List of top Engineering Mathematics Questions asked in GATE CE

Two vectors \([2 \, 1 \, 0 \, 3]^T\) and \([1 \, 0 \, 1 \, 2]^T\) belong to the null space of a \(4 \times 4\) matrix of rank 2. Which one of the following vectors also belongs to the null space?

The activities of a project are given in the following table along with their durations and dependency.

The total float of the activity \( E \) (in days) is _________ (in integer).

A pair of six-faced dice is rolled thrice. The probability that the sum of the outcomes in each roll equals 4 in exactly two of the three attempts is _________ (round off to three decimal places).

Let \(y\) be a non-zero vector of size \(2022 \times 1\). Which of the following statement(s) is/are TRUE?

Consider the polynomial \( f(x) = x^3 - 6x^2 + 11x - 6 \) on the domain \( S \) given by \( 1 \leq x \leq 3 \). The first and second derivatives are \( f'(x) \) and \( f''(x) \).
Consider the following statements:
I. The given polynomial is zero at the boundary points \( x = 1 \text{ and } x = 3. \)
II. There exists one local maxima of \( f(x) \text{ within the domain } S. \)
III. The second derivative \( f''(x)>0 \text{ throughout the domain } S. \)
IV. There exists one local minima of \( f(x) \text{ within the domain } S. \)
The correct option is:

The error in measuring the radius of a 5 cm circular rod was 0.2%. If the cross-sectional area of the rod was calculated using this measurement, then the resulting absolute percentage error in the computed area is _________ % . (round off to two decimal places).

P and Q are two square matrices of the same order. Which of the following statement(s) is/are correct?

The components of pure shear strain in a sheared material are given in the matrix form:
\[ \epsilon = \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix} \] Here, \(\text{Trace}(\epsilon) = 0\). Given, P = \text{Trace}(\epsilon^8) and Q = \text{Trace}(\epsilon^{11}). \text{The numerical value of} (P + Q) \text{ is} _________ \text{. (in integer)}.

The integral \( \int \left( \frac{x}{2} - \frac{x^2}{3} + \frac{x^3}{4} - \cdots \right) \, dx \) is equal to

The function \( f(x, y) \) satisfies the Laplace equation
\[ \nabla^2 f(x, y) = 0 \] on a circular domain of radius \( r = 1 \) with its center at point P with coordinates \( x = 0, y = 0 \). The value of this function on the circular boundary of this domain is equal to 3.
The numerical value of \( f(0, 0) \) is: