What is the number of molecules in 2.125 g of ammonia?

Identify pair of orbitals having similar $(n + l)$ values from the following.

What is the proportionality between (I) Bond length and size of atom (II) Bond length and multiplicity of bond respectively?

A mixture of 0.5 mol $\text{N}_2$ gas, 1.0 mol $\text{O}_2$ gas and 1.5 mol $\text{H}_2$ gas exerts a total pressure of 18 bar. Find the partial pressure of $\text{O}_{2(g)}$.

The enthalpy of combustion of C, $\text{H}_2$, and $\text{CH}_4$ are $-390$, $-285$ and $-890$ kJ/mol. Find the enthalpy of formation of methane.

Calculate the change in internal energy if an ideal gas expands from $0.5\ \text{dm}^3$ to $3.5\ \text{dm}^3$ at constant pressure 2 bar by absorbing 1800 J heat energy.

Which of the following processes exhibits the decrease in internal energy of a system?

There are two different solutions, A and B. The pH of solution A is 4. Find the pH of solution B having $[\text{H}^+]$ three times that of solution A.

Calculate the pH of buffer solution containing 0.1M $\text{CH}_3\text{COOH}$ and 0.1 M $\text{CH}_3\text{COONa}$ $[K_a = 1.8 \times 10^{-5}]$

What is the pH of 1 molar HCl solution? (assume complete dissociation)

What is the oxidation state of Xe in $\text{XeOF}_4$?

What is the oxidation number of Cl in $\text{HOClO}_2$?

What is the number of electrons gained by Cl atom when $n$ mole of $\text{ClO}_4^-$ is transformed into $n$ mole of $\text{ClO}_2^-$ ion?

Choose a false statement regarding the properties of sodium hydroxide.

The IUPAC name of the following compound is,

Which of the following molecule has Chiral Carbon?

Which one of the following series contains only electrophiles?

Which of the following reaction steps is known as propagation step

A metal crystallizes in a bcc unit cell having unit cell volume $2.5 \times 10^{-23}\ \text{cm}^3$. Find the number of unit cells in 18 g metal if the density of metal is $7.2\ \text{g cm}^{-3}$.

A metal has a fcc structure if the edge length of unit cell is 200 pm, calculate the volume occupied by particles in a unit cell.

Which of the following defects is observed in steel?

When the bottle of soft drink is opened, what would take place from the following?
(A) Solubility of dissolved gas decreases.
(B) bottle released internal pressure.
(C) effervences evolved from the bottle.
(D) increase in external pressure.
Identify the correct choice.

Find the osmotic pressure of 0.01 M solution at 25 °C $(R = 0.0821\ \text{L atm mol}^{-1}\text{K}^{-1})$

Identify the colligative property from the followings?

Determine the electrode potential of $\text{Sn}^{2+}(0.01\text{M})\ |\ \text{Sn(s)}$ at $25^\circ\text{C}$ if $E^\circ_{\text{Sn}}$ is $-0.136$ V.

If molar conductance at infinite dilution for $\text{CH}_3\text{COO}^-$ and $\text{H}^+$ ions are $50\ \text{S cm}^2\ \text{mol}^{-1}$ and $350\ \text{S cm}^2\ \text{mol}^{-1}$ respectively, molar conductivity of $5 \times 10^{-2}$ M $\text{CH}_3\text{COOH}$ is $20\ \text{S cm}^2\text{mol}^{-1}$. What is the hydrogen ion concentration in $\text{mol/dm}^3$ of $\text{CH}_3\text{COOH}$?

Which of the following expressions indicates the correct relationship between molar conductivity of strong electrolyte and its concentration?

What is the role of catalyst in reaction?

Calculate the rate constant of first order reaction $\text{A} \rightarrow \text{B}$ having rate $5.4 \times 10^{-6}\ \text{mol dm}^{-3}\text{s}^{-1}$ and $[\text{A}] = 0.3$ M.

What is the order and molecularity of the following elementary reaction?
$2\text{NO}_{2(g)} \rightarrow 2\text{NO}_{(g)} + \text{O}_{2(g)}$, rate $= k \times [\text{NO}_2]^2$

Which of the following nanomaterials has one dimension $< 100$ nm?

In Haber process of production of ammonia $\text{Al}_2\text{O}_3$ is used as

Which of the following pairs of elements does NOT include transition elements?

Which of the following prediction is correct when the transition metal ion is colourless?

Which of the following complex is neutral?

Which of the following coordinate complexes is heteroleptic?

What is the major product formed when 2-bromopentane reacts with alcoholic KOH?

In Finkelstein reaction, which one of the following reagents is used?

Which of the following alcohols contains the hydroxy group, at the side chain of the aromatic ring?

In the following reaction, condition 'A' is -

Which of the following compounds exhibits Schiff test?

Which of the following reactions is preferentially used to prepare the corresponding paraffins from alkanone?

Identify the reason for the highest boiling point of R-COOH as compared to alkanes, ethers, alcohols and aldehydes.

Aniline on treatment with $\text{NaNO}_2$ / HCl at about $0^\circ\text{C}$ gives a compound A, which on further treatment with CuCN / KCN gives a compound B, which when reacts with $\text{H}_2$ / Ni gives a compound C. The compound C on reaction with $\text{HNO}_2$ gives a compound D. The structure of D is:

Identify the reagent used to distinguish primary and secondary amines by Hinsberg test.

Identify the product when glucose reacts with bromine water.

What type of compound the Legumelin is?

Which of the following is fully Fluorinated polymer?

Which of the following is a cross-linked, thermosetting polymer?

What is the chemical name of Aspirin?

The statement having truth value 'T' from the following is

If $i = \sqrt{-1}$ then $\left[i^{18} + \left(\dfrac{1}{i}\right)^{25}\right]^3 =$

The number of permutations of the letters of the word INSTITUTION are .......

If $x + y = \dfrac{\pi}{4}$, then $(1 + \tan x)(1 + \tan y) =$

A straight line makes equal negative intercepts on the coordinate axes. If the perpendicular distance from the origin to the line is 4 units, then the equation of the line is ......

If the angle made by the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ with X-axis are $\alpha$ and $\beta$, then $\tan(\alpha + \beta)$ is

The equation of a circle whose center lies on $x + 2y = 0$ and touching the lines $3x - 4y + 8 = 0$ and $3x - 4y - 28 = 0$ is

If $P$ be any point on the ellipse $16x^2 + 25y^2 = 400$ with foci $S$ and $S'$ and area of $\triangle PSS'$ is 9 square units, then the abscissa of point $P$ is...........

The value of $\lim\limits_{n \to \infty}\left[\dfrac{1}{1 - n^2} + \dfrac{2}{1 - n^2} + \ldots + \dfrac{n}{1 - n^2}\right]^3$ is

If $\sim p \vee q$ is false then which of the following is correct?

The contrapositive of $\sim q \rightarrow p$ is equivalent to

The angles of $\triangle ABC$ are in A.P. and $b : c = \sqrt{3} : \sqrt{2}$ then $\angle A =$

With the usual notations, if the lengths of the sides of the triangle are 3 units, 5 units and 7 units, then the largest angle of the triangle is

If $A = \begin{bmatrix} 1 & -5 \\ -2 & 4 \end{bmatrix}$, then $A^{-1} =$

Let $A = \begin{bmatrix} 3 & 1 & 2 \\ 1 & 2 & 0 \\ 1 & 1 & 4 \end{bmatrix}$ and $pC_{11} + 4C_{21} - 5C_{32} = -2$, where $C_{ij}$ denotes the cofactor of an element $a_{ij}$ of matrix $A$, then the value of $p$ is :

If $3\sin^{-1}\left(\dfrac{2x}{1 + x^2}\right) - 4\cos^{-1}\left(\dfrac{1 - x^2}{1 + x^2}\right) + 2\tan^{-1}\left(\dfrac{2x}{1 - x^2}\right) = \dfrac{\pi}{3}$ then $x = ?$

If $2\sin^{-1}x - 3\cos^{-1}x = 4$, then $2\sin^{-1}x + 3\cos^{-1}x =$

If $f(x) = \dfrac{2x - 1}{x + 5}$, $x \neq -5$ then $f^{-1}(x)$ is equal to

If the function $f(x)$ defined by $f(x) = \begin{cases} ax + 1 & \text{if } x \leq 3 \\ bx + 3 & \text{if } x > 3 \end{cases}$ is continuous at $x = 3$, then $(a - b) =$ ..........

