Math Chapter Wise

EnglishDSSSB PGT 2021

Q21.The distance s of a particle moving in a straight line in terms of time t is given by: s = a cos (nt + ϵ), where a, n, t are constant. Then the retardation is proportional to:

As2 B1/s C2 1 s Ds

Show answer

EnglishDSSSB PGT 2021

Q22.If a particle thrown vertically upwards takes t sec to rise to a height h and t' sec in the subsequent time to reach the ground again, then:

A1 h = gtt 2 ′ B()2 1 h = g t t 2 ′ + C() 1 h = g t t 2 ′ + D() ()2 1 h = u t + t g t t 2 ′ ′ − +

Show answer

EnglishDSSSB PGT 2021

Q23.For a rectilinear motion of a particle, if an impulse I changes its velocity from u to v and E is the change of kinetic energy, then:

Au + 2v E = I 3 B2u +3v E = I 5 Cu + v E = I 2 D3u + 2v E = I 5

Show answer

EnglishDSSSB PGT 2021

Q24.If a particle describes a curve whose equation is 2 a = θ r + b under a force to the pole, then the law of force (p) is–

A3 2a + r P r ∝ B3 2r + a P r ∝ C2 2a + r P r ∝ D3 a P r ∝

Show answer

EnglishDSSSB PGT 2021

Q25.If a particle moves in a straight line according to the law x = a sin(μ μ μt + ϵ), then the velocity v is related by:

Av2 = µ(x2 – a2) Bv2 = µ2 (a2 – x2) Cv2 = µ(a2 – x2) Dv2 = µ2 (x2 – a2)

Show answer

EnglishJSSC PGT 2018

Q26.If the stream function is given by ψ ψ ψ = 6x + 12y, then the speed of flow is given by:

A–1/180ms B1/170ms C–1/3 2ms D–1/0.5ms

Show answer

EnglishJSSC PGT 2018

Q27.Digital circuit can be made by the repeated use of which gate?

AOR BNone of the given options CNOT DNAND

Show answer

EnglishJSSC PGT 2018

Q28.A solid homogeneous cone of height 'h' and semi-vertical angle α oscillates about a diameter of its base. Then the length of the simple equivalent pendulum is:

A() 2 h 2 5tan 5 + α B() 2 h 2 3tan 5 + α C() 2 h 2 3tan 3 + α D() 2 h 2 5tan 2 + α

Show answer

EnglishJSSC PGT 2018

Q29.Consider variable µ that satisfies the equation 2 d µ + µ = 2kcosθ dθ and the conditions: (i) µ has some value when π θ = ± 2 (ii) ∫ π 2 0 µdθ = 0 The value of this variable µ is given by: (for arbitrary constant 'k')

A() k sin cos µ = θ + θ B() k sin cos µ = θ+ θ C() k sin – cos µ = θ D() k sin – cos µ = θ

Show answer

EnglishJSSC PGT 2018

Q30.The moment of inertia of a uniform thin rod of mass 'M' and length 'L' about a perpendicular axis of rotation at its end is:

A2 1 ML 8 B2 1 ML 2 C2 1 ML 3 D2 1 ML 4

Show answer

EnglishJSSC PGT 2018

Q31.If P and Q are two non-intersecting forces whose directions are perpendicular, then the ratio of distance of the central axis from their lines of action is represented as:

AQ2: 2P2 B2P2: Q2 CQ2: P2 DP2: Q2

Show answer

EnglishJSSC PGT 2018

Q32.A rough uniform board of mass 'm' and length 2a rests on a smooth horizontal plane. A man of mass 'M' walks on it from one end to the other. The distance through which the board moves in this time is:

A() 3Ma m M / + B() 3Ma m 2M / + C() 2Ma m M / + D() Ma m M / +

Show answer

EnglishJSSC PGT 2018

Q33.Two ends A and B of a rod of length 20cm have the temperature at 40° ° °C and 90° ° °C respectively until steady state prevails. After the steady state has prevailed, the temperature at the ends A and B are changed to 45° ° °C and 95° ° °C respectively. The temperature distribution in the root at time t is given by () ∑ 2 k(2m–1π – t 20 m=1 2m –1 πx 20 µ x,t = Ax + B + sin.e 2m –1 π 20 ∞ where:

A3 A,B 42 2 = B5 A 45,B 2 = C5 3 A,B 2 2 = D5 A,B 45 2 =

Show answer

EnglishJSSC PGT 2018

Q34.The area under the curve given by the polar co- ordinates r = f (ⱷ) is given by:

A∫(r2/) dⱷ B3 r dr 2 ∫ C2∫(r2/) dⱷ D2 r 2 ∫ dⱷ

Show answer

EnglishJSSC PGT 2018

Q35.The moment of inertia of an ellipse of mass 'M' and semi axes a and b about a tangent is: (where p is the perpendicular from the centre on the tangent.)

A2 5M p 4 B2 5M p 6 C2 5M p 2 D2 5M p 3

Show answer

EnglishJSSC PGT 2018

Q36.Two equal uniform rods AB and AC, each of length 2b, are freely joined at A and are rested on a smooth vertical circle of radius a. If 2θ is the angle between them, then:

Aa sin3 θ = b cosθ Bb sin2 θ = a cosθ Ca sin2 θ = b cosθ Db sin3 θ = a cosθ

Show answer

EnglishJSSC PGT 2018

Q37.A particle starts from origin. The components of its velocity parallel to the axes of coordinator at time 't' are 2t + 3 and 4t. Then the path travelled by the particle is given by:

A4x2 – y2 – 4xy + 18y = 0 Bx2 + y2 + xy – 12y = 0 C3x2 + y2 + 4xy – 18y = 0 D4x2 + y2 – 4xy – 18y = 0

Show answer

EnglishJSSC PGT 2018

Q38.A solid frustum of a paraboloid of revolution of height 'h' and latus rectum 4a rests with its vertex on the vertex of a paraboloid of revolution whose latus rectum is 4b. Then the equilibrium is stable if:

A3ab h a b < + B2ab h a b < + Cab h a b > + D3ab h a b > +

Show answer

EnglishUPPSC GDC 2021

Q39.The Hamiltonian of a particle moving in one dimension whose Lagrangian is given by i 2 x L = – V(x) 2x is

A2 P H = – V(x) 2x B2 x H = + V(x) 2 i C2 x H = + V(x) 2x i D2 1 H = xP + V(x) 2

Show answer

EnglishUPPSC GDC 2021 UPPSC Polytechnic Lecturer 2021(II)

Q40.Let (p, q) and (P, Q) be two pairs of canonical variables. The transformation P = qα sin (β p) and Q = qα cos (β p) is canonical for

A1 2, 2 α = β = B2, 2 α = β = C1, 2 2 α = β = D1 1 α = β =

Show answer