 B20 m/s2 C250 m/s D125 m/s2

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q100.A uniform beam of length '2a' rests in equilibrium against a smooth vertical wall upon a peg at a distance 'b' from the wall. The inclination of the beam to the vertical is-

A2/ 3 1 b cos a − B1/ 3 1 a 2cos b − C1/ 3 1 b sin a − DNone of the above

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