Math Chapter Wise

EnglishUPPSC Polytechnic Lecturer 2021(II)

Q61.When the Lagrangian function 'L' does not contain the time explicitly, the Hamiltonian equation given an equation of -

AMoment BForce CEnergy DNone of these

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q62.The number of generalized coordinates required to describe the motion of a rigid body with one of its point fixed is -

A8 B6 C1 D3

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q63.The solution of Brachistochrone problem is -

Aa catenary Ba cardioids Ca parabola Dan inverted cycloid

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q64.If the Hamiltonian 'H' is independent of 't' explicitly, then -

Aand BImage/formula option B (see source) CBoth DNone of these

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q65.If the minimum of the surface area of revolution of a curve y = y(x) is () 2 1 x 2 x 2 y 1 y' dx π + ∫ then the curve is -

Aa line Ban ellipse Ca circle Da catenary

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q66.The Lagrangian of a system is 2 • 13 L = mx 2 + i i • 2 4mxy+ 3my – mg(x + 2y) Which one of the following is conserved?

A11x y + i B11x y − i Cx 11y + i Dx 11y − i

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q67.When the position of a body is determined by the values of a number of independent variables, it has the same number of degrees of freedom and these independent variables are said to be -

Aindependent coordinates Bgeneralized coordinates CBoth (a) and (b) DNone of these

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q68.When the geometrical relations of a dynamical system are such that a displacement represented by arbitrary infinitesimal changes in all its independent coordinates is a possible displacement, the system is said to be -

Aand BImage/formula option B (see source) CBoth DNone of these

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q69.The mechanical system in which 't' the time, does not enter explicitly in rv = rv (q1, q2...,t) is called –

AHolonomic system BRheonomic system CScleronomic system DNome of these

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q70.Consider a system with generalized coordinates q1, q2........ qn and Lagrangian function L. If pr = ∂ i r L q and H = ∑ i n r r r=1 p q -L be the Hamiltonian function, then Hamilton's canonical equations of motion are -

Aqr = r r r H H,p p q ∂ ∂ = ∂ ∂ i i Bqr = r r r H H,p p q ∂ ∂ = ∂ ∂ i Cr r H H q p, p q ∂ ∂ = − ∂ ∂ i i Dr r H H q p, p q ∂ ∂ = − = ∂ ∂ i i

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q71.Let q1, q2.........., qn denote generalized coordinates of a material system. If 'T' is the kinetic energy and 'V' is the potential energy of the system and L = T – V is the Lagrangian function, then the Lagrange's equation of motion are -

Ar r d L L 0,(r 1,2,...,n) dt q q ∂ ∂ + = ∂ ∂ i Br d L L 0,(r 1,2,...,n) dt q q ∂ ∂ − = ∂ i Cr r d L L 0,(r 1,2,...,n) dt q q ∂ ∂ − = ∂ ∂ i Dr d L L 0,(r 1,2,...,n) dt q q ∂ ∂ + = ∂ i

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q72.A circular cylinder of radius 'a' is moving in an infinite mass of liquid at rest at infinity with velocity U in the direction of the x - axis. The complex potential of this motion is -

AUz + 2 Ua z B2 Ua z CUz – 2 Ua z DNone of these

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q73.The families of curves given by constant velocity potential and constant stream function intersect each other -

Aat an acute angle Bat an obtuse angle Corthogonally DNone of these

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q74.The image of a source with regard to a circle is-

Aan equal sink at the inverse point and an equal source at the centre of the circle Ban equal source at the inverse point and an equal sink at the centre of the circle Can equal source at the inverse point and an equal source at the centre of the circle. DNone of these

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q75.If the velocity vector q is given by ˆ ˆ q = xi - yj, then the stream lines are -

Aellipses Bcircles Cparabolas Drectangular hyperbolas

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q76.The velocity in a three dimensional flow field for an incompressible fluids is ˆ ˆ ˆ q = 2xi - yj- zk. Then the equation of the stream lines passing through the point (1, 1, 1) are -

Axy2 = 1 and xz2 = 1 Bxy = 1 and yz = 1 Cx2 y = 1 and x2 z = 1 D2 x y 1 and 1 y z =

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q77.The flow for the given velocity ˆ ˆ 2 2 -iy + jx q= x + y is –

Airrotational anywhere Birrotational at the origin only Crotational at the origin Dirrotational except at the origin

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q78.In an irrotational motion, the maximum value of the speed must occur on the -

Amiddle point Bany point Cboundary DNone of these

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q79.The streamlines of the velocity potential () φ 2 2 2 1 = a x + y – 2z 2 are -

Axy = A and zy = B Bx y = A and y2 z = B Cx = Ay2 and zy2 = B DNone of these

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q80.The equation of continuity in lagrangian form, where J = ∂ (x,y,z),ρ (a,b,c) is the density of the fluid at time t and ρ0 is the density of the fluid at t = 0, is -

Aρ0 J = ρ BρJ = ρ0 Cρ = ρ0 DNone of these

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