List of practice Questions

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 ?

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

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

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

A monoatomic ideal gas, initially at temperature $T_1$, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T$_2$ by releasing the piston suddenly. If L$_1$ and L$_2$ are the lengths of the gas column before and after expansion respectively, then $T_1 / T_2$ is given by

A cubical block of side L rests on a rough horizontal surface with coefficient of friction $\mu$. A horizontal force F is applied on the block as shown. If the coefficient of friction is sufficiently high, so that the block does not slide before toppling, the minimum force required to topple the block is

One quarter section is cut from a uniform circular disc of radius R. This section has a mass M. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is

A thin wire of length L and uniform linear mass density p is bent into a circular loop with centre at O as shown. The moment of inertia of the loop about the axis XX ' is

An ideal gas is initially at temperature T and volume V. Its volume is increased by $\Delta$V due to an increase in temperature $\Delta$T, pressure remaining constant. The quantity 5 = $\Delta$V / V$\Delta$T varies with temperature as