List of practice Questions

The domain of the function $f\left(x\right)=\frac{1+2\left(x+4\right)^{-0.5}}{2-\left(x+4\right)^{0.5}}+5\left(x+4\right)^{0.5}$ is
The domain of the function $f \left(x\right)=\frac{1}{\sqrt{\left\{sin\,x\right\}+\left\{sin\left(\pi+x\right)\right\}}}$ where $\{\cdot \}$ denotes fractional part, is
The domain of the function $f(x) = {^{24- x}C_{3x-1}} + {^{40 -6x}C_{8x-10}} $ is ,
The domain of the function $f(x) =\sqrt{\log_{16} \, x^2}$ is
The domain of the function $f (x) = \log_e(x - [x]) $ is :
The objective function in the above question is
The smallest integer function $f x ) = [x]$ is
Most electropositive metals are obtained from their ores by
Pure hydrogen is obtained by carrying electrolys is of
The hydrogen electrode is dipped in a solution of pH = 3 at 25$^\circ$C. The potential of the cell would be (the value of 2.303 RT/F is 0.059 V)
Pick out the wrong statement (s) . (i) Vapour pressure of a liquid is the measure of the strength of intermolecular attractive forces. (ii) Surface tension of a liquid acts perpendicular to the surface of the liquid. (iii) Vapour pressure of all liquids is same at their freezing points. (iv) Liquids with stronger intermolecular attractive forces are more viscous than those with weaker intermolecular force.
Surface tension does not vary with
Surface tension of mercury is $ 0.465 \,N\, m^{-1} $ . The excess pressure inside a mercury drop of diameter $ 6 \,mm $ is
The speed $v$ of ripples on the surface of water depends on surface tension $ \sigma$ density p and wavelength $ \lambda $. The square of speed v is proportional to
The surface tension of a liquid at its boiling point is
The surface tension of a soap solution is $25 \times 10^{-3}\,N/m$. The excess pressure inside a soap bubble of diameter 1 cm is
Two soap bubbles of radii a and b combine to form a single bubble of radius 3) If P is the external pressure, then S.T. of the soap solutionis
A soap bubble of radius $r$ is blown up to form a bubble of radius $2 r$ under isothermal conditions. If $T$ is the surface tension of soap solution, the energy spent in the blowing
A spherical liquid drop of radius $R$ is divided into eight equal droplets. If surface tension is $T$, then work done in the process will be
The molecule which has highest bond order is
Oxygen molecule is paramagnetic in nature. What is the paramagnetic content in terms of magnetic moment in $O^{-}_{2}$?
The conditions for the combination of atomic orbitals to form molecular orbitals are stated below. Mark the incorrect condition mentioned here.
The electronic configuration of carbon is $1s^2 2s^2 2p^2$. There are $12$ electrons in $C_2$. The correct electronic configuration of $C_2$ molecule is
The increasing order of energies of various molecular orbitals of $N_2$ is given below: $\sigma 1s < \sigma^* 1s
Which contain at least one e- in $\sigma 2p$ bonding MO