If $f(x), g(x)$ be twice differentiable functions, satisfying $f''(x) = g''(x), f'(1) = 2g'(1) = 4$ and $f(2) = 3g(2) = 9$ then $f(x) - g(x)$ at $x = 4$ is equal to

If $y = \cos^2\left[\cot^{-1}\left(\sqrt{\dfrac{1 - x}{1 + x}}\right)\right]$ then $\dfrac{dy}{dx} = $ ........

If $\sqrt{\dfrac{x}{y}} + \sqrt{\dfrac{y}{x}} = 6$, then $\dfrac{dy}{dx} =$

If $x = 4t^3 + 3, y = 3t^4 + 4$ and $\dfrac{\frac{d^2x}{dy^2}}{\left(\frac{dx}{dy}\right)^n}$ is constant then the value of $n$ is

If $x = a\sin^3 t$ and $y = a\cos^3 t$, then the value of $\dfrac{d^2y}{dx^2}$ at $t = \dfrac{\pi}{3}$ is equal to

An aeroplane at an altitude of 1 km is flying horizontally at 600 km / hr, passes directly over an observer. Then the rate at which it is approaching the observer when it is 1250 meters away from him is........

The line $x + y = 0$ touches the curve $y^2 = ax^3 + b$ at $(1, -1)$ then values of $a$ and $b$ respectively are ...........

The function $f(x) = x(x + 3)e^{-\left(\frac{1}{2}\right)x}$ satisfies all the conditions of Rolle's theorem in $[-3, 0]$, then $c =$

If $\int f(x)dx = g(x) + c$ then $\int f^{-1}(x)dx =$

$\int\dfrac{\log x}{(1 + \log x)^2}dx =$

$\int\dfrac{1}{\sqrt{2x - x^2}}dx =$

$\int(x^{21} + x^6 + x^3)(2x^{18} + 7x^3 + 14)^{\frac{1}{3}}\ dx =$

The value of the integral $\int\limits_{1/e}^{e}\dfrac{|\log x|}{x^2}dx$ is

If $\int\limits_{-\pi/2}^{\pi/2}(\sin^2 x + \sin^3 x)dx = k$, then the value of $k$

If $I_n = \int\limits_0^{\pi/4}\tan^n x\ dx, n \in N$ then $I_{n+2} + I_n$ is equal to

The area in square units of the region bounded by the curve $y = \sqrt{16 - x^2}$ and lines $x = 0, x = 4$ above the X-axis is

The general solution of the differential equation $\dfrac{dy}{dx} + \dfrac{y}{x} = x^2 + 5$ is ....

The order and degree of the differential equation $\sqrt{1 + \dfrac{1}{\left(\frac{dy}{dx}\right)^2}} = \left(\dfrac{d^2y}{dx^2}\right)^{\frac{3}{2}}$, respectively are

Let $\vec{a} = 2\hat{i} + \hat{k}, \vec{b} = \hat{i} + \hat{j} + \hat{k}$, and $\vec{c} = 4\hat{i} - 3\hat{j} + 7\hat{k}$. If $\vec{r}$ is a vector such that $\vec{r} \times \vec{b} = \vec{c} \times \vec{b}$ and $\vec{r} \cdot \vec{a} = 0$, Then $\vec{r} \cdot \vec{c} =$

If $\vec{u} = \hat{i} + 2\hat{j} - 2\hat{k}, \vec{v} = 2\hat{i} + \hat{k}$ and $\vec{w}$ is unit vector then the maximum value of scalar triple product $[\vec{u}\ \vec{v}\ \vec{w}]$ is

If $\vec{a}, \vec{b}, \vec{c}$ are three non-coplanar vectors and $\vec{p}, \vec{q}, \vec{r}$ are defined as $\vec{p} = \dfrac{\vec{b} \times \vec{c}}{[\vec{a}\ \vec{b}\ \vec{c}]}, \vec{q} = \dfrac{\vec{c} \times \vec{a}}{[\vec{a}\ \vec{b}\ \vec{c}]}, \vec{r} = \dfrac{\vec{a} \times \vec{b}}{[\vec{a}\ \vec{b}\ \vec{c}]}$, then $[(\vec{a} + \vec{b}) \cdot \vec{p} + (\vec{b} + \vec{c}) \cdot \vec{q} + (\vec{c} + \vec{a}) \cdot \vec{r}]$ is equal to

The volume of the parallelopiped whose coterminous edges are $2\hat{i} + \hat{j} - \hat{k}, 3\hat{i} - \hat{j} - \hat{k}, \hat{j} + 3\hat{k}$ is

Given the following expression
A) $(\vec{a} \times \vec{b}) \cdot \vec{c}$
B) $\vec{a} \times (\vec{b} \cdot \vec{c})$
C) $\vec{a} \cdot (\vec{b} \cdot \vec{c})$
D) $|\vec{a}|(\vec{b} \cdot \vec{c})$
E) $(\vec{a} \cdot \vec{b}) \times (\vec{b} \cdot \vec{c})$
Then which of the following is not correct

If the perpendicular distance of the plane passing through the point $Q(1, 0, -1)$ and containing the line $\vec{r} = (\hat{i} - 3\hat{j} + \hat{k}) + \lambda(2\hat{i} - 2\hat{j} + \hat{k})$ from origin is $\dfrac{p}{\sqrt{53}}$ then $p = $ ...

If the line joining points $(2, 1, 4)$ and $(a - 1, 4, -1)$ is parallel to the line joining points $(0, 2, b - 1)$ and $(5, 3, -2)$ then the values of $b$ and $a$ are respectively

Lines $\vec{r} = \vec{a} + \lambda\vec{b}$ and $\vec{r} = \vec{b} + \mu\vec{a}$ intersect at point $(2, 4, -4)$. If $|\vec{a} - \vec{b}| = 4$, then $\vec{a} \cdot \vec{b} =$

The Cartesian equations of the line passing through $A(0, 1, 1)$ and parallel to the X-axis are ....

The LPP maximize $z = 2x + 5y$ subject to $x + 3y \leq 6$, $2x + 6y \leq 18$, $x \geq 0$, $y \geq 0$ has

Four cards are drawn successively with replacement from well shuffled deck of 52 cards, then the probability that only two cards are club cards is ...........

For the following probability distribution of a random variable $X$, the Expected value and Variance of $X$ are respectively

$X = x$	$1$	$2$	$3$
$P(X = x)$	$1/5$	$2/5$	$2/5$

A fair die is rolled indefinitely. Player A wins if two consecutive rolls show 3 or 5, and player B wins if two consecutive rolls show 1 or 2 or 4 or 6. The probability that player A wins in the long run is

A physical quantity $x$ is related as $x = \sqrt{a}\ b^2 c^3 d^{-4}$. Relative errors in the quantities $a$, $b$, $c$ and $d$ are 2%, 1%, 3% and 4% respectively. Relative error in $x$ will be

If two vectors $\vec{A} = 4\hat{i} + n\hat{j} + 2\hat{k}$ and $\vec{B} = 2\hat{i} + 2\hat{j} - \hat{k}$ are mutually perpendicular to each other then value of 'n' is

A particle completes 2 revolutions in a circular path of radius 3 cm. The angular displacement of the particle will be (in radian)

A car is travelling at 40 m/s on a circular path of radius 40 m. It is increasing its speed at the rate of $2\ \text{m/s}^2$. Its net acceleration is (in $\text{m/s}^2$) nearly

