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GATE XE 2025 | Question: 10
​Three villages $\text{P, Q}$, and $\text{R}$ are located in such a way that the distance $\text{PQ}=13 \mathrm{~km}$, $\mathrm{QR}=14 \mathrm{~km}$, and $\mathrm{RP}=15 ...
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GATE XE 2025 | Question: 74
A force of $\mathrm{P}=100 \mathrm{~N}$ is applied at the ends of the pliers as shown in the figure.Neglecting friction, the force exerted by the upper jaw on the workpie...
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GATE XE 2025 | Question: 1
​​​Even though I had planned to go skiing with my friends, I had to $\_\_\_\_\_\_$ at the last moment because of an injury.Select the most appropriate option to complete ...
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GATE XE 2025 | Question: 2
​​​​The President, along with the Council of Ministers, $\_\_\_\_\_\_\_$ to visit India next week.Select the most appropriate option to complete the above sentence.wishwi...
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GATE XE 2025 | Question: 3
​​​An electricity utility company charges ₹$7$ per kWh (kilo watt-hour). If a $40$ -watt desk light is left on for $10$ hours each night for $180$ days, what would be the...
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GATE XE 2025 | Question: 4
​​In the context of the given figure, which one of the following options correctly represents the entries in the blocks labelled $\text{(i), (ii), (iii)}$, and $\text{(iv...
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GATE XE 2025 | Question: 5
​​​A bag contains Violet (V), Yellow (Y), Red (R), and Green (G) balls. On counting them, the following results are obtained:The sum of Yellow balls and twice the number ...
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GATE XE 2025 | Question: 6
​​​​​"His life was divided between the books, his friends, and long walks. A solitary man, he worked at all hours without much method, and probably courted his fatal illn...
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GATE XE 2025 | Question: 7
​​​For the clock shown in the figure, if$ \begin{array}{l} \mathrm{O}^{*}=\mathrm{~O} \mathrm{~Q} \mathrm{~S} \mathrm{~Z} \mathrm{~P} \mathrm{~R} \mathrm{~T}, \text { and...
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GATE XE 2025 | Question: 8
Consider a five-digit number $PQRST$ that has distinct digits $P,Q,R,S$, and $T$, and satisfies the following conditions:$$\begin{array}{c} P<Q \\ S>P>T \\ R<T \end{array...
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GATE XE 2025 | Question: 9
A business person buys potatoes of two different varieties $\text{P}$ and $\text{Q}$, mixes them in a certain ratio and sells them at ₹ $192$ per kg.The cost of the varie...
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GATE XE 2025 | Question: 11
​​Let $X$ and $Y$ be two random variables with mean $0$, variance $1$, and correlation coefficient $\frac{1}{3}$. Then the value of $\operatorname{Var}(X+3 Y)$ is equal t...
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GATE XE 2025 | Question: 12
​​​​Consider the second order Partial Differential Equation $\textsf{(PDE)}$$$4 x^{2} \frac{\partial^{2} u}{\partial x^{2}}+4(x+y) \frac{\partial^{2} u}{\partial x \parti...
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GATE XE 2025 | Question: 13
​Consider the infinite series$$ \begin{array}{l} \text { (P) }: \sum_{n=2}^{\infty} \frac{1}{(n \log n)^{1 / n}} \\\text { (Q): } \sum_{n=1}^{\infty} \frac{n^{n}}{(2 n)!}...
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GATE XE 2025 | Question: 14
​​​​Suppose the polynomial $a+b x+c x^{2}+d x^{3}$ interpolates the data, $(-1,1),(0,3),(1,2)$ and $(2,4)$.Then which one of the following statements is correct?$a=-2 c, ...
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GATE XE 2025 | Question: 15
​​Let $C$ be the positively oriented boundary of the domain bounded by the curves $y=2 x^{2}$ and $y^{2}=4 x$. Then the value of the line integral$$\oint_{C}\left(2 y^{2}...
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GATE XE 2025 | Question: 16
Let $y(x)$ be the solution of the initial value problem,$$\begin{array}{c}x^{2} y^{\prime \prime}+x y^{\prime}-y=0, \quad x>0, \\y(1)=0, \quad y^{\prime}(1)=2 .\end{array...
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GATE XE 2025 | Question: 17
Suppose that $2$ is an eigenvalue of the matrix$$\left[\begin{array}{ccc}0 & 3 & -\alpha \\0 & 1 & 0 \\1 & -1 & 3\end{array}\right]$$Then the value of $\alpha$ is equal t...
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GATE XE 2025 | Question: 18
​​​​​Let $f(z)$ be an analytic function such that$$ {Re}\left(f^{\prime}(z)\right)=3 x^{2}-4 y-3 y^{2}, f(i)=0, f^{\prime}(0)=0, $$where $i=\sqrt{-1}$. Then the value of ...
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GATE XE 2025 | Question: 19
​​Consider the function$$ f(x, y)=x^{2} y+2 x y^{2}-2 x^{2} y^{2}.$$Then which one of the following statements is correct?$\left(\frac{3}{2}, 0\right)$ is a point of loca...
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GATE XE 2025 | Question: 20
​For $a, b \in \mathbb{R}$, consider the system of linear equations$$ \begin{array}{r} x+y+a z=2 \\ 2 y+2 z=1 \\ a x+2 z=b \end{array}$$If the system has infinitely many ...
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GATE XE 2025 | Question: 21
Let $u(x, t)$ be the solution of the initial boundary value problem$$ \begin{array}{c}\frac{\partial u}{\partial t}-\frac{\partial^{2} u}{\partial x^{2}}-u=0, \quad 0< x ...
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GATE XE 2025 | Question: 22
​​​Fluid at a constant flow rate passes through a long, straight, cylindrical pipe that has an axisymmetric convergent section at the end.Which one of the following optio...
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GATE XE 2025 | Question: 23
​​​A sharp flat plate of length $L$ and infinite width is immersed parallel to a fluid stream having velocity $u_{\infty}$. At a point on the plate, far away from the lea...
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GATE XE 2025 | Question: 24
​Consider the following Statements $ $ and $ $.Statement $ $: The Eulerian study focusses attention on individual particle and its motion is observed as a function of tim...
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GATE XE 2025 | Question: 25
​​​Statement of Reynolds Transport Theorem is given below with three blanks.The rate of change of $\_\_\_\_\_$ extensive property can be calculated by summing the rate of...
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GATE XE 2025 | Question: 26
​​​For a steady and incompressible flow, the velocity field $(\vec{V})$ in Cartesian $(x, y, z)$ coordinate system is given as:$$\vec{V}=5 x i-P y j+3 k$$Here, $i, j$, an...
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GATE XE 2025 | Question: 27
​​​Conservation of mass for a steady axisymmetric flow field in the cylindrical $(r, z)$ coordinates is:$$\frac{1}{r} \frac{\partial\left(r V_{r}\right)}{\partial r}+\fra...
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GATE XE 2025 | Question: 28
​​$\textbf{Group-I}$ indicates different properties of fluid and $\textbf{Group-II}$ defines their basic dimensions in terms of Force $(F)$, Length ( $L$ ), and Time ( $T...
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