Calculate the molar mass of an element having density $5.6 \mathrm{~g} \mathrm{~cm}^{-3}$ that forms bec structure $\left[\mathrm{a}^3 \times \mathrm{N}_{\mathrm{A}}=75 \mathrm{~cm}^3 \mathrm{~mol}^{-1}\right]$

Identify the products obtained in the ozonolysis of propene.

Identify the hybridisation and geometry of $\mathrm{SF}_4$ molecule respectively.

Which from following buffers is used to maintain the pH of human blood naturally?

Identify the carbon atoms of glucose and of fructose forming glycosidic bond in sucrose.

Resistance and conductivity of a cell containing 0.1 M KCl solution at 298 K are 115 ohm and $1.90 \times 10^{-6} \mathrm{~S} \mathrm{~cm}^{-1}$ respectively. What is the value of cell constant?

10 g each of $\mathrm{NH}_3, \mathrm{~N}_2, \mathrm{Cl}_2$ and $\mathrm{H}_2 \mathrm{~S}$ are expanded isothermally and reversibly at same temperature. Identify gas that performs maximum work.

A solution of non volatile solute has boiling point elevation 0.5 K . Calculate molality of solution $\left[\mathrm{K}_{\mathrm{b}}=2.40 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right]$.

Chlorine has two isotopes ${ }^{35} \mathrm{Cl}$ and ${ }^{37} \mathrm{Cl}$ with average atomic mass of 35.5 . What is the ratio of their relative abundance respectively?

Which among the following is NOT a true statement regarding enantiomers?

Which from following polymers is believed to leach human carcinogen in to food when used as household plastic?

Which from following molecules has trigonal planar geometry?

Which from following polymers is grouped under elastomers?

What type of following compounds is obtained in first step of Wolf-Kishner reduction of carbonyl compounds?

The reaction $2 \mathrm{~A}+\mathrm{B}+\mathrm{C} \longrightarrow \mathrm{D}+\mathrm{E}$ is found to be first order in A , second order in B and zero order in C . What is the effect of increasing concentration of all reactants twice?

Calculate mass in kg of $4.48 \mathrm{dm}^3$ carbon dioxide at STP.

Calculate the molar mass of solute in a solution prepared by dissolving 1 gram in $0.3 \mathrm{~dm}^3$ solvent having osmotic pressure 0.2 atm at 300 K.

$$\left[\mathrm{R}=0.082 \mathrm{~dm}^3 \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]$$

Identify the product obtained when chlorobenzene is heated with conc. $\mathrm{HNO}_3$ in presence of conc. $\mathrm{H}_2 \mathrm{SO}_4$.

Which from following is a correct priority order for selection of principal functional group for nomenclature of polyfunctional compound?

Which of the following is used to avoid leakage of electrolyte in dry cell?

Identify the polymer used to obtain LCD screen from following.

Identify the product X in the following reaction.

Sodium propanoate $\xrightarrow[\Delta]{\text { soda-lime }} \mathrm{X}+$ sodium carbonate

Which of the following changes involves transfer of 5 electrons?

Identify order of following reaction.

$$\mathrm{H}_2 \mathrm{O}_{2(\mathrm{~g})} \longrightarrow 2 \mathrm{H}_2 \mathrm{O}_{(\mathrm{l})}+\mathrm{O}_{2(\mathrm{~g})}$$

Assuming complete ionisation, arrange the following solutions in order of increasing osmotic pressure.

a) $0.5 \mathrm{~m} \mathrm{~Li}_2 \mathrm{SO}_4$

b) $\mathrm{0.5 ~m~KCl}$

c) $0.5 \mathrm{~m} \mathrm{~Al}_2\left(\mathrm{SO}_4\right)_3$

d) $0.1 \mathrm{~m~BaCl}_2$

Which isomer of $\mathrm{C}_4 \mathrm{H}_9 \mathrm{OH}$ has lower boiling point?

Which element from following in +2 state exhibits highest magnetic moment?

Which from following anions has maximum coagulating power for precipitation of positive sol?

What is the oxidation state of central metal ion in $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{4-}$ complex?

Which one of the following compounds does not react with acetyl chloride?

