List of top Questions asked in GATE XE

Among the following non-dimensional numbers, which one characterizes periodicity present in a transient flow?

For an incompressible boundary layer flow over a flat plate (figure shown), the momentum thickness is expressed as

Among the shear stress versus shear strain rate curves shown in the figure, which one corresponds to a shear thinning fluid?

Consider steady incompressible flow over a flat plate, where the dashed line represents the edge of the boundary layer, as shown in the figure. Which one among the following statements is true?

An inviscid steady incompressible flow is formed by combining a uniform flow with velocity $U_\infty$ and a clockwise vortex of strength $K$ at the origin, as shown in the figure. Velocity potential ($\phi$) for the combined flow in polar coordinates $(r,\theta)$ is

Which one of the following functions is differentiable at $z=0$ but NOT differentiable at any other point in the complex plane $\mathbb{C}$?

If the polynomial \[ P(x)=a_0+a_1x+a_2\,x(x-1)+a_3\,x(x-1)(x-2) \] interpolates the points $(0,2)$, $(1,3)$, $(2,2)$, and $(3,5)$, then the value of $P\!\left(\tfrac{5}{2}\right)$ is ____________ (round off to 2 decimal places).

The value of $m$ for which the vector field \[ \vec F(x,y)=\big(4x^{m}y^{2}-2xy^{m}\big)\,\mathbf{i}+\big(2x^{4}y-3x^{2}y^{2}\big)\,\mathbf{j} \] is a conservative vector field, is ____________________ (in integer).

Let \[ P=\begin{bmatrix}4 & -2 & 2\\ 6 & -3 & 4\\ 3 & -2 & 3\end{bmatrix}, \qquad Q=\begin{bmatrix}3 & -2 & 2\\ 4 & -4 & 6\\ 2 & -3 & 5\end{bmatrix}. \] The eigenvalues of both $P$ and $Q$ are $1,1,2$. Which one of the following statements is TRUE?

The surface area of the portion of the paraboloid \[ z=x^2+y^2 \] that lies between the planes $z=0$ and $z=\tfrac{1}{4}$ is

The probability of a person telling the truth is $\dfrac{4}{6}$. An unbiased die is thrown by the same person twice and the person reports that the numbers appeared in both the throws are the same. Then the probability that actually the numbers appeared in both the throws are same is ______________ (rounded off to 2 decimal places).

The information contained in DNA is used to synthesize proteins necessary for life. DNA is composed of four nucleotides: Adenine (A), Thymine (T), Cytosine (C), and Guanine (G). Coding regions—where nucleotide triplets code for amino acids—constitute only about 2% of human DNA. Based only on the information above, which of the following statements can be inferred with {certainty}? (i) The majority of human DNA has no role in the synthesis of proteins. (ii) The function of about 98% of human DNA is not understood.

Which one of the given figures P, Q, R and S represents the graph of the following function? \[ f(x)=\left|\,|x+2|-|x-1|\,\right| \]

An opaque cylinder (shown below) is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The cylinder can be reoriented in any direction within the light beam. Under these conditions, which one of the shadows P, Q, R, and S is {NOT} possible?

Let $A$ be a $3 \times 3$ real matrix having eigenvalues $1,2,3$. If \[ B = A^2 + 2A + I, \] where $I$ is the $3 \times 3$ identity matrix, then the eigenvalues of $B$ are:

Let $f:\mathbb{R}^2 \to \mathbb{R}$ be defined by \[ f(x,y)= \begin{cases} \dfrac{xy}{|x|+y}, & y \neq -|x|, \\[6pt] 0, & \text{otherwise}. \end{cases} \] Then which one of the following statements is TRUE?

If the quadrature formula \[ \int_{-1}^{1} f(x)\,dx \;\approx\; \frac{1}{9}\Big(c_1 f(-1) + c_2 f\!\left(\tfrac{1}{2}\right) + c_3 f(1)\Big) \] is exact for all polynomials of degree less than or equal to $2$, then

The second smallest eigenvalue of the eigenvalue problem \[ \frac{d^2 y}{dx^2} + (\lambda - 3)\,y = 0,\qquad y(0)=y(\pi)=0, \] is

Disagree : Protest :: Agree : ____________ (By word meaning)

A ‘frabjous’ number is defined as a 3-digit number with all digits odd, and no two adjacent digits being the same. For example, 137 is a frabjous number, while 133 is not. How many such frabjous numbers exist?

Which one among the following statements must be TRUE about the mean and the median of the scores of all candidates appearing for GATE 2023?

In the given diagram, ovals are marked at different heights ($h$) of a hill. Which one of the following options P, Q, R, and S depicts the {top view} of the hill?

Residency is a famous housing complex with many well-established individuals among its residents.
A survey revealed:
1. All residents who are well established in their respective fields are academicians.
2. Most of these academicians are authors of some best-selling books.
Based only on this information, which one of the following statements can be logically inferred with {certainty}?

Ankita has to climb 5 stairs starting at the ground, while respecting the following rules:

At any stage, Ankita can move either one or two stairs up.
At any stage, Ankita cannot move to a lower step.
Let $F(N)$ denote the number of possible ways in which Ankita can reach the $N^{\text{th}}$ stair. For example, $F(1)=1$, $F(2)=2$, $F(3)=3$. The value of $F(5)$ is ____________.

The village was nestled in a green spot, __________ the ocean and the hills.