A solution of non volatile solute has boiling point elevation 1.75 K . Calculate molality of solution $\left[\mathrm{K}_

Which from following metal ions in their respective oxidation states forms coloured compound?

Calculate the density of an element having molar mass $63 \mathrm{~g} \mathrm{~mol}^{-1}$ that forms fcc structure $\lef

Which from following groups is selected as principal functional group for nomenclature of a polyfunctional compound acco

Identify the structure of $\mathrm{XeF}_4$ molecule from following.

Calculate $\left[\mathrm{H}_3 \mathrm{O}^{+}\right]$in 0.02 M solution of monobasic acid if dissociation constant is $1.

Which from following statements is NOT true according to principles of green chemistry?

The molar conductivity of 0.02 M KCl solution is $410 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ at $25^{\circ} \mat

What is the coordination number of a particle in hcp structure?

Identify essential amino acid from following.

Identify the formula of pentaaquaisothiocyanatoiron(III) ion from following.

If bond formation energy of $\mathrm{H}-\mathrm{H}$ bond is $-433 \mathrm{~kJ} \mathrm{~mol}^{-1}$ find the bond dissoci

Identify homopolymer from following.

Which from following molecules has two lone pair of electrons in valence shell of its central atom?

Identify the product ' B ' in the following sequence of reactions. Propanone $\xrightarrow{\mathrm{B_a}(\mathrm{OH})_2}

What time is required for 100 g of reactant to reduce to 25 g in a first order reaction having half life 5760 year?

What is the value of standard enthalpy of formation of dihydrogen?

What is the amount of energy associated with first orbit of monopositive helium ion? $\left[\mathrm{R}_{\mathrm{H}}=2.18

Which of the following statements is correct about zero order reaction?

Calculate Gibbs energy change for a reaction having $\Delta \mathrm{H}=31400 \mathrm{~J}, \Delta \mathrm{~S}=32 \mathrm{

Identify the substrate 'S' in the following reaction.

Which from following is an example of multimolecular colloids?

Which of the following is secondary benzylic alcohol?

Identify the reagent ' R ' used in the following reaction. Benzoyl chloride $$ \to $$ Benzaldehyde

What is the representation of an element having mass number of 40 and 21 neutrons in it?

How many moles of dioxygen are present in $8.314 \times 10^{-3} \mathrm{~m}^3$ of it at 318 K having pressure $3.18 \tim

Which of the following compounds has difficulty in breaking the $\mathrm{C}-\mathrm{Cl}$ bond?

Identify the alkene obtained as major product in the following Hofmann elimination reaction. $$ \left(\mathrm{C}_3 \mat

Calculate the amount of electricity required to convert 1.1 mol of $\mathrm{Cr}_2 \mathrm{O}_7^{2-}$ to $\mathrm{Cr}^{+3

Which of the following on reaction with Grignard reagent followed by hydrolysis forms secondary alcohol?

Which of the following compounds does not undergo haloform reaction?

Which from following properties is NOT identical for Enantiomers?

Which from following combinations represents water gas?

Which from the following statements is correct for aqueous solution of $6 \mathrm{~g} \mathrm{~L}^{-1}$ urea and $17 \cd

Identify the element with lowest electronegativity.

Calculate the volume occupied by all atoms in bcc unit cell if the volume of unit cell is $1.5 \times 10^{-22} \mathrm{~

What is the number of electrons present in 3d orbital of Ti in +2 state?

Identify molecular formula of laevulose

Which of the following pair of compounds does not demonstrate the law of multiple proportion?

What is the coordination number of central metal ion in $\left[\mathrm{Fe}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right

Which from following polymers is obtained by ring opening polymerization method?

What is IUPAC name of propylene glycerol?

Which of the following equations represents the relation between solubility and solubility product for salt BA$_3$?

Which of the following catalysts is used to convert to form cis-alkene?

For a reaction, $$2 \mathrm{~N}_2 \mathrm{O}_{5(\mathrm{~g})} \longrightarrow 4 \mathrm{NO}_{2(\mathrm{~g})}+\mathrm{O}_

Calculate the molar mass of nonvolatile solute when 1.5 g of it is dissolved in 90 g solvent decreases its freezing poin

Which of the following does not have intermolecular hydrogen bonding?

Which of the following statements is NOT correct for $\mathrm{H}_2-\mathrm{O}_2$ fuel cell?

Identify the element reduced in following reaction. $$\mathrm{Cr}_2 \mathrm{O}_7^{2-}+14 \mathrm{H}^{+}+6 \mathrm{I}^{-}

Calculate the pH of buffer solution containing 0.027 M weak acid and 0.054 M of its salt with strong base if $\mathrm{pK

If $\int \frac{\mathrm{d} x}{\cos ^3 x \sqrt{2 \sin 2 x}}=(\tan x)^A+C(\tan x)^B+K$, where K is a constant of integratio

$$\int \frac{2 x^2-1}{\left(x^2+4\right)\left(x^2-3\right)} d x=$$

Let $\mathrm{f}(x)=\frac{1-\tan x}{4 x-\pi}, x \neq \frac{\pi}{4}, x \in\left[0, \frac{1}{2}\right], \quad \mathrm{f}(x)

The number of possible distinct straight lines passing through $(2,3)$ and forming a triangle with co-ordinate axes whos

The differential equation $\left[\frac{1+\left(\frac{d y}{d x}\right)^2}{\left(\frac{d^2 y}{d x^2}\right)}\right]^{\frac

A triangular park is enclosed on two sides by a fence and on the third side a straight river bank. The two sides having

If p and q are statements, then _________ is a contingency.

If $\int_\limits0^{\frac{\pi}{3}} \frac{\tan \theta}{\sqrt{2 k \sec \theta}} d \theta=1-\frac{1}{\sqrt{2}},(k>0)$, then

A random variable x has the following probability distribution. Then value of $k$ is _________ and $\mathrm{P}(3 .tg {

If $y=\log \left[\mathrm{e}^{5 x}\left(\frac{3 x-4}{x+5}\right)^{\frac{4}{3}}\right]$, then $\frac{\mathrm{d} y}{\mathrm

 Let $f$ be a twice differentiable function such that $\mathrm{f}^{\prime \prime}(x)=-\mathrm{f}(x), \mathrm{f}^{\prime}

The area (in sq. units) of the parallelogram whose diagonals are along the vectors $8 \hat{\mathrm{i}}-6 \hat{\mathrm{j}

The line L given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line K is parallel to L and has

If $|\bar{a}|=\sqrt{27},|\bar{b}|=7$ and $|\bar{a} \times \bar{b}|=35$, then $\bar{a} \cdot \bar{b}$ is equal to

The number of real solutions of $\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^2+x+1}=\frac{\pi}{2}$ is

Let $S=\left\{x \in(-\pi, \pi) \mid x \neq 0, \pm \frac{\pi}{2}\right\}$. The sum of all distinct solutions of the equat

The number of four letter words that can be formed using letters of the word BARRACK

A stone is dropped into a quiet lake and waves move in circles at speed of $8 \mathrm{~cm} / \mathrm{sec}$. At the insta

The area (in sq. units) of the region bounded by the curve $x^2=4 y$ and the straight line $x=4 y-2$ is

If the half life of substance is 5 years, then the total amount of the substance left after 15 years, when initial amoun

Equation of the plane containing the straight line $\frac{x}{3}=\frac{y}{2}=\frac{z}{4}$ and perpendicular to the plane

The number of roots of the equation, $(81)^{\sin ^2 x}+(81)^{\cos ^2 x}=30$ in the interval $[0, \pi]$, is equal to

If $\quad \int(2 x+4) \sqrt{x-1} d x=a(x-1)^{5 / 2}+b(x-1)^{3 / 2}+c$ where $c$ is a constant of integration, then the v

Let $\mathrm{X} \sim \mathrm{B}\left(6, \frac{1}{2}\right)$, then $\mathrm{P}[|x-4| \leqslant 2]$ is

The mean of $n$ observations is $\bar{x}$. If three observations $\mathrm{n}+1, \mathrm{n}-1,2 \mathrm{n}-1$ are added s

If $y=\sec \left(\tan ^{-1} x\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=1$ is equal to

The equation of the concentric circle, with the circle $\mathrm{C}_1$ having equation $x^2+y^2-6 x-4 y-12=0$ and having

Let $\alpha(a)$ and $\beta(a)$ be the roots of the equation $$(\sqrt[3]{1+a}-1) x^2+(\sqrt{1+a}-1) x+(\sqrt[6]{1+a}-1)=0

Let $2 \sin ^2 x+3 \sin x-2>0$ and $x^2-x-2

If $\mathrm{A} \equiv(1,-1,0), \mathrm{B} \equiv(0,1,-1)$ and $\mathrm{C} \equiv(-1,0,1)$, then the unit vector $\overli

