Math Chapter Wise

EnglishBihar (TRE 1.0) -2023

Q01.Kepler’s law of planetary motion are given below: I. The square of the periodic time of planets are proportional to the cubes of the major axes of their orbits. II. The radius vector drawn from the sun to the planet describes equal arc in equal time. III. Each planet describes the ellipse having the sun in one of its foci. The order of these three laws are as follows:

AI, II, III BIII, II, I CIII, I, II DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q02.In planetary motion

AThe total angular momentum remains constant BThe angular speed remains constant CThe linear speed remains constant DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q03.A particle coming rest from infinity will reach the earth’s surface with a velocity

Agr B2gr C2 gr DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q04.The point in the immersed body through which the resultant pressure of the liquid may be taken to is known as

Acentre of gravity Bcentre of depth Ccentre of pressure DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q05.In an inclined plane submerged in water, the centre of pressure is located

Aat the centroid Bbelow the centroid Cabove the centroid DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q06.A fine uniform cycloidal tube is held with its axis vertical and vertex downwards and equal weights of two liquids occupy lengths a and b. Then the heights of the free surfaces of the liquids above the vertex are in the ratio

A(3a + b)2: (3b + a)2 B(3a + b): (3b + a) C(3b + a)2: (3a + b)2 DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q07.In polar coordinate system the component of velocity along radius vector and perpendicular to radius vector is

Adr d and r dt dt θ B2 d r d and r dt dt θ Cdr 1 d and dt r dt θ DMore than one of the above ENone of the above

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EnglishRPSC PGT 2022

Q08.A particle described distances 25m and 33m in 5th and 7th seconds respectively, moving under constant acceleration in a line. Its acceleration is -

A2 m /sec2 B6 m /sec2 C4 m /sec2 D8 m /sec2

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EnglishRPSC PGT 2022

Q09.The necessary and sufficient condition for a curve to be a helix is that its curvature and torsion are-

Ain a cubic relation Bin a linear relation Cin a constant ratio Dalways equal

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EnglishRPSC PGT 2022

Q10.The least velocity with which a cricket ball can be thrown at horizontal distance 200 meters is: (g = 9.8 m/sec2)

A44.3 m/sec. B45.3 m/sec. C43.3 m/sec. D34.3 m/sec.

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EnglishRPSC PGT 2022

Q11.If the displacement, velocity and acceleration at a particular instant of a particle describing simple harmonic motion are respectively 1 cm, 1 cm/second and 1 cm/sec2, then the maximum velocity of the particle is -

A6π cm/sec. B2 2 cm/sec. C1 2 cm/sec. D2 cm/sec.

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EnglishRPSC PGT 2022

Q12.If a heavy string hangs over two fixed small smooth pegs such that the two ends of the string are free and the central portion hangs in a centenary, then the free ends of the hanging portion will be-

Aon the directrix of the catenary Bon the tangent at vertex of the catenary Cinclination of the tangent at vertex DNone of these

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EnglishRPSC PGT 2022

Q13.Length of chord of curvature perpendicular to radius vector of curve p = f(r) is-

A2f (r)/f '(r) B2 2 2 r [f (r)] f '(r) − C2r 2 1 [f (r)] f '(r) − D2 2 1 [f (r)] f '(r) −

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EnglishRPSC PGT 2022

Q14.Length of the arc of the cycloid x = a (θ + sinθ), y = a (1 – cosθ) from the vertex to any point (x,y) is -

A4a sin 2 θ B2a sin 2 θ C4a cos 2 θ Da sin 2 θ

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EnglishRPSC PGT 2022

Q15.Moment of force about a point is -

Aa positive number Ba negative number Ca real number equal to magnitude of force Da vector quantity

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EnglishDSSSB PGT 2021

Q16.If a particle is thrown vertically upward with a velocity u and v be its velocity at a time t at a height h above the starting point, then which of the following is not true? 1 h = ut – 1 2 gt2 2. v2 – u2 = 2 gh 3. v = u – gt

AOnly 1 and 2 BOnly 2 COnly 3 DOnly 2 and 3

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EnglishDSSSB PGT 2021

Q17.If a particle describes cardioid r = a (1 - cosθ) under a force to the pole then the law of force (P) is.

A3 1 P r ∝ B4 1 P r ∝ C2 1 P r ∝ D1 P r5 ∝

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EnglishDSSSB PGT 2021

Q18.A stone is thrown horizontally with a velocity 2gh from the top of a tower of height h. At what distance will it strike the horizontal ground from of the tower?

A3h Bh C2h D6h

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EnglishDSSSB PGT 2021

Q19.A particle describes an ellipse under a force which is always directed towards the major axis. The law of force (F) is

A3 1 F y ∝ B2 1 F x ∝ C3 1 F x ∝ DF ∝ y2

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EnglishDSSSB PGT 2021

Q20.If a particle describes a curve r = aekθ under a central force toward the pole, then the law of force (P) is–

A2 1 P r ∝ B1 P r ∝ CP ∝ r3 D3 1 P r ∝

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