For the reaction, $\mathrm{N}_{2(\mathrm{g})}+3 \mathrm{H}_{2(\mathrm{g})} \longrightarrow 2 \mathrm{NH}_{3(\mathrm{g})}$ $\mathrm{NH}_3$ is formed at a rate of $0.088 \mathrm{~mol} \mathrm{~dm}^{-3} \mathrm{~s}^{-1}$. Calculate consumption rate of $\mathrm{N}_{2(\mathrm{g})}$.

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

Which of the following elements does not react with water to form metal hydroxide?

Identify the major product formed when 2-Methylhexan-3-ol is heated with concentrated sulphuric acid.

What is the highest oxidation state of third row transition elements?

Calculate the solubility of sparingly soluble salt BA in $\mathrm{mol} \mathrm{dm}^{-3}$ at 300 K if its solubility product is $4.9 \times 10^{-9}$ at same temperature.

Which of the following amines undergoes acylation reaction?

Which from following is a formula of sodium hexafluoroaluminate(III)?

Identify the factor from following on which heat of reaction does not depend.

What type of following forces is present ethylene glycol?

Calculate the volume of fcc unit cell if radius of a particle in it is 106.05 pm.

Identify product ' B ' in the following reaction.

Cumene $\mathrm{A} \xrightarrow{\mathrm{H}_3 \mathrm{O}^{+}} \mathrm{B}$

What is the name of isobutyl alcohol according to carbinol system?

Which from following elements has highest value of ionization enthalpy $\left(\Delta_{\mathrm{I}} \mathrm{H}_1\right)$ ?

Calculate the pH of buffer solution containing 0.04 M NaF and $0.02 \mathrm{~M~HF}\left[\mathrm{pK}_a=3 \cdot 142\right]$.

Which from following is NOT a globular protein?

What is the quantity of electricity required to produce 4.8 g of Mg (molar mass $=24 \mathrm{~g} \mathrm{~mol}^{-1}$ ) from its salt solution?

Which parameter is indicated by the number of waves passing through a given point in one second?

For the reaction,

$$2 \mathrm{H}_{2(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})} \longrightarrow 2 \mathrm{H}_2 \mathrm{O}_{(\mathrm{g})}, \Delta \mathrm{H}^{\circ}=-573.2 \mathrm{~kJ}$$

What is heat of decomposition of water per mol?

Which is the most commonly used refrigerant Freon-12?

The maximum value of $z=4 x+2 y$, subject to the constraints $3 x+4 y \geqslant 12, x+y \leqslant 5, x, y \geqslant 0$ is

The value of $\int \frac{x+1}{x\left(1+x \mathrm{e}^x\right)^2} \mathrm{dx}$ is equal to

If $\mathrm{p} \rightarrow(\sim \mathrm{p} \vee \sim \mathrm{q})$ is false, then the truth values of p and q are respectively

Let $\alpha, \beta$ be the roots of the equation $x^2-\mathrm{p} x+\mathrm{r}=0$ and $\frac{\alpha}{2}, 2 \beta$ be the roots of the equation $x^2-q x+r=0$. Then the value of r is

Let $\quad \overline{\mathrm{a}}=\alpha \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}, \quad \overline{\mathrm{b}}=3 \hat{\mathrm{i}}-\beta \hat{\mathrm{j}}+4 \hat{\mathrm{k}} \quad$ and $\overline{\mathrm{c}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}$, where $\alpha, \beta \in \mathbb{R}$, be three vectors. If the projection at $\overline{\mathrm{a}}$ on $\overline{\mathrm{c}}$ is $\frac{10}{3}$ and $\overline{\mathrm{b}} \times \overline{\mathrm{c}}=-6 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}$, then the value of $\alpha^2+\beta^2-\alpha \beta$ is equal to

The function $\mathrm{f}(x)=2 x^3-6 x+5$ is an increasing function, if

Let $2 \sin ^2 x+3 \sin x-2>0$ and $x^2-x-2<0$ ($x$ is measured in radians). Then $x$ lies in the interval

Let $\overline{\mathrm{a}}, \overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ be vectors of magnitude 2,3 and 4 respectively. If $\bar{a}$ is perpendicular to $(\bar{b}+\bar{c}), \bar{b}$ is perpendicular to $(\bar{c}+\bar{a})$ and $\bar{c}$ is perpendicular to $(\bar{a}+\bar{b})$, then the magnitude of $\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}}$ is equal to

A square plate is contracting at the uniform rate $3 \mathrm{~cm}^2 / \mathrm{sec}$, then the rate at which the perimeter is decreasing, when the side of the square is 15 cm , is

The area (in sq. units), in the first quadrant bounded by the curve $y=x^2+2$ and the lines $y=x+1, x=0$ and $x=2$, is

The vector $\bar{a}=\alpha \hat{i}+2 \hat{j}+\beta \hat{k}$ lies in the plane of the vectors $\overline{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$ and $\overline{\mathrm{c}}=\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and bisects the angle between $\overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$. Then which one of the following gives possible values of $\alpha$ and $\beta$ ?

$2 \pi-\left(\sin ^{-1} \frac{4}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{16}{65}\right)$ is equal to

For the matrix $A=\left[\begin{array}{ccc}2 & 0 & -1 \\ 3 & 1 & 2 \\ -1 & 1 & 2\end{array}\right]$, the matrix of cofactors is

If $y=\sin ^{-1}\left(\frac{3 x}{2}-\frac{x^3}{2}\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

A unit vector coplanar with $\hat{i}+\hat{j}+\hat{k}$ and $2 \hat{i}+\hat{j}+\hat{k}$ and perpendicular to $\hat{i}+\hat{j}-\hat{k}$ is

Negation of the statement ' Horses have wings if and only if crows have tails. ' is

A plane which is perpendicular to two planes $2 x-2 y+z=0$ and $x-y+2 z=4$, passes through $(1,2,1)$. The distance of the plane from the point $(2,3,4)$ is

If $\log (x+y)=\sin (x+y)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is

$$\int \sqrt{\mathrm{e}^x-1} \mathrm{dx}=$$

The variance of 20 observations is 5 . If each observation is multiplied by 3 and then 8 is added to each number, then variance of resulting observations is

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

Four persons can hit a target correctly with probabilities $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is

A poster is to be printed on a rectangular sheet of paper of area $18 \mathrm{~m}^2$. The margins at the top and bottom of 75 cm each and at the sides 50 cm each are to be left. Then the dimensions i.e. height and breadth of the sheet so that the space available for printing is maximum, are _______ respectively.

The approximate value of $(3.978)^{3 / 2}$ is

The number of integral values of $k$, for which the equation $7 \cos x+5 \sin x=2 \mathrm{k}+1$ has a solution, is

The domain of definition of the function $f(x)$ given by the equation $2^x+2^y=2$ is

Let $\bar{a}=3 \hat{i}-\alpha \hat{j}+\hat{k}$ and $\bar{b}=\hat{i}+\alpha \hat{j}+3 \hat{k}$. If the area of the parallelogram whose adjacent sides are represented by the vectors $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$, is $8 \sqrt{3}$ sq. units, then $\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}$ is equal to

If $\mathrm{A}, \mathrm{B}, \mathrm{C}$ are the angles of a triangle with $\tan \frac{A}{2}=\frac{1}{3}, \tan \frac{B}{2}=\frac{2}{3}$ then the value of $\tan \frac{C}{2}$ is

A line with positive direction cosines passes through the point $\mathrm{P}(2,1,2)$ and makes equal angles with the coordinate axes. The line meets the plane $2 x+y+\mathrm{z}=9$ at point Q . The length of the line segment PQ equals $\qquad$ units.

The equation of the tangent to the curve $x=\operatorname{acos}^3 \theta, y=\operatorname{asin}^3 \theta$ at $\theta=\frac{\pi}{4}$ is

$$\lim _\limits{x \rightarrow \frac{\pi}{2}} \frac{(1-\sin x)\left(8 x^3-\pi^3\right) \cos x}{(\pi-2 x)^4}$$

The integral $\int_{\frac{\pi}{6}}^{\frac{\pi}{4}} \frac{d x}{\sin 2 x\left(\tan ^5 x+\cot ^5 x\right)}$ is equal to

The equation of the circle, concentric with the circle $x^2+y^2-6 x-4 y-12=0$ and touching the $\mathrm{X}$-axis is

Let $\mathrm{f}(x)=\mathrm{e}^x, \mathrm{~g}(x)=\sin ^{-1} x$ and $\mathrm{h}(x)=\mathrm{f}(\mathrm{g}(x))$, then $\left(\frac{h^{\prime}(x)}{h(x)}\right)^2$ is equal to

The joint equation of pair of lines through the origin and making an angle of $\frac{\pi}{6}$ with the line $3 x+y-6=0$ is

A line $4 x+y=1$ passes through the point $\mathrm{A}(2,-7)$ meets the line BC whose equation is $3 x-4 y+1=0$ at the point $B$. The equation of the line $A C$ so that $A B=A C$ is

The value of $\int \frac{\mathrm{d} x}{(x+1)^{3 / 4}(x-2)^{5 / 4}}$ is equal to

The smallest positive value of $x$ in degrees satisfying the equation $\tan \left(x+100^{\circ}\right)=\tan \left(x+50^{\circ}\right) \tan (x) \tan \left(x-50^{\circ}\right)$ is

If $\int \frac{\cos x-\sin x}{\sqrt{8-\sin 2 x}} d x=a \sin ^{-1}\left(\frac{\sin x+\cos x}{b}\right)+c$ Where c is a constant of integration, then the ordered pair $(\mathrm{a}, \mathrm{b})$ is equal to

Let L be the line of intersection of the planes $2 x+3 y+z=1$ and $x+3 y+2 z=2$. If L makes an angle $\alpha$ with the positive X -axis, then $\cos \alpha$ equals

Consider a group of 5 boys and 7 girls. The number of different teams, consisting of 2 boys and 3 girls that can be formed from this group if there are two specific girls A and B , who refuse to be the members of the same team, is

If the mean and the variance of a Binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than one is equal to

The general solution of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{y+\sqrt{x^2-y^2}}{x}$ is

A bag contains 4 red and 3 black balls. One ball is drawn and then replaced in the bag and the process is repeated. Let X denote the number of times black ball is drawn in 3 draws. Assuming that at each draw each ball is equally likely to be selected, then probability distribution of $X$ is given by

In a certain culture of bacteria, the rate of increase is proportional to the number present. If there are $10^4$ at the end of 3 hours and $4 \cdot 10^4$ at the end of 5 hours, then there were _________ the beginning.

The number of solutions, of $2^{1+|\cos x|+|\cos x|^2+\ldots \ldots \cdots \cdots}=4$ in $(-\pi, \pi)$, is

Let $\mathrm{f}(x)=x\left[\frac{x}{2}\right]$, for $-10< x<10$, where $[t]$ denotes the greatest integer function. Then the number of points of discontinuity of $f$ is equal to

Let $\hat{a}$ and $\hat{b}$ be two unit vectors. If the vectors $\overline{\mathrm{c}}=\hat{\mathrm{a}}+2 \hat{\mathrm{~b}}$ and $\overline{\mathrm{d}}=5 \hat{\mathrm{a}}+4 \hat{\mathrm{~b}}$ are perpendicular to each other, then the angle between $\hat{a}$ and $\hat{b}$ is

Integrating factor of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}+y=\frac{1+y}{x}$ is

A service station manager sells gas at an average of ₹ 100 per hour on a rainy day, ₹ 150 per hour on a dubious day, ₹ 250 per hour on a fair day and ₹ $300$ on a clear sky. If weather bureau statistics show the probabilities of weather as follows, then his mathematical expectation is

A stationary wave is formed having 3 nodes along the length of the string 90 cm . The wavelength of the wave is

The spectral series observed for hydrogen atom found in visible region is

Three liquids of densities $\rho_1, \rho_2$ and $\rho_3$ (with $\rho_1>\rho_2>\rho_3$ ) having same value of surface tension T , rise to the same height in three identical capillaries. Angle of contact $\theta_1, \theta_2$ and $\theta_3$ respectively obey

The following figures show the variation of displacement with time of a particular object.

A particle of mass ' m ' is rotating in a circular path of radius ' $r$ '. Its angular momentum is ' $L$ ' The centripetal force acting on it is ' $F$ '. The relation between ' $F$ ', ' $L$ ', ' $r$ ' and ' $m$ ' is

Two identical galvanometers are converted into voltmeter and millivoltmeter. As compared to the series resistance of voltmeter, the series resistance of millivoltmeter will be

The diagram shows the propagation of a progressive wave. A, B, C, D, E are five points on this wave

Which of the following points are in the same state of vibration?

Using Einstein's photoelectric equation, the graph between kinetic energy of emitted photoelectrons and the frequency of incident radiation is shown correctly by graph

A string of mass 0.2 Kg is under a tension of 2.5 N . The length of the string is 2 m. A transverse wave starts from one end of the string. The time taken by the wave to reach the other end is

In the Young's double slit experiment, the intensity at a point on the screen, where the path difference is $\lambda(\lambda=$ wavelength $)$ is $\beta$. The intensity at a point where the path difference is $\lambda / 3$, will be $\left.\cos \frac{\pi}{3}=1 / 2\right]$

The P-V diagrams for particular gas of different thermodynamic processes are given by

A musical instrument ' $P$ ' produces sound waves of frequency ' $n$ ' and amplitude ' $A$ '. Another musical instrument ' $Q$ ' produces sound waves of frequency $\frac{\mathrm{n}}{4}$. The waves produced by ' $P$ ' and ' $Q$ ' have equal energies. If the amplitude of waves produced by ' $P$ ' is ' $A_P$ ', the amplitude of waves produced by ' $Q$ ' will be

Concave and convex lenses are placed touching each other. The ratio of magnitudes of their power is $2: 3$. The focal length of the system is 30 cm . The focal lengths of individual lens are

The figure shows the variation of photocurrent with anode potential for four different radiations. Let $f_a, f_b, f_c$ and $f_d$ be the frequencies for the curves $a, b, c$ and $d$ respectively

A disc at rest is subjected to a uniform angular acceleration about its axis. Let $\theta$ and $\theta_1$ be the angle made by the disc in $2^{\text {nd }}$ and $3^{\text {rd }}$ second of its motion. The ratio $\frac{\theta}{\theta_1}$ is

Let ' $n$ ' is the number of liquid drops, each with surface energy ' $E$ '. These drops join to form single drop. In this process

The van de Graaff Generator is not based on

Two coils of self-inductance 25 mH and 9 mH are placed close together such that the effective flux in one coil is completely linked with the other The mutual inductance between these coils is

The electric flux over a sphere of radius ' $r$ ' is ' $\phi$ '. If the radius of the sphere is doubled without changing the charge, the flux will be

Consider the following circuit. By keeping $\mathrm{S}_1$ closed, the capacitor is fully charged and then $S_1$ is opened and $S_2$ is closed, then

In the working of photodiode, the reverse current depends on

A satellite is revolving around a planet in a circular orbit close to its surface. Let ' $\rho$ ' be the mean density and ' $R$ ' be the radius of the planet. Then the period of the satellite is ( $\mathrm{G}=$ universal constant of gravitation)

A current carrying circular loop of radius ' $R$ ' and current carrying long straight wire are placed in the same plane. $I_c$ and $I_w$ are the currents through circular loop and long straight wire respectively. The perpendicular distance between centre of the circular loop and wire is ' d '. The magnetic field at the centre of the loop will be zero when separation ' $d$ ' is equal to

A square loop ABCD is moving with constant velocity ' $\vec{v}$ ' in a uniform magnetic field ' $\vec{B}$ ' which is perpendicular to the plane of paper and directed outward. The resistance of coil is ' $R$ ', then the rate of production of heat energy in the loop is [ L - length of side of loop]

The fringe width in an interference pattern is ' X '. The distance between the sixth dark fringe from one side of central bright band to the fourth bright fringe on other side is

A particle is executing a linear simple harmonic motion. Let ' $\mathrm{V}_1$ ' and ' $\mathrm{V}_2$ ' are its speed at distance ' $x_1$ ' and ' $x_2$ ' from the equilibrium position. The amplitude of oscillation is

In hydrogen atom, if $\mathrm{V}_{\mathrm{n}}$ and $\mathrm{V}_{\mathrm{p}}$ are orbital velocities in $\mathrm{n}^{\text {th }}$ and $\mathrm{p}^{\text {th }}$ orbit respectively, then the ratio $\mathrm{V}_{\mathrm{p}}: \mathrm{V}_{\mathrm{n}}$ is

