$$\mathrm{O}-\mathrm{O}$$ bond length in $$\mathrm{H}_{2} \mathrm{O}_{2}$$ is $$\underline{\mathrm{X}}$$ than the $$\mat

All structures given below are of vitamin C. Most stable of them is :

'$$\mathrm{X}$$' is :

In a reaction, reagents 'X' and 'Y' respectively are :

Given below are two statements : Statement I : Sulphanilic acid gives esterification test for carboxyl group. Statement

Which element is not present in Nessler's reagent?

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A)

The effect of addition of helium gas to the following reaction in equilibrium state, is : $$\mathrm{PCl}_{5}(\mathrm{g})

Which one of the following sets of ions represents a collection of isoelectronic species? (Given : Atomic Number : $$\ma

For electron gain enthalpies of the elements denoted as $$\Delta_{\mathrm{eg}} \mathrm{H}$$, the incorrect option is :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R) Assertion (A)

The complex cation which has two isomers is :

The structures of major products A, B and C in the following reaction are sequence.

The graph which represents the following reaction is :

Among following compounds, the number of those present in copper matte is ___________. A. $$\mathrm{CuCO_{3}}$$ B. $$\ma

$$1 \times 10^{-5} ~\mathrm{M} ~\mathrm{AgNO}_{3}$$ is added to $$1 \mathrm{~L}$$ of saturated solution of $$\mathrm{AgB

Testosterone, which is a steroidal hormone, has the following structure. The total number of asymmetric carbon atom/s i

$$20 \%$$ of acetic acid is dissociated when its $$5 \mathrm{~g}$$ is added to $$500 \mathrm{~mL}$$ of water. The depres

$$0.3 \mathrm{~g}$$ of ethane undergoes combustion at $$27^{\circ} \mathrm{C}$$ in a bomb calorimeter. The temperature o

The molality of a $$10 \%(\mathrm{v} / \mathrm{v})$$ solution of di-bromine solution in $$\mathrm{CCl}_{4}$$ (carbon tet

The spin only magnetic moment of $$\left[\mathrm{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$$ complexes i

$$\mathrm{A}$$ $$\rightarrow \mathrm{B}$$ The above reaction is of zero order. Half life of this reaction is $$50 \mathr

Let $$9=x_{1}

Let $$P(S)$$ denote the power set of $$S=\{1,2,3, \ldots ., 10\}$$. Define the relations $$R_{1}$$ and $$R_{2}$$ on $$P(

The sum of the absolute maximum and minimum values of the function $$f(x)=\left|x^{2}-5 x+6\right|-3 x+2$$ in the interv

Let $$\vec{a}=5 \hat{i}-\hat{j}-3 \hat{k}$$ and $$\vec{b}=\hat{i}+3 \hat{j}+5 \hat{k}$$ be two vectors. Then which one o

For the system of linear equations $$\alpha x+y+z=1,x+\alpha y+z=1,x+y+\alpha z=\beta$$, which one of the following stat

If $$y(x)=x^{x},x > 0$$, then $$y''(2)-2y'(2)$$ is equal to

The value of the integral $$\int\limits_{ - {\pi \over 4}}^{{\pi \over 4}} {{{x + {\pi \over 4}} \over {2 - \cos 2x}}

The area of the region given by $$\{ (x,y):xy \le 8,1 \le y \le {x^2}\} $$ is :

The number of integral values of k, for which one root of the equation $$2x^2-8x+k=0$$ lies in the interval (1, 2) and i

Let $$a,b$$ be two real numbers such that $$ab

If $$A = {1 \over 2}\left[ {\matrix{ 1 & {\sqrt 3 } \cr { - \sqrt 3 } & 1 \cr } } \right]$$, then :

Two dice are thrown independently. Let $$\mathrm{A}$$ be the event that the number appeared on the $$1^{\text {st }}$$ d

Let $$\vec{a}=2 \hat{i}-7 \hat{j}+5 \hat{k}, \vec{b}=\hat{i}+\hat{k}$$ and $$\vec{c}=\hat{i}+2 \hat{j}-3 \hat{k}$$ be th

Let $$S = \left\{ {x \in R:0 If $$\mathrm{n(S)}$$ denotes the number of elements in $$\mathrm{S}$$ then :

Let $$f:\mathbb{R}-{0,1}\to \mathbb{R}$$ be a function such that $$f(x)+f\left(\frac{1}{1-x}\right)=1+x$$. Then $$f(2)$$

