List of top Engineering Mathematics Questions

If population variance is 14.8, sample variance is 15.4 and the number of degrees of freedom is 10, then Chi-square value is __________________ (round off to 2 decimal places).

Most probable value of a quantity

The probability of having 53 Sundays in a randomly selected leap year is __________.

The root of the equation $ \sin x - 4x + 1 = 0 $ after its first iteration, using the Newton-Raphson method with an initial guess of $ x_0 = 0.2 $, is _____.$ \textit{[Round off to three decimal places.]}$

The slope of the function $ f(x) = 2x^4 - 3x^2 + 5x $ at $ x = 2 $ is _____. $\textit{[Answer in integer.]}$

The matrix \[ \begin{bmatrix} 3 - x & 2 & 2 \\ 2 & 4 - x & 1 \\ -2 & -4 & -1 - x \end{bmatrix} \] is singular for the following values of $x$.

Work done by a moving particle in the force field $ \mathbf{F} = 6x^2 \hat{i} + (3xz + y) \hat{j} + 4z \hat{k} $, moving along the straight line from (0,0,0) to (1,2,3) is _____. $\textit{[Answer in integer]}$

The power consumption readings (in watt) by an instrument at fixed intervals of time (in seconds) are tabulated below:

\[ \begin{array}{|c|c|} \hline \text{Time (s)} & \text{Power consumption (W)} \\ \hline 0.0 & 8.6 \\ 0.6 & 9.2 \\ 1.2 & 7.8 \\ 1.8 & 6.4 \\ 2.4 & 7.2 \\ 3.0 & 8.6 \\ 3.6 & 11.2 \\ \hline \end{array} \]
Using Simpson's 1/3rd rule, the energy expenditure of the instrument in joules is _____.[Round off to two decimal places]

The function $ (x - 2)^2 (x + 2)^2 $ has

Function $ f(x) $ by Maclaurin's series (as an infinite series) can be expressed as:

Determinant of a matrix remains unaltered if __________.

Let $x$ be a real number and $i=\sqrt{-1}$. Then the real part of $\cos(ix)$ is

In a cosmopolitan city, the population comprises of 30% female and 70% male. Suppose that 5% of females and 30% of males in the population are foreigners. A person is selected at random from this population. Given that the selected person is a foreigner, the probability that the person is a female is ________ (round off to three decimal places).

If the quadrature rule \[ \int_{-1}^1 f(x) \, dx \approx f(\alpha) + \gamma f(\beta), \] where $ \alpha, \beta $ and $ \gamma $ are real constants, is exact for all polynomials of degree $ \leq 3 $, then $ \gamma + 3 (\alpha^2 + \beta^2) + (\alpha^3 + \beta^3) $ is equal to ________.

Let \[ A = \begin{pmatrix} 2 & 0 & 1 \\ 1 & 2 & 5 \\ 0 & 3 & 0 \\ 0 & 0 & 1 \end{pmatrix} \] . Then the sum of the geometric multiplicities of the distinct eigenvalues of $ A $ is equal to ________.

Let $ A $ and $ B $ be $ n \times n $ matrices with real entries. Consider the following statements:

P: If $ A $ is symmetric, then rank($ A $) = Number of nonzero eigenvalues (counting multiplicity) of $ A $
Q: If $ AB = 0 $, then rank($ A $) + rank($ B $) $ \leq n $

Then:

Let $ f : (0, \infty) \to \mathbb{R} $ be the continuous function such that:

\[ f(x) = 2 + \frac{g(x)}{x} \quad \text{for all} \ x > 0, \quad g(x) = \int_1^x f(t) \, dt \quad \text{for all} \ x > 0. \]

Then $ f(2) $ is equal to:

Let $ f : \mathbb{R}^2 \to \mathbb{R} $ be given by \[ f(x, y) = 4xy - 2x^2 - y^4 + 1. \] The number of critical points where $ f $ has local maximum is equal to ________.

Let $ \mathbb{C} = \{ z = x + iy : x \text{ and } y \text{ are real numbers}, i = \sqrt{-1} \} $ be the set of complex numbers. Let the function $ f(z) = u(x, y) + i v(x, y) $ for $ z = x + iy \in \mathbb{C} $ be analytic in $ \mathbb{C} $, where \[ u(x, y) = x^3 y - y x^3 \quad \text{and} \quad v(x, y) = \frac{x^4}{4} + \frac{y^4}{4} - \frac{3}{2} x^2 y^2. \] If $ f'(z) $ denotes the derivative of $ f(z) $, then:

If the partial differential equation \[ (x + 2) \frac{\partial^2 u}{\partial x^2} + 2(x + y) \frac{\partial^2 u}{\partial x \partial y} + 2(y - 1) \frac{\partial^2 u}{\partial y^2} - 3y^2 \frac{\partial u}{\partial y} = 0 \] is parabolic on the circle $ (x - a)^2 + (y - b)^2 = r^2 $, then the values of $ a $, $ b $, and $ r $ are given by: