List of practice Questions

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
A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is $f_1$. If the train's speed is reduced to 17 m/s, the frequency registered is $f_2$. If the speed of sound is 340 m/s, then the ratio $f_1/ f_2$ is
A block of ice at I0$^{\circ}$C is slowly heated and converted to steam at 100$^{\circ}$C. Which of the following curves represents the phenomena qualitatively?
Which of the following has maximum hydration energy?
Which species does not exist?
You are provided three bulbs of 15, 40 and 60 watt. Which of them has lowest resistance:
Which of the birds cannot fly?
When the displacement is half the amplitude the ratio of potential energy to the total energy is:
When light of wavelength 300 nm falls on a photoelectric emitter, photoelectrons are liberated. For another emitter, however light of 600 nm wavelength is sufficient for creating photoemission. What is the ratio of the work functions of the two emitters:
What is the weight of 1 mole atoms of Ag?
What is the pH for a neutral solution at the body temperature $ \left( 38{}^\circ C \right) $ ?
What is the name of class to which pearl oyster belongs?
What is the end product in the following reaction? $ {{C}_{2}}{{H}_{5}}N{{H}_{2}}\xrightarrow{HN{{O}_{2}}}A\xrightarrow{PC{{l}_{5}}}B\xrightarrow{N{{H}_{3}}}C $
What is obtained, when aniline is sulphonated?
Vinyl chloride reacts with $ HCl $ to form:
Two point charges + 3 $ \mu C $ and + 8 $ \mu C $ repel each other with a force of 40 N. If a charge of - 5 $ \mu C $ is added to each of them, then the force between them will become:
The dominant mechanisms for motion of charge carriers in forward and reverse biased silicon $ \text{p-n} $ junctions are:
The compound that is not a Lewis acid, is
The co-ordination number of bcc crystal is: