List of top Questions asked in VITEEE

The value of $2 \,tan^{-1} (cosec \,tan^{-1} x - tan \,cot^{-1} x))$ is

The sum of the series $ \displaystyle\sum_{r = 0}^{n}\left(-1\right)^{r}\, ^{n}C_{r}\left(\frac{1}{2^{r}}+\frac{3^{r}}{2^{2r}}+\frac{7^{r}}{2^{3r}}+\frac{15^{r}}{2^{4r}}+...m \text{terms}\right)$ is

A network of resistances, cell and capacitor $C( = 2 \,\mu F)$ is shown in adjoining figure. In steady state condition, the charge on $2 \,\mu F $capacitor is $Q$, while $R$ is unknown resistance. Values of $Q$ and $R$ are respectively

A students plots a graph between inverse of magnification 1/$m$ produced by a convex thin lens and the object distance $u$ as shown in figure. What was the focal length of the lens used?

A table fan rotating at a speed of 2400 rpm is switched off and the resulting variation of revolution/minute with time is shown in figure. The total number of revolutions of the fan before it, comes to rest is

The time dependence of a physical quantity $P$ is given by $P=P_{0} e \alpha P\left(-\alpha t^{2}\right)$ where $\alpha $ is a constant and $t$ is time. The constant $\alpha $

When $1 \,$ mole of $CO_{2(g)}$ occupying volume $10\,L$ at $27^{\circ}C$ is expanded under adiabatic condition, temperature falls to $150\, K$. Hence, final volume is

If | $x^2 - x - 6 | = x + 2$, then the values of $x$ are

The dimensional formula of magnetic flux is

The centre of a wheel rolling on a plane surface moves with a speed $v_{ 0}$. A particle on the rim of the wheel at the same level as the centre will be moving at speed

The pressure on a square plate is measured by measuring the force on the plate. If the maximum error in the measurement of force and length are respectively $4\%$ and $2\%$, then the maximum error in the measurement of pressure is

What is the EAN of $[Al(C_4O_4)_3]^{3-}$ ?

Seven resistance are connected between points $A$ and $B$ as shown in adjoining figure. The equivalent resistance between $A$ and $B$ is

Mobilities of electrons and holes in a sample of intrinsic germanium at room temperature are $0.36\,m^2V^{-1}s^{-1}$ and $0.17\,m^2V^{-1}s^{-1}$. The electron and hole densities are each equal to $2.5 \times 10^{19} m^3$. The electrical conductivity of germanium is

If the work done in turning a magnet of magnetic moment $M$ by an angle of 90$^{\circ}$ from the magnetic meridian is $n$ times the corresponding work done to turn it through an angle of 60$^{\circ}$, then the value of $n$ is

The density of solid argon is $1.65\, g\, per\, cc$ at - $233^\circ C$. If the argon atom is assumed to be a sphere of radius $1.54 \times 10^{-8}\, cm$, what per cent of solid argon is apparently empty space? $(Ar = 40)$

For the cell reaction $2 Ce^{4+}+Co \rightarrow 2 Ce^{3+}+Co^{3+} ; E^{\circ}_{cell}$ cell is $1.89\, V$. If $E_{Co^{2+}/Co}$ is $- 0.28 \,V$, what is the value of $E^{\circ} _{Ce^{4+}/Ce ^{3+} }$?

If $\alpha$ and $\beta$ are the roots of $x^{2}-ax+b=0$ and if $\alpha^{n}+\beta^{n}=V_{_n},$ then

If the points ($x_1$, $y_1$), ($x_2$, $y_2$) and ($x_3$, $y_3$) are collinear, then the rank of the matrix $\begin{bmatrix}x_{_1}&y_{_1}&1\\ x_{_2}&y_{_2}&1\\ x_{_3}&y_{_3}&1\end{bmatrix}$will always be less than

The line joining two points $A(2,0), B(3,1)$ is rotated about $A$ in anti-clockwise direction through an angle of $15^{\circ}$. The equation of the line in the now position,is

The line $2x+\sqrt{6y}=2$ is a tangent to the curve $x^{2}-2y^{2}=4$. The point of contact is

The number of integral values of $K$, for which the equation $7\, \cos \,x + 5\, \sin\, x = 2K + 1$ has a solution, is

If $(-3, 2)$ lies on the circle $x^2 + y^2 + 2gx + 2fy + c = 0$, which is concentric with the circle $x^2 + y^2 + 6x + 8y - 5 = 0,$ then c is equal to

If $A = \begin{bmatrix}1&-5&7\\ 0&7&9\\ 11&8&9\end{bmatrix}$, then trace of matrix $A$ is

Match List I (Equations) with List II (Types of process) and select the correct option.