A bullet is shot horizontally and its distance S cm at time t second is given by $\mathrm{S}=1200 \mathrm{t}-15 \mathrm{

If $|z|=1$ and $w=\frac{z-1}{z+1}$ (where $\left.z \neq-1\right)$, then $\operatorname{Re}(w)$ is

If $g(x)=x^2+x-1$ and (gof) $(x)=4 x^2-10 x+5$, then $\mathrm{f}(2)$ is equal to

The shaded area in the figure below is the solution set for a certain linear programming problem, then the linear constr

The equation of the normal to the curve $x=\theta+\sin \theta, y=1+\cos \theta$ at $\theta=\frac{\pi}{2}$ is

If $\tan x=\frac{3}{4}$ and $\pi

The value of $m$, such that $\frac{x-4}{1}=\frac{y-2}{1}=\frac{2 z-m}{3}$ lies in the plane $2 x-5 y+2 z=7$, is

The image of the line $\frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-5}$ in the plane $2 x-y+z+3=0$ is the line

Let the vectors $\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$ be such that $|\overline{\mathrm{a

A person throws an unbiased die. If the number shown is even, he gains an amount equal to the number shown. If the numbe

Let $\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$ and $\overline{\mathrm{b}}=\hat{\math

If $\theta$ and $\alpha$ are not odd multiples of $\frac{\pi}{2}$ then $\tan \theta=\tan \alpha$ implies principal solut

The approximate value of $\cos \left(30^{\circ}, 30^{\prime}\right)$ is given that $1^{\circ}=0.0175^{\circ}$ and $\cos

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Let X denote the random variabl

The value of $\int \frac{(x-1) \mathrm{e}^x}{(x+1)^3} \mathrm{~d} x$ is equal to

Let $\mathrm{P}(2,3,6)$ be a point in space and Q be a point on the line $\bar{r}=(\hat{i}-\hat{j}+2 \hat{k})+\mu(-3 \ha

Consider the following statements p : the switch $\mathrm{S}_1$ is closed. q : the switch $\mathrm{S}_2$ is closed. $r$

Let $\bar{a}, \bar{b}, \bar{c}$ be three non-coplanar vectors and $\overline{\mathrm{p}}, \overline{\mathrm{q}}, \overli

If $A=\left[\begin{array}{cc}2 & -2 \\ 4 & 3\end{array}\right]$, then $A^{-1}=$

The differential equation of family of circles, whose centres are on the X -axis and also touch the Y -axis is

A ball ' $A$ ' is projected vertically upwards with certain initial speed. Another ball 'B' of same mass is projected at

A small sphere oscillates simple harmonically in a watch glass whose radius of curvature is 1.6 m . The period of oscill

The path difference between two waves $\mathrm{Y}_1=\mathrm{a}_1 \sin \left(\omega \mathrm{t}-\frac{2 \pi \mathrm{x}}{\l

Two equal point charges ' $q$ ' each exert a force ' $F$ ' on each other, when they are placed distance ' $x$ ' apart in

An alternating voltage $\mathrm{v}=200 \sqrt{2} \sin (100 \mathrm{t})$ is connected to a $1 \mu \mathrm{~F}$ capacitor t

Three charges $2 q,-q$ and $-q$ are located at the vertices of an equilateral triangle. At the centre of the triangle

A gardening pipe having an internal radius ' $R$ ' is connected to a water sprinkler having ' $n$ ' holes each of radius

A magnetic needle of magnetic moment $6 \times 10^{-2} \mathrm{Am}^2$ and moment of inertia $9.6 \times 10^{-5} \mathrm{

In case of rotational dynamics, which one of the following statements is correct? [$\vec{\omega}=$ angular velocity, $\o

A convex lens of focal length ' $f$ ' $m$ forms a real, inverted image twice in size of the object. The object distance

The ratio of the wavelength of a photon of energy ' $E$ ' to that of the electron of same energy is ( $\mathrm{m}=$ mass

The r.m.s. velocity of hydrogen at S.T.P. is ' $u$ ' $\mathrm{m} / \mathrm{s}$. If the gas is heated at constant pressur

The distance of the two planets A and B from the sun are $r_A$ and $r_B$ respectively. Also $r_B$ is equal to $100 r_A$.

