Recent questions tagged gatexe-2023

Let $A$ be a $3 \times 3$ real matrix having eigenvalues $1,2,$ and $3$. If $B=A^{2}+2 A+I$, where $I$ is the $3 \times 3$ identity matrix, then the eigenvalues of $B$ ar...

Let $f: \mathbb{R}^{2} \rightarrow \mathbb{R}$ be a function defined by $f(x, y)=\left\{\begin{array}{cc}\frac{x y}{|x|+y}, & y \neq-|x| \\ 0, & \text { otherwise. }\end{...

If the quadrature formula $\int_{-1}^{1} f(x) d x \approx \frac{1}{9}\left(c_{1} f(-1)+c_{2} f\left(\frac{1}{2}\right)+c_{3} f(1)\right)$is exact for all polynomials of d...

The second smallest eigenvalue of the eigenvalue problem$\frac{d^{2} y}{d x^{2}}+(\lambda-3) y=0, \quad y(0)=y(\pi)=0$,is$4$$3$$7$$9$

Which one of the following functions is differentiable at $z=0$ but NOT differentiable at any other point in the complex plane $\mathbb{C}$?$f(z)=z|z|, \quad z \in \mathb...

The value of $m$ for which the vector field$\vec{F}(x, y)=\left(4 x^{m} y^{2}-2 x y^{m}\right) \hat{\imath}+\left(2 x^{4} y-3 x^{2} y^{2}\right) \hat{\jmath}$is a conserv...

If the polynomial $P(x)=a_{0}+a_{1} x+a_{2} x(x-1)+a_{3} x(x-1)(x-2)$interpolates the points $(0,2),(1,3),(2,2)$, and $(3,5)$, then the value of $P\left(\frac{5}{2}\right...

Let $P=\left[\begin{array}{lll}4 & -2 & 2 \\ 6 & -3 & 4 \\ 3 & -2 & 3\end{array}\right]$, and $Q=\left[\begin{array}{lll}3 & -2 & 2 \\ 4 & -4 & 6 \\ 2 & -3 & 5\end{array}...

The probability of a person telling the truth is $\frac{4}{6}$. An unbiased die is thrown by the same person twice and the person reports that the numbers appeared in bot...

The surface area of the portion of the paraboloid $z=x^{2}+y^{2}$that lies between the planes $z=0$ and $z=\frac{1}{4}$ is$\frac{\pi}{6}(2 \sqrt{2}-1)$$\frac{\pi}{2}(2 \s...

Let $u(x, t)$ be the solution of the initial boundary value problem$\frac{\partial u}{\partial t}-\frac{\partial^{2} u}{\partial x^{2}}=0, \quad x \in(0,2), t>0$$u(x, 0)=...

Among the following non-dimensional numbers, which one characterizes periodicity present in a transient flow?Froude numberStrouhal numberPeclet numbeLewis number

Match the following measuring instruments with the appropriate figures.I - Pitot probeII - Pitot-static probeIII - Piezometer$\text{I - P; II - Q; III - R}$$\text{I - R; ...

For an incompressible boundary layer flow over a flat plate shown in the figure, the momentum thickness is expressed as$\int_0^{\infty} \frac{u}{U_{\infty}} d y$$\int_0^{...

Among the shear stress versus shear strain rate curves shown in the figure, which one corresponds to a shear thinning fluid ? $\mathrm{P}$$\mathrm{Q}$$\mathrm{R}$$\mathrm...

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 follow...

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 ...

Which of the following statements are true?$\text{(i)}$ Conservation of mass for an unsteady incompressible flow can be represented as $\nabla \cdot \vec{V}=0$, where $\v...

A stationary object is fully submerged in a static fluid, as shown in the figure. Here, $\text{CG}$ and $\mathrm{CB}$ stand for center of gravity and center of buoyancy, ...

For a two-dimensional flow field given as $\vec{V}=-x \hat{\imath}+y \hat{\jmath}$, a streamline passes through points $(2,1)$ and $(5, p)$. The value of $p$ is$5$$5 / 2$...