JNTU
JNTU B.Tech I Year MATHEMATICS-II Previous Question Paper (May - 2019 - R16)
Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks.
PART- A
Find L-1{1/(s-2)2}.
Answer
Using the shifting property L-1{F(s-a)} = eatf(t), where L-1{1/s2} = t, we get L-1{1/(s-2)2} = e2tt.
Define Unit step function and find its Laplace transform.
Answer
The unit step function u(t-a) is defined as 0 for t < a and 1 for t ≥ a. For a=0, u(t) = 1 for t ≥ 0. Its Laplace transform is L{u(t-a)} = e-as/s. For the standard unit step function u(t), L{u(t)} = 1/s.
Evaluate Γ(3/2).
Answer
Sign in to view the complete answer paper.
Evaluate the integral of (x5(1-x)6) from 0 to 1.
Answer
Sign in to view the complete answer paper.
Using triple integral, find the volume of a rectangular box whose length is 6 ft, breadth is 5 ft and height is 4 ft.
Answer
Sign in to view the complete answer paper.
Evaluate the double integral of (x+y) over x=0 to 1 and y=0 to x2.
Answer
Sign in to view the complete answer paper.
Define solenoidal vector.
Answer
Sign in to view the complete answer paper.
Prove that r is an irrotational vector where r = xi + yj + zk.
Answer
Sign in to view the complete answer paper.
State stokes theorem.
Answer
Sign in to view the complete answer paper.
Evaluate the volume integral of div(f) over a sphere of radius 'a' where f = xi + yj + zk.
Answer
Sign in to view the complete answer paper.
PART-B
Find the Laplace transform of (sin t + cos t)2.
Answer
Sign in to view the complete answer paper.
Find the inverse Laplace transform of 1 / ((s2+1)(s2+1)).
Answer
Sign in to view the complete answer paper.
Solve y'' + 2y' + 5y = e-t, y(0)=1, y'(0)=1 using Laplace transform.
Answer
Sign in to view the complete answer paper.
Evaluate the integral from 0 to infinity of e-xx3 dx.
Answer
Sign in to view the complete answer paper.
Evaluate the integral from 0 to 1 of x(1-x)4 dx.
Answer
Sign in to view the complete answer paper.
Evaluate the integral from 0 to infinity of e-xx7 dx.
Answer
Sign in to view the complete answer paper.
Evaluate the integral from 0 to 1 of x2(1-x4) dx.
Answer
Sign in to view the complete answer paper.
Evaluate the integral over x=0 to 2 and y=0 to sqrt(2x-x2) of (x2+y2) dydx by changing to polar coordinates.
Answer
Sign in to view the complete answer paper.
Evaluate the double integral of y dxdy where R is the region bounded by y2=4x and x2=4y.
Answer
Sign in to view the complete answer paper.
Evaluate the triple integral of xyz dxdydz taken through the positive octant of the sphere x2+y2+z2=a2.
Answer
Sign in to view the complete answer paper.
Evaluate the triple integral from 0 to a, 0 to x, 0 to x+y of ex+y+z dz dy dx.
Answer
Sign in to view the complete answer paper.
Find the directional derivative of f(x,y,z) = xy2z - 4, at the point (1, -1, 2) along i+j+k.
Answer
Sign in to view the complete answer paper.
A butterfly is located at (2, -1, 3) and desires to fly towards fragrance surface f(x,y,z)=x2+yz2. Along which direction should it fly to get fragrance at the earliest?
Answer
Sign in to view the complete answer paper.
Show that grad(rn) = n*rn-2*r.
Answer
Sign in to view the complete answer paper.
Prove that div(r3*r) = 3*r3.
Answer
Sign in to view the complete answer paper.
Verify Green's theorem for the integral (y-sin x)dx + cos x dy where C is the triangle enclosed by the lines y=0, x=pi/2, and pi*y=2x.
Answer
Sign in to view the complete answer paper.
Verify stokes theorem for a vector field defined by F = y3i - x3j in the region x2+y2<=1, z=0.
Answer
Sign in to view the complete answer paper.