List of practice Questions

Two radioactive materials $X_1$ and $X_2$ have decay constants $10\lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $X_1$ to that of $X_2$ will be 1/e after a time

Two long parallel wires are at a distance 2d apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field B along the line XX' is given by

The order of reactivities of the following alkyl halides for a $S_N$2 reaction is-

The incentre of the triangle with vertices $(1, \sqrt{3}), (0,0)$ and $ (2,0) is $

The compressibility of a gas is less than unity at STP. Therefore,

Starting with the same initial conditions, an ideal gas expands from volume V$_1$ to V$_2$ in three different ways, the work done by the gas is W$_1$ if the process is purely isothermal, W$_2$ if purely isobaric and W$_3$ if purely adiabatic, then

Propyne and propene can be distinguished by

In a compound microscope, the intermediate image is

For the equilibrium,${ MgCO_3(s) <=>[\triangle] MgO(s)+CO_2 (g)} $ which of the following expressions is correct ?

Let $f(x) = \begin{cases} |x|, & \quad \text{for}\, 0 < | x | \le 2 \\ 1, & \quad \text{for} \, x = 0 \end{cases}$ then at x = 0, f has

For all $x\,\in\,(0,1)$

Benzoyl chloride is prepared from benzoic acid by

At 100$^\circ$C and 1 atm. if the density of liquid water is 1.0 g $cm^{-3}$ and that of water vapour is 0.0006 g $cm^{-3}$, then the volume occupied by water molecules in 1 litre of steam at that temperature

An ionized gas contains both positive and negative ions. If it is subjected simultaneously to an electric field along the + x-direction and a magnetic field along the +z-direction, then

An infinitely long conductor PQR is bent to form a right angle as shown in figure. A current I flows through PQR. The magnetic field due to this current at the point M is $H_1$. Now, another infinitely long straight conductor QS is connected at Q, so that current is I/2 in QR as well as in QS, the current in PQ remaining unchanged. The magnetic field at M is now $H_2.$ The ratio $H_1 /H_2$ is given by

Amongst $H_2O , H_2S, H_2Se$ and $H_2Te,$ the 1one with the highest boiling point is

Amongst the following, identify the species with an atom in + 6 oxidation state

The number of $P - O - P$ bonds in cyclic metaphosphoric acid is

Ammonia can be dried by

The rms velocity of hydrogen is $\sqrt{7}$ times the rms velocity of nitrogen. If T is the temperature of the gas

A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to

If $a, b, c, d$ are positive real numbers such that $a + b +c + d = 2,$ then $M =(a + b) (c+d) $ satisfies the relation.

For $2 \le \, r \, \le \, n,\binom{n}{r}+2 \binom{n}{r-1}+\binom{n+2}{r}$ is equal to

if $\ f ( x )$ $=\bigg \{ \begin {array} \ e^{\cos x}\sin \ x \\ 2 \\ \end {array} \begin {array} \ for |x|\le 2 \\ \text{otherwise} \\ \end {array}$ then $\int^{3}_{-2} f ( x ) \ dx$ is equal to

The value of the integral $ \int^{e^2}_{e^{-1}} \bigg | \frac{ \log_e \, x }{ x } \bigg | \, dx $ is