Identify fibrous protein from following.

For the reaction,

$$\mathrm{C}_3 \mathrm{H}_{8(\mathrm{~g})}+5 \mathrm{O}_{2(\mathrm{~g})} \longrightarrow 3 \mathrm{CO}_{2(\mathrm{~g})}+4 \mathrm{H}_2 \mathrm{O}_{(\mathrm{l})}$$

at constant temperature, $\Delta \mathrm{H}-\Delta \mathrm{U}$ is

Which from following reactions is not possible for benzene due to reversible nature?

Calculate the volume of unit cell when metal having density $1 \mathrm{~g} \mathrm{~cm}^{-3}$ and molar mass $23 \mathrm{~g} \mathrm{~mol}^{-1}$ crystallises to form bec structure.

Which polymer is obtained from monomers using

Which from following elements belongs to the actinoids?

Which of the following rules states that it is impossible to determine simultaneously the exact position and exact momentum of an electron?

Calculate the cryoscopic constant of solvent when 2.5 gram solute is dissolved in 35 gram solvent lowers its freezing point by 3 K. (molar mass of solute is $117 \mathrm{~g} \mathrm{~mol}^{-1}$)

Which of the following solvents reduces the environmental pollution?

What is the number of electrons present in d-subshell if its atomic number is 27 and oxidation state is +2 ?

What is the volume occupied by 1 molecule of water, if its density is $1 \mathrm{~g} \mathrm{~cm}^{-3}$ ?

Identify the reason for the solubility of polar solute in polar solvent from the following.

Identify biodegradable polymer from following.

What is the pOH of millimolar solution of $\mathrm{Ca}(\mathrm{OH})_2$ ?

Which from following pairs is an example of isotones?

What is change in internal energy of the system when work done by the system is 150 J and system release 300 J of heat?

Which from following coordinate complexes is a heteroleptic complex?

Identify glycosidic linkage present in maltose.

What is the number of moles of Cl atoms and N atoms respectively present in n moles of tear gas?

What is bond angle $\mathrm{F}-\mathrm{B}-\mathrm{F}$ in $\mathrm{BF}_3$ ?

Which from the following statements about $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$ complex is NOT correct?

What is the relation between edge length and total volume occupied by atoms in bec unit cell?

What is the value of $x$ and $y$ in order to balance following redox reaction?

$$\mathrm{xCuO}+\mathrm{yNH}_3 \longrightarrow \mathrm{xCu}+\mathrm{N}_2+\mathrm{xH}_2 \mathrm{O}$$

Molar conductivity of 0.02 M weak acid is $7.92 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ and its molar conductivity at infinite dilution is $232.7 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. Calculate degree of dissociation of weak acid.

Which from following compounds is most covalent?

What is the total number of atoms present in fcc unit cell?

For which electrolyte the molar conductivity at infinite dilution can not be obtained graphically?

The major product formed in carbylamine reaction is

Which among the following elements has highest electronegativity?

Consider the reaction $3 \mathrm{I}^{-}+\mathrm{S}_2 \mathrm{O}_8^{2-} \longrightarrow \mathrm{I}_3^{-}+2 \mathrm{SO}_4^{2-}$, at a particular time t , $\frac{\mathrm{d}\left[\mathrm{SO}_4^{2-}\right]}{\mathrm{dt}}$ is $2.2 \times 10^{-2} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}$. What is the value of $\frac{\mathrm{d}\left[\mathrm{S}_2 \mathrm{O}_8^{2-}\right]}{\mathrm{dt}}$ ?

For the reaction, $\mathrm{NO}_{2(\mathrm{~g})}+\mathrm{CO}_{(\mathrm{g})} \longrightarrow \mathrm{NO}_{(\mathrm{g})}+\mathrm{CO}_{2(\mathrm{~g})}$ rate of reaction is proportional to square of $\left[\mathrm{NO}_2\right]$ and independent of [CO]. What is the rate law equation?

Which among the following compounds does not correctly match with its formula?

Which among the following forces of attraction is developed between polar and non polar molecules?

Which among the following is correct conjugate acid base pair for the equation stated below?

$$\mathrm{HCl}+\mathrm{NH}_3 \rightleftharpoons \mathrm{NH}_4^{+}+\mathrm{Cl}^{-}$$

Which among the following compounds is NOT a tertiary amine?

Which among the following reactions is used for the preparation of alkyl fluorides?

What type of colloid is milk?

What is the osmotic pressure of solution prepared by dissolving 3 gram solute in $2 \mathrm{dm}^3$ water at 300 K . (Molar mass of solute $=60 \mathrm{~g} \mathrm{~mol}^{-1}$, $\mathrm{R}=0.0821 \mathrm{dm}^3 \mathrm{~atm} \mathrm{~K} \mathrm{~mol}^{-1})$

Which among the following is the method for the preparation of ethers?

