Engineering Mathematics II Past Questions
Engineering Mathematics II past questions are arranged by marks for quick revision. Tap any question to open its exact workbook page, complete solution and video area.
36 Questions of 2 Marks31 Questions of 4 MarksRepeated Questions RetainedOR Questions Included
2 Marks Questions
36 Questions- 1 Question 1.If \(u=\sin^{-1}\!\left(\frac{x^2+y^2}{x+y}\right)\), show the required result.2083 Baisakh • Q. 1(a) • 2 Marks • Page 1
- 2 Question 2.Show \(xu_x+yu_y=\sin 2u\) for the given inverse tangent.2082 Bhadra • Q. 1(a) • 2 Marks • Page 1
- 3 Question 3.Use Euler's theorem for \(u=\tan^{-1}(x^2+2y^2)\).2081 Ashwin • Q. 1(a) • 2 Marks • Page 1
- 4 Question 4.Find \(\frac{\partial(u,v,w)}{\partial(x,y,z)}\) for the given functions.2083 Baisakh • Q. 1(b) • 2 Marks • Page 2
- 5 Question 5.Find \(\frac{\partial(x,y)}{\partial(r,\theta)}\) for polar coordinates.2082 Bhadra • Q. 1(b) • 2 Marks • Page 2
- 6 Question 6.If \(u=x^2\) and \(v=y^2\), find the Jacobian.2081 Ashwin • Q. 1(b) • 2 Marks • Page 2
- 7 Question 7.Evaluate \(\int_1^2\!\int_0^x\frac{dy\,dx}{x^2+y^2}\).2083 Baisakh • Q. 2(a) • 2 Marks • Page 3
- 8 Question 8.Evaluate the given triple integral of \(x+y+z\).2081 Ashwin • Q. 2(a) • 2 Marks • Page 3
- 9 Question 9.Find the mass with density \(\rho=z(y+2)\).2083 Baisakh • Q. 2(b) • 2 Marks • Page 4
- 10 Question 10.Evaluate the mass with density \(\rho=z(y+2)\).2081 Ashwin • Q. 2(b) • 2 Marks • Page 4
- 11 Question 11.Find the moment about the \(x\)-axis of the lamina.2082 Bhadra • Q. 2(a) • 2 Marks • Page 4
- 12 Question 12.Find the area between \(x=y^2\) and \(x=2y-y^2\).2082 Bhadra • Q. 2(b) • 2 Marks • Page 4
- 19 Question 19.Find the directional derivative at \((1,2,1)\).2083 Baisakh • Q. 3(a) • 2 Marks • Page 5
- 20 Question 20.Find the directional derivative at \((1,2,1)\).2081 Ashwin • Q. 3(a) • 2 Marks • Page 5
- 21 Question 21.Find velocity and acceleration at \(t=\frac{\pi}{3}\).2082 Bhadra • Q. 3(a) • 2 Marks • Page 6
- 22 Question 22.Find velocity and acceleration at \(t=\frac{\pi}{4}\).2081 Ashwin • Q. 3(b) • 2 Marks • Page 6
- 23 Question 23.Prove that the given vector field is solenoidal.2083 Baisakh • Q. 3(b) • 2 Marks • Page 7
- 24 Question 24.If \(\mathbf F=\mathrm{grad}(x^3+y^3+z^3-3xyz)\), find \(\mathrm{div}\,\mathbf F\).2082 Bhadra • Q. 3(b) • 2 Marks • Page 7
- 25 Question 25.Find \(\mathrm{div}(\mathrm{grad}\,\phi)\) at \((1,-1,1)\).2081 Ashwin • Q. 3(c) • 2 Marks • Page 7
- 26 Question 26.Find \(\nabla\times(\nabla\phi)\) for the given scalar function.2083 Baisakh • Q. 3(c) • 2 Marks • Page 8
- 27 Question 27.Find work done along \(x^2+y^2=1\), \(z=0\).2082 Bhadra • Q. 3(c) • 2 Marks • Page 8
- 39 Question 39.State existence criteria and find \(\mathcal L\!\left\{\frac{1-e^t}{t}\right\}\).2083 Baisakh • Q. 4(a) • 2 Marks • Page 9
- 40 Question 40.State the condition and find \(\mathcal L\{t\sin3t\}\).2082 Bhadra • Q. 4(a) • 2 Marks • Page 9
- 41 Question 41.Find \(\mathcal L\!\left\{\frac{1-e^t}{t}\right\}\).2081 Ashwin • Q. 4(a) • 2 Marks • Page 9
- 42 Question 42.Find \(\mathcal L^{-1}\!\left\{\frac{1}{s^2-3s+2}\right\}\).2083 Baisakh • Q. 4(b) • 2 Marks • Page 10
- 43 Question 43.Find \(\mathcal L^{-1}\{\cot^{-1}(s+1)\}\).2082 Bhadra • Q. 4(b) • 2 Marks • Page 10
- 44 Question 44.Find \(\mathcal L^{-1}\!\left\{\frac{s}{(s+2)^3}\right\}\).2081 Ashwin • Q. 4(b) • 2 Marks • Page 10
- 48 Question 48.Find the rank of the given \(3\times3\) matrix.2083 Baisakh • Q. 5(a) • 2 Marks • Page 11
- 49 Question 49.Find the rank of the given \(3\times4\) matrix.2082 Bhadra • Q. 5(a) • 2 Marks • Page 11
- 50 Question 50.Find the rank of the given \(3\times5\) matrix.2081 Ashwin • Q. 5(a) • 2 Marks • Page 11
- 51 Question 51.Test whether the three given vectors are linearly independent.2081 Ashwin • Q. 5(b) • 2 Marks • Page 12
- 52 Question 52.Find the eigenvalues of the given \(3\times3\) matrix.2083 Baisakh • Q. 5(b) • 2 Marks • Page 12