A tube of uniform bore of cross-sectional area ' $A$ ' has been set up vertically with open end facing up. Now ' $M$ ' g

An n-p-n transistor can be considered to be equivalent to two diodes connected. The correct figure out of the following

The fundamental frequency of an air column in a pipe open at both ends is ' $\mathrm{f}_1$ '. Now $80 \%$ of its length

Earth has mass ' $M_1$ ' radius ' $R_1$ ' and for moon mass ' $M_2$ ' and radius ' $R_2$ '. Distance between their centr

In an interference experiment, the $\mathrm{n}^{\text {th }}$ bright fringe for light of wavelength $\lambda_1(\mathrm{n

Three inductances are connected as shown in figure. The equivalent inductance is

There are two samples A and B of a certain gas, which are initially at the same temperature and pressure. Both are compr

A single slit diffraction pattern is formed with light of wavelength $6195 \mathop A\limits^o$. The second secondary max

Two rods, one of aluminium and the other of steel, having initial lengths ' $\mathrm{L}_1$ ' and ' $\mathrm{L}_2$ ' are

In an a. c. generator, when the plane of the coil is perpendicular to the magnetic field

Two circular metal plates each of radius ' $r$ ' are kept parallel to each other distance ' $d$ ' apart. The capacitance

Ratio of radius of gyration of a circular disc to that of circular ring each of same mass and radius around their respec

In an $A C$ circuit $E=200 \sin (50 t)$ volt and $\mathrm{I}=100 \sin \left(50 \mathrm{t}+\frac{\pi}{3}\right) \mathrm{m

In the following circuit, a power of 50 watt is absorbed in the section AB of the circuit. The value of resistance ' $x$

A ray of light is incident at $60^{\circ}$ on one face of a prism of angle $30^{\circ}$ and the emergent ray makes $30^{

Given that ' $x$ ' joule of heat is incident on a body. Out of that, total heat reflected and transmitted is ' $y$ ' jou

In the uranium radioactive series, the initial nucleus is ${ }_{92}^{238} \mathrm{U}$ and that the final nucleus is ${ }

When photons of energy hv fall on a photosensitive surface of work function $\mathrm{E}_0$, photoelectrons of maximum en

The pressure inside two soap bubbles, (A) is 1.01 and that of (B) is 1.02 atmosphere respectively. The ratio of their re

The pitch of a whistle of an engine appears to drop by $30 \%$ of original value when it passes a stationary observer. I

A transformer having efficiency $90 \%$ is working on 200 V and 3 kw power supply. If the current in the secondary coil

A diatomic ideal gas is used in Carnot engine as a working substance. If during the adiabatic expansion part of the cycl

The range of voltmeter of resistance ' $G$ ' $\Omega$ is ' $V$ ' volt. The resistance required to be connected in series

Find the magnitude of current in the given circuit.

An inductance coil has a resistance of $80 \Omega$. When on AC signal of frequency 480 Hz is applied to the coil, the vo

The displacement of a wave is given by $y=0.002 \sin (100 t+x)$ where ' $x$ 'and ' $y$ ' are in metre and ' $t$ ' is in

A current of 5 A flows through a toroid having a core of mean radius 20 cm . If 4000 turns of the conducting wire are wo

A metal ball of radius $9 \times 10^{-4} \mathrm{~m}$ and density $10^4 \mathrm{~kg} / \mathrm{m}^3$ falls freely under

When wavefronts pass from denser medium to rarer medium, the width of the wavefront

The relation between total magnetic field (B), magnetic intensity $(\mathrm{H})$, permeability of free space $\left(\mu_

In common emitter transistor amplifier, load resistance is $6.5 \mathrm{k} \Omega$ and an input resistance is $1.3 \math

A particle having a charge 50 e is revolving in a circular path of radius 0.4 m with $1 \mathrm{r} . \mathrm{p} . \mathr

Two blocks of masses 6 kg and 4 kg are placed in contact with each other on a smooth surface as shown. If a force of 5 N

Two circular loops P and Q of radii ' r ' and ' nr ' are made respectively from a uniform wire. Moment of inertia of loo

Two spherical black bodies of radii ' $R_1$ ' and ' $\mathrm{R}_2$ ' and with surface temperature ' $\mathrm{T}_1$ ' and

If ' $\lambda_1$ ' and ' $\lambda_2$ ' are the wavelengths of the first line of the Lyman and Paschen series respectivel

An electric dipole of moment $\overrightarrow{\mathrm{p}}$ is lying along a uniform electric field $\overrightarrow{\mat