List of top Questions asked in VITEEE- 2014

If the points $(1, 2, 3)$ and $(2, -1, 0)$ lie on the opposite sides of the plane $2x + 3y - 2z = k,$ then

If the system of equations $x + ky - z = 0, 3x - ky - z = 0$ and $x - 3y + z = 0$, has non-zero solution, then $k$ is equal to

The minimum value of $\frac{x}{\log \, x}$ is

If a plane meets the coordinate axes at $A,B$ and $C$ such that the centroid of the triangle is $(1, 2, 4)$, then the equation of the plane is

Two lines $ \frac{x-1}{2} = \frac{y+1}{3} = \frac{z -1}{4}$ and $ \frac{x-3}{1} = \frac{y-k}{2} = z $ intersect at a point, if $k$ is equal to

The solution of $\frac{dy}{dx} = \frac{x^{2} + y^{2} + 1}{2xy}$, satisfying $ y\left(1\right) = 0$ is given by

If $\Delta (x) \begin{vmatrix}1&\cos x&1 -\cos x\\ 1+ \sin x& \cos x &1+ \sin x - \cos x\\ \sin x &\sin x&1\end{vmatrix},$ then $ \int\limits^{\pi / 4}_{0} \Delta\left(x\right)dx $ is equal to

The value of $c$ from the Lagrange�s mean value theorem for which $f(x) = \sqrt{25 - x^2}$ in $[1,5]$, is

The area in the first quadrant between $x^2 + y^2 = \pi^2$ and $y = \sin \, x$ is

The differential equation of the rectangular hyperbola hyperbola, where axes are the asymptotes of the hyperbola, is

The statement $(p \Rightarrow q ) \Leftrightarrow ( \sim p \Lambda q)$ is a

$2.76\, g$ of silver carbonate on being strongly heated yields a residue weighing

An installation consisting of an electric motor driving a water pump left $75\, L$ of water per second to a height of $4.7\, m$. If the motor consumes a power of $5\, kW$, then the efficiency of the installation is

The amplification factor of a triode is $50$. If the grid potential is decreased by $0.20\, V$. What increase,in plate potential will keep the plate current unchanged?

If the integers $m$ and $n$ are chosen at random from $1$ to $100$ , then the probability that a number of the form $7^{n}+7^{m}$ is divisible by $5$ , equals to