List of top Mathematics Questions asked in GATE Aerospace Engineering

The eigenvalues of the matrix
\[ \begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix} \]
are _______ .

For any real symmetric matrix $ A $, the transpose of $ A $ is ________ .

The eigenvalues of the matrix \[ \begin{bmatrix} 1 & 2
0 & 3 \end{bmatrix} \] are \_\_\_\_\_ .

Solve the system of equations: \[ 2x + 3y + z = 0 \] \[ x + y = 0 \] \[ y + z = 0 \] The given system of equations has:

For any real symmetric matrix $ A $, the transpose of $ A $ is \_\_\_\_ .

The eigenvalues of the matrix \[ \begin{bmatrix} 1 & 2
0 & 3 \end{bmatrix} \] are \_\_\_\_\_ .

Solve the system of equations: \[ 2x + 3y + z = 0 \] \[ x + y = 0 \] \[ y + z = 0 \] The given system of equations has:

For any real symmetric matrix $ A $, the transpose of $ A $ is \_\_\_\_ .

Solve the system of equations: \[ 2x + 3y + z = 0 \] \[ x + y = 0 \] \[ y + z = 0 \] The given system of equations has:

If two distinct non-zero real variables $x$ and $y$ are such that $(x+y)$ is proportional to $(x-y)$ then the value of $\dfrac{x}{y}$ is ?

For positive non-zero real variables $p$ and $q$, if \[ \log(p^2 + q^2) = \log p + \log q + 2 \log 3, \] then, the value of \[ \frac{p^4 + q^4}{p^2 q^2} \] is ?

A rectangular paper sheet of dimensions $54\text{ cm} \times 4\text{ cm}$ is taken. The two longer edges of the sheet are joined together to create a cylindrical tube. A cube whose surface area is equal to the area of the sheet is also taken. Then, the ratio of the volume of the cylindrical tube to the volume of the cube is

A rectangular paper of $20 \, \text{cm} \times 8 \, \text{cm}$ is folded 3 times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. The perimeter of the final folded sheet (in cm) is:

A circle of radius $R$ is centered at the origin. The shaded top portion is bounded above by the circle and below by the horizontal chord through the point where the radius makes $60^\circ$ with the $\boldsymbol{y}$-axis (see figure). The solid formed by a complete rotation of this shaded part about the $y$-axis has volume $k\pi R^{3}$. Find $k$.

Given the function $y(x)=(x+3)(x-2)$, for $-4<x<4$. What is the value of $x$ at which the function has a minimum?

Which of the following shapes can be used to tile (completely cover by repeating) a flat plane infinitely in all directions, without leaving gaps or overlaps?

Find the coefficient of $x^4$ in $(x-1)^3(x-2)^3$.

In the given figure, $PQRS$ is a parallelogram with $PS = 7\text{ cm}$, $PT = 4\text{ cm}$ and $PV = 5\text{ cm}$. What is the length of $RS$ (in cm)? (The diagram is representative.) \begin{center} \includegraphics[width=0.5\textwidth]{01.jpeg} \end{center}

A line of symmetry divides a figure into two parts that are mirror images. The given figure consists of 16 unit squares. Three are already black. What is the minimum number of additional squares that must be coloured black so that both $PQ$ (vertical midline) and $MN$ (diagonal) are lines of symmetry? \begin{center} \includegraphics[width=0.5\textwidth]{02.jpeg} \end{center}