List of practice Questions

The roots $\alpha$ and $\beta$ of the quadratic equation $px^2 + qx + r = 0$ are real and opposite signs. The roots of $\alpha(x - \beta^2)+ \beta (x - \alpha)^2 = 0$ are

The roots of the equation $(3 -x)^4 + (2-x)^4$ = $(5 - 2x)^4$ are

Let $f(x)=[x^3-3],[x]=$ G.I.F. Then the no. of points in the interval (1,2) where function is discontinuous is

The domain and range of the function $f=\left\{\left(\frac{1}{1-x^{2}}\right) : x \in R, x \ne \pm 1\right\}$ are respectively

The domain of $f\left(x\right) = \frac{1}{\sqrt{2x -1}} - \sqrt{1-x^{2}} $ is :

The domain of $f(x) = \sin^{-1} \left( \frac{2x -3}{5} \right)$

The domain of $f(x) = \frac{|x|}{x}$ is

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 $f(x) =\sqrt{\log_{16} \, x^2}$ 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) = \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)

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

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