Two spheres are projected at angles $30^\circ$ and $45^\circ$ with the horizontal. The maximum height reached by both is same. The ratio of their initial velocities is, $\left(\sin 45^\circ = \dfrac{1}{\sqrt{2}}, \sin 30^\circ = 0.5\right)$

Three blocks of different masses connected with inextensible string are pulled by a force $F$ on a frictionless surface as shown in the figure. The ratio of tensions $T_1$ to $T_2$ is

A solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. The ratio of moment of inertia of the sphere about its tangent to the moment of inertia of the disc about a tangent in its plane will be $x : y$. The value of $x$ and $y$ respectively is

Select the correct statement out of the following

If we dip capillary tubes of different radii $r_n$ in water and the water rises to different heights $h_n$ in them, then ($n = 1, 2, 3$ .........)

A small metal sphere is falling through a viscous liquid. The variation of velocity ($V$) with time ($t$) is shown correctly in graph

On opposite sides of a wide vertical vessel filled with water (density $\rho$), two identical holes are drilled, each having cross-section area $A$. The height difference between holes is $x$. The resultant force of reaction of water flowing out of vessel is ($g$ = acceleration due to gravity)

Two stars A and B radiate maximum energy at wavelength $3.9 \times 10^{-7}$ m and $5.2 \times 10^{-7}$ m respectively. The ratio of the temperature of star A to that of star B will be

A piece of metal of 850 K is dropped into 1 kg of water at 300 K. If equilibrium temperature of water is 350 K then the heat capacity of the metal expressed in $\dfrac{J}{K}$ is $\left(\text{Sp. heat of water} = 1\ \dfrac{\text{cal}}{\text{g}^\circ\text{C}}\right)$

A sphere having temperature 600 K is losing heat due to radiation. At this temperature its rate of cooling is $R$. The rate of cooling of this sphere at 400 K is $\dfrac{x}{243}$. The value of $x$ is (Temperature of surrounding is 300 K)

A black body is at temperature of 5780 K. The energy of radiation emitted by the body at wavelength 300 nm is $U_1$, at wavelength 500 nm is $U_2$ and that at 900 nm is $U_3$ respectively. Wien's constant $b = 2.89 \times 10^6\ \text{nmK}$. This shows that

The efficiency of Carnot engine which operates between the two temperatures $T_1 = 500$ K and $T_2 = 300$ K is

An ideal gas having pressure $P$, volume $V$ and temperature $T$ is expanded isothermally, to a volume $3V$ and final pressure $P_I$. The same gas is expanded adiabatically to a volume $3V$, the final pressure being $P_A$. The ratio $\dfrac{P_A}{P_I}$ is $\left(\dfrac{C_P}{C_V} = \gamma\right)$

The displacement of a particle varies with time according to the relation
$x = a\sin\omega t + b\cos\omega t$

For a particle executing S.H.M., the potential energy is $n$ times the kinetic energy when its displacement from mean position is $\left(\dfrac{2\sqrt{2}}{3}\right)A$, where $A$ is the amplitude of S.H.M. The value of $n$ is

A particle is performing S.H.M. about $x = 0$, with an amplitude $a$ and time period $T$. The speed of the particle at $x = \dfrac{a}{3}$ will be

Two sound waves each of wavelength $\lambda$ and same amplitude $A$ interfere at point $Q$. If the path difference is $\dfrac{\lambda}{4}$, the amplitude of the resultant wave at point $Q$ is $\left[\sin\dfrac{\pi}{2} = 1, \cos\dfrac{\pi}{2} = 0\right]$

Two monoatomic ideal gases '1' and '2' of molecular masses $m_1$ and $m_2$ respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas '1' to that in gas '2' is

Two waves are represented as
$y_1 = a_1\sin\left(\omega t - \dfrac{2\pi x}{\lambda}\right)$ and
$y_2 = a_2\cos\left(\omega t - \dfrac{2\pi x}{\lambda} + \dfrac{\pi}{6}\right)$
The path difference between two waves is

The equation of a wave on a string of linear mass density $0.02\ \text{kg m}^{-1}$ is $Y = 0.01\sin\left[2\pi\left(\dfrac{t}{0.02} - \dfrac{x}{0.50}\right)\right]$ m. The tension in the string is

If charge $+q$ is taken from one point to another over an equipotential surface, then

A charge $Q$ is placed at each corner of a cube of side $r$. The potential at the centre of the cube is ($\epsilon_0$ = permittivity of free space)

Select the 'WRONG' statement about polar molecules.

