Q. Consider the function f(x) = sin(x) in the interval [π/4, 7π/4]. The number and location(s) of the local minima of this function are

View solution

Q. The bisection method is applied to compute a zero of the function f(x) = x^4 – x^3 – x^2 – 4 in the interval [1,9]. The method converges to a solution after _______ iterations.

View solution

Q. Newton-Raphson method is used to compute a root of the equation x^2-13=0 with 3.5 as the initial value. The approximation after one iteration is

View solution

Q. What is the value of Limn->∞(1-1/n)^2n ?

View solution

Q. Two alternative packages A and B are available for processing a database having 10k records.Package A requires 0.0001n^2 time units and package B requires 10nlog10n time units to process n records.What is the smallest value of k for which package B will be preferred over A?

View solution

Q. The minimum number of equal length subintervals needed to approximate the following expression to an accuracy of 1/3 * 10^-6 at least  using the trapezoidal rule is

View solution

Q. A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve 3x^4 - 16x^3 + 24x^2 + 37

View solution

Q. Consider the following two statements about the function f(x)=|x|

P. f(x) is continuous for all real values of x
Q. f(x) is differentiable for all real values of x

Which of the following is TRUE?

View solution

Q. Consider the series Xn+1 = Xn/2 + 9/(8 Xn), X0 = 0.5 obtained from the Newton-Raphson method. The series converges to

View solution

Q. Consider the polynomial p(x) = a0 + a1x + a2x^2 + a3x^3 , where ai ≠ 0 ∀i. The minimum number of multiplications needed to evaluate p on an input x is:

View solution

Q. Consider the following system of equations:

3x + 2y = 1
4x + 7z = 1
x + y + z = 3
x – 2y + 7z = 0

The number of solutions for this system is __________________

View solution

Q. The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a 4-by-4 symmetric positive definite matrix is _____________________.

View solution

Q. A non-zero polynomial f(x) of degree 3 has roots at x = 1, x = 2 and x = 3. Which one of the following must be TRUE?

View solution

Q. In the Newton-Raphson method, an initial guess of x0 = 2 is made and the sequence x0, x1, x2 … is obtained for the function

0.75x^3 – 2x^2 – 2x + 4 = 0

Consider the statements
(I) x3 = 0.
(II) The method converges to a solution in a finite number of iterations.

Which of the following is TRUE?

View solution

Q. Consider a function f(x) = 1 – |x| on –1 ≤ x ≤ 1. The value of x at which the function attains a maximum and the maximum value of the function are:

View solution

Q. Let f(x) = x^ –(1/3) and A denote the area of the region bounded by f(x) and the X-axis, when x varies from –1 to 1. Which of the following statements is/are True?

1. f is continuous in [–1, 1]
2. f is not bounded in [–1, 1]
3. A is nonzero and finite

View solution

Q. The velocity v (in kilometer/minute) of a motorbike which starts from rest, is given at fixed intervals of time t(in minutes) as follows:

t 2 4 6 8 10 12 14 16 18 20
v 10 18 25 29 32 20 11 5 2 0

The approximate distance (in kilometers) rounded to two places of decimals covered in 20 minutes using Simpson’s 1/3rd rule is _________.

View solution

Q. Let X and Y be two exponentially distributed and independent random variables with mean α and β, respectively. If Z = min(X,Y), then the mean of Z is given by

View solution

Q. If f(1) = 2,f(2) = 4 and f(4) = 16, what is the value of f(3)using Lagrange’s interpolation formula?

View solution

Q. Consider the following iterative root finding methods and convergence properties:

Iterative root finding Convergence properties methods
(Q) False Position                        (I) Order of convergence = 1.62
(R) Newton Raphson                 (II) Order of convergence = 2
(S) Secant                                         (III) Order of convergence = 1 with guarantee of convergence
(T) Successive Approximation (IV) Order of convergence = 1 with no guarantee of convergence

View solution