JNTU B.Tech II MATHEMATICS-II Previous Question Paper (September/October - 2023 - R13)

Calculate the Curl of the vector xyz i + 3x²y j + (xz² - y²z)k.

Is the gradient describing the motion of a fluid as Irrotational? Explain.

Find the constant term in the Fourier series expansion for the function f(x) = x in (0, 2π).

State the change of scale property for the Fourier Transform and prove it.

Write the geometrical interpretation of the Newton-Raphson method.

Find the interpolating polynomial for the data:

Explain the regula-falsi method.

Write the Newton-Raphson procedure to find N^1/3.

State the Simpson’s 3/8 rule.

Prove that ∇(fⁿ) = nf^n-1∇f.

Evaluate ∫_C F·dr around the boundary C of the region R by Green’s Theorem, where F = (x² - y)i + (x+y²)j and R is 1 ≤ x² + y² ≤ 4, x ≥ 0, y ≥ 0.

At what point P(x, y, z) does the directional derivative of f = 25x² + 9y² + 16z² be in the direction from P to the origin?

Evaluate ∫∫_S F·n dS, where F = (0, sinh z, cosh y) and S: x² + y² = 4, 0 ≤ z ≤ 5, x ≥ 0, y ≥ 0.

Find the Fourier series for the given function with period 2π and deduce the sum of the series 1 + 1/9 + 1/25 + ...

Find the Fourier series for f(x) = lx - x² in 0 < x < l.

Find the Fourier transform of f(x) = a² - x² if |x| < a, else 0. Hence evaluate the specific integral provided.

Find the inverse Fourier sine transform of F(p) = p / (1 + p²).

Construct Newton’s forward interpolation polynomial for the given data and evaluate y at x = 5.

Evaluate (i) Δ² sin(px + q), (ii) Prove the identity involving central differences.

Prove the specified identity involving finite differences.

Fit a curve of the form y = ax² from the provided data.

Find the real root of xe^x = 2 by false position method.

Find the real root of x - cos x = 0 by Newton-Raphson method.

Apply iteration method to find real roots of e^-x - sin x = 0.

Derive formula for k-th root of N using Newton-Raphson and solve tan x = 1.2x.

Solve dy/dx = 1/(x² + y) with y(4) = 4 for y(4.1) and y(4.2) using Taylor’s series.

Solve dy/dx = x + xy⁴, y(0) = 3 for y(0.1) and y(0.2) by Picard’s method.