The work done in splitting a water drop of radius R into 64 droplets is ( $\mathrm{T}=$ Surface tension of water)

The potential difference that must be applied across the series and parallel combination of 4 identical capacitors is such that the energy stored in them becomes the same. The ratio of potential difference in series to parallel combination is

A metal rod of weight ' $W$ ' is supported by two parallel knife-edges A and B . The rod is in equilibrium in horizontal position. The distance ' between two knife-edges is ' $r$ '. The centre of mass of the rod is at a distance ' $x$ ' from $A$. The normal reaction on A is

Potential difference between the points A and B is nearly

An ideal gas $(\gamma=1.5)$ is expanded adiabatically. To reduce root mean square velocity of molecules two times, the gas should be expanded

An e.m.f. $E=E_0 \cos \omega t$ is applied to circuit containing L and R in series. If $\mathrm{X}_{\mathrm{L}}=2 \mathrm{R}$, then the power dissipated in the circuit is

In the following circuit, the reading in the ammeter is

A black body radiates power ' P ' and maximum energy is radiated by it at a wavelength $\lambda_0$. The temperature of the black body is now so changed that it radiates maximum energy at the wavelength $\frac{\lambda_0}{4}$. The power radiated by it at new temperature is

In Young's double slit experiment using monochromatic light of wavelength ' $\lambda$ ', the maximum intensity of light at a point on the screen is ' K ' units. The intensity of light at a point where the path difference is $\frac{\lambda}{6}$ ' is $\left(\cos 60^{\circ}=\sin 30^{\circ}=0.5, \sin 60^{\circ}=\cos 30^{\circ}=\sqrt{3} / 2\right)$

When a capacitor is connected in series LR circuit, the alternating current flowing in the circuit

The correct relation between total magnetic field $(B)$, magnetic intensity $(\mathrm{H})$, permeability of free space $\left(\mu_0\right)$ and susceptibility $(\chi)$ is

The resultant gate and its Boolean expression in the given circuit is

The temperature of a liquid falls from 365 K to 359 K in 3 minutes. The time during which temperature of this liquid falls from 342 K to 338 K is [Let the room temperature be 296 K ]

Air capacitor has capacitance of $1 \mu \mathrm{~F}$. Now the space between two plates of capacitor is filled with two dielectrics as shown in figure. The capacitance of the capacitor is [ $\mathrm{d}=$ distance between two plates of capacitor, $\mathrm{K}_1$ and $\mathrm{K}_2$ are dielectric constants of first dielectric and second dielectric respectively]

In an isobaric process of an ideal gas, the ratio of work done by the system (W) during the expansion and the heat exchanged $(\mathrm{Q})$ is $\left(\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}\right)$

A long solenoid carrying a current produces magnetic field B along its axis. If the number of turns per cm are tripled and the current is made $\left(\frac{1}{4}\right)^{\text {th }}$ then the new value of magnetic field will be

An astronomical telescope has a large aperture to

A sonometer wire is in unison with a tuning fork of frequency ' $n$ ' when it is stretched by a weight of specific gravity ' $d$ '. When the weight is completely immersed in water, ' $x$ ' beats are produced per second, then

The radius of the planet is double that of the earth, but their average densities are same. $\mathrm{V}_{\mathrm{p}}$ and $V_E$ are the escape velocities of planet and earth respectively. If $\frac{V_P}{V_E}=x$, the value of ' $x$ ' is

Three thin rods, each mass ' 2 M ' and length ' L ' are placed along $\mathrm{x}, \mathrm{y}$ and z axis which are mutually perpendicular. One end of each rod is at origin. Moment of inertia of the system about x - axis is

The magnetic potential energy stored in certain inductor is $64 \times 10^{-3} \mathrm{~J}$, when the current in the inductor is 80 mA . This inductor is of inductance

Two identical drops of water are falling through air with steady velocity ' V '. If the two drops come together to form a single drop. The new velocity of the single drop is

The equations of two waves are given as

$$\begin{aligned} & y_1=a \sin \left(\omega t+\phi_1\right) \\ & y_2=a \sin \left(\omega t+\phi_2\right) \end{aligned}$$

If amplitude and time period of resultant wave is same as the individual waves, then $\left(\phi_1-\phi_2\right)$ is