List of practice Questions

The value of $[ \vec{a} - \vec{b} \,\,\,\,\,\, \vec{b} - \vec{c} \,\,\,\,\,\, \vec{c} - \vec{a} ]$ where $|\vec{a}| = 1 , |\vec{b} | = 5 , |\vec{c}| = 3 $
The capacitance of the Earth considered as a conducting sphere of radius $6408 \, km$ is
The kinetic energy of the photoelectrons increases by $0.52 \, eV$ when the wavelength of incident light is changed from $500 \, nm$ to another wavelength which is approximately
The maximum value of $ f(x) = \frac{\log x}{x} , 0 < x < \infty$ is
Two points separated by a distance of 0.1 mm can just be observed using a microscope when light $\lambda = 600\: nm$ is used. If light of wavelength 480 nm is used, this limit of resolution becomes
The speed of electromagnetic radiation in vacuum
Bakelite is manufactured by using a mixture of
Oxygen molecule is
Fog is a colloid consisting of
A spring balance carries a load. When the load is pulled aside so that the balance makes an angle of $30^{\circ}$ with the vertical, the balance reads $4 \, kg\, wt$. The mass of the load is
Cuprous ion is
Which one of the following is a matching pair of a body feature and the animal possessing it?
Geometrical isomerism is exhibited by
If $x^y = \log x$ , then $\frac{dy}{dx} $ at the point where the curve cuts the $x-axis$ is
If $y = \tan^{-1} ( \sec x - \tan x) $, then $ \frac{dy}{dx} = $
Let $f(x) = \begin{cases} -2 \sin x, &x \leq - \pi /2 \\ a \sin x +b, & - \pi /2 < x < \pi /2 \\ \cos \, x , & x \geq \pi /2 \end{cases}$ then the? values of a and b so that $f(x)$ is continuous are
If $a$ and $ b$ are positive integers such that $a^2 - b^2$ is a prime number, then $a^2 - b^2$ is
If the medians $AD$ and $BE$ of the triangle with vertices $A(0, b), B(0, 0), C(a, 0)$ are mutually perpendicular, then
If $A, B, C, D$ are four points and $\vec{AB} = \vec{DC}$ , then $\vec{AC} + \vec{BD} = $
The $ pH $ of a $ 10^{-8} $ molar solution of $ HCl $ in water is
The solubility of $ AgCl $ is $ 1 \times 10^{-5}\, mol/L $ . Its solubility in $ 0.1 $ molar sodium chloride solution is
Peptization denotes
Freundlich adsorption isotherm is
An open $ U $ -tube contains mercury. When $ 11.2 \,cm $ of water is poured into one of the arms of the tube, how high does the mercury rise in the other arm from its initial unit ?
We consider a thermodynamic system. If $ \Delta U $ represents the increase in its internal energy and $ W $ the work done by the system, which of the following statements is true ?