Let $$\alpha x=\exp \left(x^{\beta} y^{\gamma}\right)$$ be the solution of the differential equation $$2 x^{2} y \mathrm

If the $$x$$-intercept of a focal chord of the parabola $$y^{2}=8x+4y+4$$ is 3, then the length of this chord is equal t

If $$\int\limits_0^\pi {{{{5^{\cos x}}(1 + \cos x\cos 3x + {{\cos }^2}x + {{\cos }^3}x\cos 3x)dx} \over {1 + {5^{\cos x

Let the sixth term in the binomial expansion of $${\left( {\sqrt {{2^{{{\log }_2}\left( {10 - {3^x}} \right)}}} + \root

The sum of the common terms of the following three arithmetic progressions. $$3,7,11,15, \ldots ., 399$$, $$2,5,8,11, \l

Number of integral solutions to the equation $$x+y+z=21$$, where $$x \ge 1,y\ge3,z\ge4$$, is equal to ____________.

If the term without $$x$$ in the expansion of $$\left(x^{\frac{2}{3}}+\frac{\alpha}{x^{3}}\right)^{22}$$ is 7315 , then

The total number of six digit numbers, formed using the digits 4, 5, 9 only and divisible by 6, is ____________.

Given below are two statements : One is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\math

The escape velocities of two planets $$\mathrm{A}$$ and $$\mathrm{B}$$ are in the ratio $$1: 2$$. If the ratio of their

The ratio of average electric energy density and total average energy density of electromagnetic wave is :

Equivalent resistance between the adjacent corners of a regular n-sided polygon of uniform wire of resistance R would be

A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magn

Given below are two statements: One is labeled as Assertion A and the other is labeled as Reason R. Assertion A : Two me

Choose the correct length (L) versus square of the time period ($$\mathrm{T}^{2}$$) graph for a simple pendulum executin

If the velocity of light $$\mathrm{c}$$, universal gravitational constant $$\mathrm{G}$$ and Planck's constant $$\mathrm

The Young's modulus of a steel wire of length $$6 \mathrm{~m}$$ and cross-sectional area $$3 \mathrm{~mm}^{2}$$, is $$2

Choose the correct statement about Zener diode :

As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle $$3

Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature

For a body projected at an angle with the horizontal from the ground, choose the correct statement.

As shown in the figure, a long straight conductor with semicircular arc of radius $$\frac{\pi}{10}$$m is carrying curren

The threshold frequency of a metal is $$f_{0}$$. When the light of frequency $$2 f_{0}$$ is incident on the metal plate,

For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume

Figures (a), (b), (c) and (d) show variation of force with time. The impulse is highest in figure.

An electron of a hydrogen like atom, having $$Z=4$$, jumps from $$4^{\text {th }}$$ energy state to $$2^{\text {nd }}$$

A square shaped coil of area $$70 \mathrm{~cm}^{2}$$ having 600 turns rotates in a magnetic field of $$0.4 ~\mathrm{wbm}

A block is fastened to a horizontal spring. The block is pulled to a distance $$x=10 \mathrm{~cm}$$ from its equilibrium

As shown in the figure, in Young's double slit experiment, a thin plate of thickness $$t=10 \mu \mathrm{m}$$ and refract

Nucleus A having $$Z=17$$ and equal number of protons and neutrons has $$1.2 ~\mathrm{MeV}$$ binding energy per nucleon.

Moment of inertia of a disc of mass '$$M$$' and radius '$$R$$' about any of its diameter is $$\frac{M R^{2}}{4}$$. The m

The surface of water in a water tank of cross section area $$750 \mathrm{~cm}^{2}$$ on the top of a house is $$h \mathrm

A force $$\mathrm{F}=\left(5+3 y^{2}\right)$$ acts on a particle in the $$y$$-direction, where $$\mathrm{F}$$ is in newt

For a train engine moving with speed of $$20 \mathrm{~ms}^{-1}$$, the driver must apply brakes at a distance of 500 $$\m

In the given circuit, the value of $$\left| {{{{\mathrm{I_1}} + {\mathrm{I_3}}} \over {{\mathrm{I_2}}}}} \right|$$ is __

A cubical volume is bounded by the surfaces $$\mathrm{x}=0, x=\mathrm{a}, y=0, y=\mathrm{a}, \mathrm{z}=0, z=\mathrm{a}$