List of top Questions asked in VITEEE- 2014

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

If there is an error of $k\%$ in measuring the edge of a cube, then the percent error in estimating its volume is

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

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

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

Let $f ' (x),$ be differentiable $\forall \, x.$ If $f (1) = -2$ and $f '(x) \geq 2 \forall x \in [1, 6],$ then

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

If $a, b, c$ are three non-coplanar vectors and $p, q, r$ are reciprocal vectors, then $(la + mb + nc). (lp + mq + nr)$ is equal to

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

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 triangle formed by the tangent to the curve $f (x) = x2 + bx - b$ at the point $(1,1)$ and the coordinate axes lies in the first quadrant. If its area is $2$, then the value of b is

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

The volume strength of $1.5 \, N \, H_2O_2$ solution is

Peptisation involves

The equivalent conductivity of a solution containing $2.54\, g$ of $CuSO _{4}$ per $L$ is $91.0\, W ^{-1} cm ^{2} eq ^{-1}$. Its conductivity would be

The rate constant for forward reaction and backward reaction of hydrolysis of ester are $1.1 \times 10^{-2}$ and $1.5 \times 10^{-3}$ per minute respectively. Equilibrium constant for the reaction is $CH _{3} COOC _{2} H _{5}+ H _{2} O \rightleftharpoons CH _{3} COOH + C _{2} H _{5} OH$

The solubility product of $Ag _{2} CrO _{4}$ is $32 \times 10^{-12}$. What is the concentration of $CrO _{4}^{-}$ions in that solution?

A gaseous reaction $X_2(g) \to Y + \frac{1}{2} Z(g)$ There is increase in pressure from $100 \,mm$ to $120 \,mm$ in $5$ minutes. The rate of disappearance of $X_2$ is

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

According to Bohr?s theory, the angular momentum for an electron of $3rd$ orbit is

A metal has bcc structure and the edge length of its unit cell is $3.04\, ?$. The volume of the unit cell in $cm^3$ will be

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