List of practice Questions

If Young?s double slit experiment is done with white light, which of the following statements will be true ?

Let $\vec{\alpha } = \hat{i} + \hat{j} + \hat{k} , \vec{\beta} = \hat{i} - \hat{j} - \hat{k}$ and $\vec{\gamma} = - \hat{i} + \hat{j} - \hat{k}$ be three vectors. A vector $\vec{\delta} $, in the plane of $\vec{\alpha}$ and $\vec{\beta}$, whose projection on $\vec{\gamma}$ is $\frac{1}{\sqrt{3}}$, is given by

On the set $R$ of real numbers, the relation $\rho$ is defined by $x \rho y, (x, y) \in R$

If $\int \, f(x) \, \sin \, x \, \cos \, x \, dx = \frac{1}{2(b^2 - a^2)} \log f(x) + c$, where c is the constant of integration , then f(x) =

The approximate value of $\sin \, 31^{\circ}$ is

The value of $\displaystyle\lim_{n \to \infty} \frac{1}{n} \left\{ \sec^2 \frac{\pi}{4 n} + \sec^2 \frac{2 \pi }{4n} + ..... \sec^2 \frac{n \pi}{4n} \right\}$ is

Which is least thermally stable?

The ease of hydrolysis in the compounds $CH _{3} COCl ( I ), CH _{3}- CO - O - COCH _{3}( II )$ $CH _{3} COOC _{2} H _{5}( III )$ and $CH _{3} CONH _{2}( IV )$ is of the order

The main reason the $SiCl_4$ is easily hydrolysed as compared to $CCl_4$ is that

In the extraction of Cu, the metal is formed in the bessemer converter due to the reaction:

Ionisation energy of $He^+$ is $19.6 \times 10^{-18}\, J$ atom$^{-1}$. The energy of the first stationary state $(n= 1)$ of $Li^{2+}$ is

In a compound, atoms of element Y form ccp lattice and those of element X occupy $2/3^{rd}$ of tetrahedral voids. The formula of the compound will be

In case of nitrogen, $NCl_3$ is possible but not $NCl_5$ while in case of phosphorus, $PCl_3$ as well as $PCl_5$ are possible. It is due to

In Williamson synthesis if tertiary alkyl halide is used than

A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of 0.02 cm/s. The rate of increase of its volume when the radius is 10 cm is ___________$\pi$ cm/s

A large number of liquid drops each of radius r coalesce to from a single drop of radius R. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given, surface tension of liquid T, density $\rho$)

For the LPP; maximise $z =x + 4y$ subject to the constraints $x + 2y \leq 2, x +2 y \ge 8, x, y \ge 0$

An element occuring in the bcc structure has $12.08 \times 10^{23}$ unit cells. The total number of atoms of the element in these cells will be

A metal disc of radius $100 \,cm$ is rotated at a constant angular speed of $60$ rad/s in a plane at right angles to an external field of magnetic induction $0.05\, Wb/m^2$. The emf induced between the centre and a point on the rim will be

One mole of a mono-atomic ideal gas undergoes a quasi-static process, which is depicted by a straight line joining points $(V_0, T_0)$ and $(2V_0, 3T_0)$ in a $V-T$ diagram. What is the value of the heat capacity of the gas at the point $(V_0, T_0)$ ?

Which one is a synthetic Auxin:

Match the items given in Column I with those in Column II and select the correct option given below:

A tuning fork is used to produce resonance in glass tube. The length of the air column in the tube can be adjusted by a variable piston, A room temperature of $27^{\circ} C$ two successive resonances are produced at $20\, cm$ and $73\, cm$ column length. If the frequency of the tuning for is $320\, Hz$, the velocity of sound in air at $27^{\circ} C$

Which part of poppy plant is used to obtain the drug "Smack" ?

Which of the following is not an autoimmune disease ?