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Questions without a selected answer in Engineering Mathematics

1 1 vote
1 1 answer
GATE IN 2026 | Question: 1
A matrix $P \in \mathbb{R}^{3 \times 3}$ satisfies $P^{3}-4 P^{2}+5 P-2 I=0$ where $I$ is a $3 \times 3$ identity matrix.The set of all possible eigenvalues of matrix $P$...
0 0 votes
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GATE IN 2026 | Question: 2
Which one among the following statements is true for the function $f(x)=x\mid x \mid $?$f(x)$ is discontinuous but not differentiable at $x=0$.$f(x)$ is discontinuous and...
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GATE IN 2026 | Question: 3
Consider a function $f(z)=z^{2}+z+1$ where $z \in \mathbb{C}$ is a complex variable. A simple closed contour $\gamma$ in $z$-plane encloses the point $z=1+0 j$.The value ...
2 2 votes
1 1 answer
GATE IN 2026 | Question: 4
Consider a matrix$A=\left[\begin{array}{ccc}1 & 0 & 2 \\-1 & 1 & 0 \\0 & 1 & 2\end{array}\right]$Let $\boldsymbol{b}=\left[\begin{array}{l}1 \\ 3 \\ 0\end{array}\right]$ ...
0 0 votes
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GATE IN 2026 | Question: 21
A data set is given to be $[1,2,0,-1,-3,1,2,0,1]$.The median of the data set is $\_\_\_\_$ . (rounded off to the nearest integer)
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GATE IN 2026 | Question: 26
A box contains three apples and two oranges. Two fruits are removed randomly in succession. The probability that the first is an apple and the second is an orange is $\_\...
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GATE IN 2026 | Question: 44
Given a differential equation $\dfrac{d^{2} x}{d t^{2}}+x=0$ with $x(0) \neq 0$.Which of the following statements is/are true?$\mid x(t) \mid ^{2}+\left|\dfrac{d x(t)}{d ...
0 0 votes
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GATE IN 2025 | GA | Question: 3
If $P e^{x}=Q e^{-x}$ for all real values of $x$, which one of the following statements is true?$P=Q=0$$P=Q=1$$P=1 ; Q=-1$$\frac{P}{Q}=0$
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GATE IN 2025 | GA | Question: 8
Which one of the following options is correct for the given data in the table?$\begin{array}{|c|c|c|c|c|}\hline\text{Iteration (i)} & 0 & 1 & 2 & 3 \\ \hline\text{Input (...
4 4 votes
2 2 answers
GATE IN 2025 | Question: 1
A $2 n \times 2 n$ matrix $A=\left[a_{i j}\right]$ has its elements as$$ a_{i j}=\begin{cases} \beta & \text { if }(i+j) \text { is odd } \\ -\beta & \text { if }(i+j) \t...
0 0 votes
1 1 answer
GATE IN 2025 | Question: 2
The solution of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}=9 \frac{x}{y}$ representsa hyperbolaa parabolaan ellipsea circle
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GATE IN 2025 | Question: 22
If one of the eigenvectors of the matrix $A=\left[\begin{array}{cc}-1 & -1 \\ x & -4\end{array}\right]$ is along the direction of $\left[\begin{array}{c}\alpha \\ 2 \alph...
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GATE IN 2025 | Question: 23
Consider the function $f(z)=\frac{2 z+1}{z^{2}-z}$, where $z$ is a complex variable. The sum of the residues at singular points of $f(z)$ is ______________ (in integer).
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GATE IN 2025 | Question: 26
The value of the surface integral $\iint_{S}(2 x+z) \mathrm{d} y \mathrm{~d} z+(2 x+z) \mathrm{d} x \mathrm{~d} z+(2 z+y) \mathrm{d} x \mathrm{~d} y$ over the sphere $S: ...
0 0 votes
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GATE IN 2025 | Question: 27
Newton-Raphson method is used to compute the inverse of the number $1.6$. Among the following options, the initial guess of the solution that results in non-convergence o...
0 0 votes
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GATE IN 2025 | Question: 28
The value of the integral $\int_{-\pi}^{\pi}\left(\cos ^{6} x+\cos ^{4} x\right) \mathrm{d} x$ is$\frac{\pi}{2}$$\frac{5 \pi}{8}$$\frac{11 \pi}{8}$$\frac{9 \pi}{8}$
0 0 votes
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GATE IN 2025 | Question: 39
Choose the correct statement(s) from the following options, regarding Cauchy's theorem on complex integration $\oint_{C} f(z) \mathrm{d} z$ where $C$ is a simple closed p...
0 0 votes
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GATE IN 2025 | Question: 42
The probability of a student missing a class is $0.1$. In a total number of $10$ classes, the probability that the student will not miss more than one class is __________...
0 0 votes
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GATE IN 2024 | Question: 1
​​​Let $\boldsymbol{z}=x+i y$ be a complex variable and $\overline{\boldsymbol{z}}$ be its complex conjugate. The equation $\bar{z}^{2}+z^{2}=2$ represents aparabolahyper...
2 2 votes
1 1 answer
GATE IN 2024 | Question: 9
A matrix $M$ is constructed by stacking three column vectors $v_{1}, v_{2}, v_{3}$ as$$ M=\left[\begin{array}{lll} v_{1} & v_{2} & v_{3} \end{array}\right]$$Choose the se...
