List of practice Questions

If $\vec{a} , \vec{b} , \vec{c}$ are mutually perpendicular vectors having magnitudes 1, 2, 3 respectively, then $[\vec{a} + \vec{b} + \vec{c} \, \, \vec{b} - \vec{a} - \vec{c}] = ?$

If $2 \sin \left( \theta + \frac{\pi}{3}\right) = \cos \left( \theta -\frac{\pi}{6}\right) , $ then $\tan \, \theta = $

An electric bulb, a capacitor, a battery and a switch are all in series in a circuit. How does the intensity of light vary when the switch is turned on ?

What will be the current flowing through the $6 \,K \Omega$ resistor in the circuit shown, where the breakdown voltage of the zener is $6\, V$ ?

On $R$, a relation $\rho$ is defined by $x \rho y$ if and only if $x - y$ is zero or irrational. Then

The value of the integral $I = \int\limits^{2014}_{1/2014} \frac{\tan^{-1} x}{x} dx $ is

The electrostatic force between the metal plate of an isolated parallel plate capacitor $C$ having charge $Q$ and area $A$, is

Consider the change in oxidation state of Bromine corresponding to different emf values as shown in the diagram below : is Then the species undergoing disproportionation is

All of the following are part of an operon except

If $f : R \to R$ be defined by $f(x) = e^x $ and $g : R \to R $ be defined by $g(x) = x^2$. The mapping $g of : R \to R $ be defined by $(g o f ) (x) = g[f(x)] \forall x \in R$ , Then

$C_4H_10 O { ->[{K_2Cr_2O_7}][{H_2SO_4}] }C_4H_5O { ->[{I_2/NaOH}][{\text{Warm}}] }CHI_3$ Here, N is

If aniline is treated with conc. $H_2SO_4$ and heated at $200^{\circ}C$, the product is

Ferric ion forms a Prussian blue precipitate due to the formation of

A compound formed by elements $X$ and $Y$ crystallizes in the cubic structure, where $X$ atoms are at the corners of a cube and $Y$ atoms are at the centres of the body. The formula of the compound is

The nucleus ${^{64}_{29}Cu}$ accepts an orbital electron to yield.

Select the INCORRECT statement with reference to DNA fingerprinting. It is _________

If $z_1$ and $z_2$ be two non zero complex numbers such that $\frac{z_1 }{z_2 } + \frac{z_2}{z_1} = 1 $, then the origin and the points represented by $z_1$ and $z_2$

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