Two point charges placed in air separated by distance $R$ exert a force $F$ on each other. Now the space between those charges is filled with dielectric constant $K$. At distance $R_1$ between the charges, the same force is exerted as $F$. Then

Figure shows a potentiometer wire AB having resistance of $5\ \Omega$ and length 10 m. An e.m.f. is $0.4$ V of battery, the balancing length AP is (internal resistance is negligible)

The currents in different parts of the electric circuit are shown in following figure. The value of current $i$ is

An electron is moving with initial velocity $\vec{v} = V_0\hat{j}$ in a magnetic field $\vec{B} = B_0\hat{i}$. Its de-Broglie wavelength will

A thin circular wire carrying current $I$ has magnetic moment $M$. The shape of the wire is changed to a square and it carries the same current. It will have magnetic moment $M_1$. The ratio $M$ to $M_1$ is

A circular arc of wire of radius of curvature $r$ subtends an angle of $\dfrac{\pi}{5}$ radian at its centre. If current $i$ is flowing in it then the magnetic induction at its centre is ($\mu_0$ = permeability of free space)

A solenoid of 1000 turns is wound uniformly on a glass tube 4 m long and $0.3$ m in diameter. The magnetic intensity at the centre of the solenoid when a current of 4 A flows through it is

A circular disc of radius 20 cm is placed in uniform magnetic field of induction $\dfrac{7}{22}\ \text{Wb/m}^2$ in such a way that its axis makes an angle of $60^\circ$ with $\vec{B}$. The magnetic flux linked with the disc is $(\cos 60^\circ = 0.5)$

An aeroplane having a wing span of 30 m flies due north with the speed of 170 m/s. Magnetic field $B = 3.6 \times 10^{-5}$ T. The potential difference between the tips of the wings will be

In an LCR series circuit an alternating voltage source of frequency $F$ is connected. The current leads the voltage by $45^\circ$. The value of $L$ is

Given below are the two circuits, choose the correct option.

In a L-R circuit of 4 mH inductance and $3\ \Omega$ resistance, e.m.f. $E = \cos(1000t)$ V is applied. The amplitude of current is

A current of 4 A is flowing at 230 V in the primary coil of a transformer. If the voltage produced in the secondary coil is 2300 V and 40 % of power is lost, then the current in the secondary will be

A thin glass prism has refractive index $1.5$. The correct relation between the angle of minimum deviation $(\delta m)$ and angle of refraction $(r)$ is

In diffraction experiment from single slit, the angular width of the central maxima does NOT depend upon

To improve the resolving power of a compound microscope we should

In the diffraction pattern, the first maximum is at $30^\circ$, when a monochromatic light of wavelength $\lambda$ is incident on a slit of width $a$. For the same wavelength, if the slit width is changed, so that first maximum is at $45^\circ$. The slit width is changed by $\left(\sin 30^\circ = \dfrac{1}{2}, \sin 45^\circ = \dfrac{1}{\sqrt{2}}\right)$

The ratio of de-Broglie wavelength of an $\alpha$-particle and proton accelerated from rest by the same potential is $\dfrac{1}{\sqrt{m}}$. The value of $m$ is

The kinetic energy of the electron in an orbit of radius $r$ in hydrogen atom is proportional to ($e$ = electronic charge)

Which of the following is an integral multiple of $\dfrac{h}{2\pi}$ in Bohr's model of an hydrogen atom?

Activity of a radioactive sample decreases to $\left(\dfrac{1}{4}\right)^{th}$ of its original value in 4 days. Then in 16 days its activity will become $x$ times the original value. The value of $x$ is

In Boolean expression $A + B = Y$ implies that

The depletion region of p-n junction