- 58 Question 58.Reduce \(17x_1^2-30x_1x_2+17x_2^2\) to canonical form.2082 Bhadra • Q. 5(b) • 2 Marks • Page 13
- 60 Question 60.Express \(1+x-x^2\) using Legendre polynomials.2083 Baisakh • Q. 6 • 2 Marks • Page 14
- 61 Question 61.Express \(4+2x+x^2\) using Legendre polynomials.2082 Bhadra • Q. 6 • 2 Marks • Page 14
- 62 Question 62.Express \(2x^2-4x+2\) using Legendre polynomials.2081 Ashwin • Q. 6 • 2 Marks • Page 14
4 Marks Questions
31 Questions- 13 Question 13.Change the order and evaluate the given infinite integral.2083 Baisakh • Q. 8 • 4 Marks • Page 16
- 14 Question 14.Change the order of \(\int_0^1\!\int_{x^2}^{2-x}xy\,dy\,dx\).2082 Bhadra • Q. 8 • 4 Marks • Page 16
- 15 Question 15.Change the order and evaluate the given triangular-region integral.2081 Ashwin • Q. 8 • 4 Marks • Page 16
- 16 Question 16.Find the extreme value subject to \(x+2y+4z=60\).2083 Baisakh • Q. 7 • 4 Marks • Page 15
- 17 Question 17.Find extrema of \(x^2+y^2+z^2\), subject to \(x+y+z=1\).2082 Bhadra • Q. 7 • 4 Marks • Page 15
- 18 Question 18.Find the minimum value using Lagrange multipliers.2081 Ashwin • Q. 7 • 4 Marks • Page 15
- 28 Question 28.Prove the condition \(\mathbf a\cdot\frac{d\mathbf a}{dt}=0\).2083 Baisakh • Q. 9 • 4 Marks • Page 17
- 29 Question 29.Prove the condition \(\mathbf a\times\frac{d\mathbf a}{dt}=0\).2082 Bhadra • Q. 9 • 4 Marks • Page 17
- 30 Question 30.Prove the condition \(\mathbf a\times\frac{d\mathbf a}{dt}=0\).2081 Ashwin • Q. 9 • 4 Marks • Page 17
- 31 Question 31.Use Green's theorem to find the area of an astroid.2083 Baisakh • Q. 10 • 4 Marks • Page 18
- 32 Question 32.Use Green's theorem to find the hypocycloid's area.2082 Bhadra • Q. 10 • 4 Marks • Page 18
- 33 Question 33.Find the astroid's area using Green's theorem.2081 Ashwin • Q. 10 • 4 Marks • Page 18
- 34 Question 34.Apply Gauss' theorem to the first-octant tetrahedron.2083 Baisakh • Q. 11 • 4 Marks • Page 19
- 35 Question 35.Apply Gauss' theorem to the given parallelepiped.2082 Bhadra • Q. 11 • 4 Marks • Page 19
- 36 Question 36.Apply Gauss' theorem to the closed cylinder.2081 Ashwin • Q. 11 • 4 Marks • Page 19
- 37 Question 37.Apply Stokes' theorem around the given square.2083 Baisakh • Q. 11 OR • 4 Marks • Page 20
- 38 Question 38.Apply Stokes' theorem around the given triangle.2082 Bhadra • Q. 11 OR • 4 Marks • Page 20
- 45 Question 45.Solve \(y''+4y'+4y=e^{-t}\) using Laplace transforms.2083 Baisakh • Q. 12 • 4 Marks • Page 21
- 46 Question 46.Solve \(x''-3x'+2x=e^{-t}\) using Laplace transforms.2082 Bhadra • Q. 12 • 4 Marks • Page 21
- 47 Question 47.Solve \(y''-y'+6y=e^{-t}\) using Laplace transforms.2081 Ashwin • Q. 12 • 4 Marks • Page 21
- 53 Question 53.Find the eigenvalues and eigenvectors of the given matrix.2081 Ashwin • Q. 13 • 4 Marks • Page 22
- 54 Question 54.Test consistency and solve the given system of equations.2083 Baisakh • Q. 13 • 4 Marks • Page 23
- 55 Question 55.Use Cayley-Hamilton theorem to find \(A^{-1}\).2082 Bhadra • Q. 13 • 4 Marks • Page 24
- 56 Question 56.Diagonalise the given \(2\times2\) matrix.2082 Bhadra • Q. 14 • 4 Marks • Page 25
- 57 Question 57.Reduce the given quadratic form to canonical form.2083 Baisakh • Q. 14 • 4 Marks • Page 26
- 59 Question 59.Reduce the given quadratic form to canonical form.2081 Ashwin • Q. 14 • 4 Marks • Page 26
- 63 Question 63.Solve \(y''-4xy'+(4x^2-2)y=0\) by power series.2083 Baisakh • Q. 15 • 4 Marks • Page 27
- 64 Question 64.Solve \(y''+xy'+y=0\) by power series.2082 Bhadra • Q. 15 • 4 Marks • Page 27
- 65 Question 65.Solve \(y''-4xy'+(4x^2-2)y=0\) by power series.2081 Ashwin • Q. 15 • 4 Marks • Page 27
- 66 Question 66.Prove the stated formula for \(J_{5/2}(x)\).2083 Baisakh • Q. 15 OR • 4 Marks • Page 28
- 67 Question 67.Prove the stated formula for \(J_{5/2}(x)\).2082 Bhadra • Q. 15 OR • 4 Marks • Page 28
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