0 0 votes
1 1 answer
GATE IN 2024 | Question: 16
A $3 \times 3$ matrix $P$ with all real elements has eigenvalues $\dfrac{1}{4}, 1$, and $-2$. The value of $\mid P^{-1}\mid$ is $\_\_\_\_\_\_$ (rounded off to nearest int...
0 0 votes
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GATE IN 2024 | Question: 24
Consider a system given by the following first order differential equation:$$ \frac{d y}{d t}=y+2 t-t^{2} $$where, $y(0)=1$ and $0 \leq t<\infty$. Using a step size $h=0....
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GATE IN 2024 | Question: 25
Indian Premier League has divided the sixteen cricket teams into two equal pools: Pool-A and Pool-B. Four teams of Pool-A have blue logo jerseys while the rest four have ...
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GATE IN 2024 | Question: 36
​​Let $C$ be the closed curve in the $x y$-plane, traversed in the counterclockwise direction along the boundary of the rectangle with vertices at $(0,0),(2,0),(2,1),(0,1...
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GATE IN 2024 | Question: 39
​​The complex functions $f(z)=u(x, y)+i ~v(x, y)$ and $\overline{f(z)}=u(x, y)-i~ v(x, y)$ are both analytic in a given domain. Choose the correct option(s) from the foll...
0 0 votes
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GATE IN 2024 | Question: 40
The readings recorded from a $20$ -psig pressure gauge are given in the Table. The regression line obtained for the data is $y=0.04~ x+10.32$. The regression coefficient ...
0 0 votes
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GATE IN 2024 | Question: 54
The solution of an ordinary differential equation $y^{\prime \prime \prime}+3 y^{\prime \prime}+3 y^{\prime}+y=30 e^{-t}$ is$$y(t)=\left(c_{0}+c_{1} t-c_{2} t^{2}+c_{3} t...
0 0 votes
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GATE IN 2024 | Question: 55
A random variable $X$ has a probability density function$$f_{X}(x)=\begin{cases} e^{-x}, & x \geq 0 \\ 0, & \text { otherwise } \end{cases}$$The probability of $X>2$ is $...
0 0 votes
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GATE IN 2023 | Question: 1
Choose solution set $S$ corresponding to the systems of two equations$$\begin{array}{r}x-2 y+z=0 \\x-z=0\end{array}$$Note: $\mathscr{R}$ denotes the set of real numbers$S...
0 0 votes
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GATE IN 2023 | Question: 9
$F(z)=\frac{1}{1-z}$, when expanded as a power series around $z=2$, would result in $F(z)=\sum_{k=0}^{\infty} a_k(z-2)^k$, with the region of convergence $\text{(ROC) } |...
0 0 votes
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GATE IN 2023 | Question: 10
The solution $x(t), t \geq 0$, to the differential equation $\ddot{x}=-k \dot{x}, k>0$ with initial conditions $x(0)=1$ and $\dot{x}(0)=0$ is$x(t)=2 e^{-k t}+2 k t-1$$x(t...
0 0 votes
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GATE IN 2023 | Question: 13
What is $\lim _{x \rightarrow 0} f(x)$, where $f(x)=x \sin \frac{1}{x} ?$$0$$1$$\infty$Limit does not exist
0 0 votes
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GATE IN 2023 | Question: 22
$X$ is a discrete random variable which takes values $0,1$ and $2.$ The probabilities are $P(X=0)=0.25$ and $P(X=1)=0.5$. With $E[ .]$ denoting the expectation operator, ...
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GATE IN 2023 | Question: 29
Let $f(z)=j \frac{1-z}{1+z}$, where $z$ denotes a complex number and $j$ denotes $\sqrt{-1}$. The inverse function $f^{-1}(z)$ maps the real axis to the___________.unit c...
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GATE IN 2023 | Question: 43
Five measurements are made using a weighing machine, and the readings are $80 \mathrm{~kg}, 79 \mathrm{~kg}, 81 \mathrm{~kg}, 79 \mathrm{~kg}$ and $81 \mathrm{~kg}$. The ...
0 0 votes
1 1 answer
GATE IN 2023 | Question: 47
Consider the real-valued function $g(x)=\max \left\{(x-2)^2,-2 x+7\right\}$, where $x \in(-\infty, \infty)$. The minimum value attained by $g(x)$ is_____________(rounded ...
2 2 votes
1 1 answer
GATE IN 2023 | Question: 53
The rank of the matrix $A$ given below is one. The ratio $\frac{\alpha}{\beta}$ is __________ (rounded off to the nearest integer).$$A=\left[\begin{array}{cc}1 & 4 \\-3 &...
1 1 vote
0 0 answers
GATE IN 2022 | Question: 14
Given $\text{M} = \begin{bmatrix} 2 & 3 & 7 \\ 6 & 4 & 7 \\ 4 & 6 & 14 \end{bmatrix},$ Which of the following statement(s) is/are correct?The rank of $\text{M}$ is $2$The...
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GATE IN 2022 | Question: 18
The global minimum of $x^{3} e^{-|x|}$ for $x \in (-\infty, \infty)$ occurs at $x = $ _________ (round off to one decimal place)
0 0 votes
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GATE IN 2022 | Question: 22
A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and third balls drawn are re...
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