Gate

The table lists the unit selling price of five products P, Q, R, S, and T. On a particular day, 250 items were sold with the average selling price of Rs. 60. The following observat...

Column I presents common air pollutants, and column II presents treatment technologies commonly employed to control air pollutants. Air pollutant 1 Dust (size 5-25 µm) 2 Carbon mon...

Let $f(x) = \begin{vmatrix} x^3 & \sin x & \cos x \\ 6 & -1 & 0 \\ p & p^2 & p^3 \end{vmatrix}$ where $p$ is a constant. The value of $\frac{d^3}{dx^3} f(x)$ at $x = 0$ is

Let $f(x)$ be a continuous function defined in $[0,2] \rightarrow \mathbb{R}$ and satisfying the equation $\int_{0}^{2} f(x)[x - f(x)]dx = \frac{2}{3}$. The value of $f(1)$ is

Vector field $\vec{V}$ is defined as $\vec{V} = 3x^2yz \hat{i} - 5xy \hat{j} + 6yz^2 \hat{k}$ The curl of $\vec{V}$ at point (2,-1,1) is

The shaft of a 6 m wide gate in the figure will fail at a moment of 3924 kN.m about the hinge P. The maximum value of water depth h (in m) that the gate can hold is ________ (round...

Both the numerator and the denominator of $\frac{3}{4}$ are increased by a positive integer, x, and those of $\frac{15}{17}$ are decreased by the same integer. This operation resul...

Given the statements: • P is the sister of Q. • Q is the husband of R. • R is the mother of S. • T is the husband of P. Based on the above information, T is ________ of S.

⊕ and ⊙ are two operators on numbers p and q such that p ⊕ q = p^2 + q^2 / pq and p ⊙ q = p^2 / q; If x ⊕ y = 2 ⊙ 2, then x =

Four persons P, Q, R and S are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and R cannot sit adjacent to each other. S should be s...

A function is defined in Cartesian coordinate system as $f(x, y) = xe^y$. The value of the directional derivative of the function (in integer) at the point (2, 0) along the directi...

The soil profile at a construction site is shown in the figure (not to scale). Ground water table (GWT) is at 5 m below the ground level at present. An old well data shows that the...

The value (up to two decimal places) of a line integral $\int_{C} \mathbf{F}(\mathbf{r}) \cdot d\mathbf{r}$, for $\mathbf{F}(\mathbf{r})=x^{2}\hat{i}+y^{2}\hat{j}$ along C which is...