List of practice Questions

Which of the following relation is called mirror equation?

A car moving on a straight road covers $ 1/3 $ of the distance with $ 25\,km/h $ and rest with $ 75\,km/h $ . The average speed is

All substances that conduct electricity in aqueous solutions are called?

Find the length of the diagonal of the parallelepiped formed by planes drawn through the points $ (2,3,5) $ and $ (5,9,7), $ parallel to the co-ordinate planes?

For transistor the value of $ \beta $ is $50$ then, the value of $\alpha$ is

Light from a point source in air falls on a spherical glass surface ( $ n=1.67 $ and radius of curvature $ =25\,cm $ ). The distance of the light source from the glass surface is $ 95\,cm $ . At what position, the image is formed?

In acidic medium, $H_2O_2 $ changes $ Cr_2O_7^{2-} $ to $CrO_5 $ which has two (-O-O-) bonds. Oxidation state of Cr in $CrO_5 $ is

Let $n\ge2$ be an integer, $A=\begin{pmatrix}\cos\left(2\pi/ n\right)&\sin \left(2\pi / n\right)&0\\ -\sin\left(2\pi / n\right)&\cos\left(2\pi / n\right)&0\\ 0&0&1\end{pmatrix}$ and $?$ is the identity matrix of order $3$. Then

Suppose $M=\int\limits_{0}^{\pi / 2} \frac{\cos x}{x+2} d x$, $N=\int\limits_{0}^{\pi / 4} \frac{\sin x \cos x}{(x+1)^{2}} d x$ Then, the value of $(M-N)$ equals

Out of $7$ consonants and $4 $ vowels, the number of words (not necessarily meaningful) that can be made, each consisting of $3$ consonants and $2 $ vowels, is

The angle of intersection between the curves $y=\left[\left|\sin\,x\right|+\left|\cos\,x\right|\right]$ and $x^{2}+y^{2}=10, $ where $[x]$ denotes the greatest integer $= x,$ is

The minimum value of $2^{\sin\, x} + 2^{\cos\, x}$ is

The hydrides of the first elements in groups $15 - 17$, namely $NH_3, H_2O$ and $HF$ respectively show abnormally high values for melting and boiling points. This is due to

The coefficient of $x^3$ in the infinite series expansion of $\frac{2}{\left(1-x\right)\left(2-x\right)},$ for $\left|x\right|< 1,$ is

To observe an elevation of boiling point of $0.05^?C$, the amount of solute (Mol. $Wt. = 100$) to be added to $100\, g$ of water $(K_b=0.5)$ is

Metal ion responsible for the Minamata disease is

The compound that will have a permanent dipole moment among the following is

Let \(R\) be the set of all real numbers and \(f : R \rightarrow R\) be given by \(f(x) = 3x^2 + 1\).Then the set \(f ^{-1}\left(\left[1, 6\right]\right)\) is

The equation of the common tangent with positive slope to the parabola $y^{2}=8\sqrt{3x}$ and the hyperbola $4x^2 - y^2 = 4$ is

To determine the coefficient of friction between a rough surface and a block, the surface is kept inclined at $45^{\circ}$ and the block is released from rest. The block takes a time $t$ in moving a distance $d$. The rough surface is then replaced by a smooth surface and the same experiment is repeated. The block now takes a time $t / 2$ in moving down the same distance $d$. The coefficient of friction is

Three capacitors $3\, \mu F , 6 \, \mu F$ and $6\, \mu F$ are connected in series to a source of $120 \, V$. The potential difference, in volt, across the $3 \, \mu F$ capacitor will be

The remainder obtained when \(1!+2!+3!+.....+11!\) is divided by 12 is

The point on the parabola $y^2 = 64x$ which is nearest to the line $4x + 3y + 35 = 0$ has coordinates

When phenol is treated with $D_2SO_4/D_2O$, some of the hydrogens get exchanged. The final product in this exchange reaction is

Two gases $X$ (Mol. Wt. $M_x$) and $Y$ (Mol. Wt. $M_Y; M_Y > M_x$) are at the same temperature T in two different containers. Their root mean square velocities are $C_X$ and $C_Y$ respectively. If the average kinetic energies per molecule of two gases $X$ and $Y$ are $E_x$ and $E_Y$ respectively, then which of the following relation (s) is (are) true?