Identify the bond line formula for propan-1-ol

IUPAC name of the compound

Dissociation constant and degree of dissociation of weak acid are $1.8 \times 10^{-5}$ and 0.03 respectively. What will be the concentration of solution of weak acid?

The decreasing order of reactivity of following alcohols with halo acid is

(I) $\mathrm{CH}_3 \mathrm{OH}$

(II) $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{OH}$

(III)

(IV)

What is the product obtained in the reaction?

$\mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_2-\mathrm{CHO} \xrightarrow[\text { (i) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {(i) } \mathrm{LAH}_4}$ product

Two moles of an ideal gas is expanded isothermally from a volume of $300 \mathrm{~cm}^3$ to 2.5 $\mathrm{dm}^3$ at 298 K against a constant pressure at 1.9 bar. Calculate the work done in joules.

Identify name of from following.

Which of the following compounds is used to convert acetaldehyde into acetaldehyde cynanohydrin?

What volume of chlorine gas (molar mass 71) is evolved at STP during electrolysis of fused NaCl by passage of 1 amp current for 965 second? (At STP, V $=22.4 \mathrm{~dm}^3$ )

Identify the test from following so that aldehyde when boiled with ammoniacal silver nitrate solution deposts silver.

Find the percentage of unreacted reactant for zero order reaction in 90 second having rate constant $1 \mathrm{~mol} \mathrm{~dm}^{-3} \mathrm{~s}^{-1}$.

If $A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & a & 3 \\ 3 & 2 & 2\end{array}\right]$ and $B=\left[\begin{array}{ccc}-2 & 0 & b \\ 7 & -1 & -2 \\ c & 1 & 1\end{array}\right]$ and if matrix $B$ is the inverse of matrix $A$, then value of $4 a+2 b-c$ is

If $\int \mathrm{f}(x) \mathrm{d} x=\psi(x)$, then $\int x^5 \mathrm{f}\left(x^3\right) \mathrm{d} x$ is equal to

The population of a town increases at a rate proportional to the population at that time. If the population increases from 40 thousand to 80 thousand in 40 years, then the population in another 40 years will be

If X is a random variable with distribution given below

Then the value of $k$ and its variance are respectively given by

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability, that the three balls have different colours, is

The area (in sq. units) bounded by the curves $y=(x+1)^2, y=(x-1)^2$ and the line $y=\frac{1}{4}$ is

If $\int \frac{d x}{\sqrt[3]{\sin ^{11} x \cos x}}=-\left(\frac{3}{8} f(x)+\frac{3}{2} g(x)\right)+c$ then

A random variable X takes values $-1,0,1,2$ with probabilities $\frac{1+3 \mathrm{p}}{4}, \frac{1-\mathrm{p}}{4}, \frac{1+2 \mathrm{p}}{4}, \frac{1-4 \mathrm{p}}{4}$ respectively, where p varies over $\mathbb{R}$. Then the minimum and maximum values of the mean of X are respectively.

Let C be a curve given by $y(x)=1+\sqrt{4 x-3}$, $x>\frac{3}{4}$. If P is a point on C , such that the tangent at P has slope $\frac{2}{3}$, then a point through which the normal at P passes, is

The equation of the circle, the end points of whose diameter are the centres of the circles $x^2+y^2+6 x-14 y+5=0$ and $x^2+y^2-4 x+10 y-4=0$ is

The equation of the plane, passing through the point $(1,1,1)$ and perpendicular to the planes $2 x+y-2 z=5$ and $3 x-6 y-2 z=7$, is

If for $x \in\left(0, \frac{1}{4}\right)$, the derivative of $\tan ^{-1}\left(\frac{6 x \sqrt{x}}{1-9 x^3}\right)$ is $\sqrt{x} \cdot g(x)$, then $g(x)$ equals

If the vectors $a \hat{i}+\hat{j}+\hat{k}, \hat{i}+b \hat{j}+\hat{k}, \hat{i}+\hat{j}+c \hat{k}$ $(a \neq b, c \neq 1)$ are coplanar, then $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}$ has the value __________.

The sides of a triangle are $\sin \theta, \cos \theta$ and $\sqrt{1+\sin \theta \cos \theta}$ for some $0<\theta<\frac{\pi}{2}$, then the greatest angle of a triangle is

If $\lim\limits_{x \rightarrow \infty}\left(\frac{x^2+x+1}{x+1}-a x-b\right)=4$ then

If $y=y(x)$ is the solution of the differential equation $x \frac{\mathrm{dy}}{\mathrm{d} x}+2 y=x^2$ satisfying $y(1)=1$, then the value of $y\left(\frac{1}{2}\right)$ is

The value of $\cos ^{-1}\left\{\frac{1}{\sqrt{2}}\left(\cos \frac{9 \pi}{10}-\sin \frac{9 \pi}{10}\right)\right\}$ is

Consider the statements given by following :

(A) If $3+3=7$, then $4+3=8$.

(B) If $5+3=8$, then earth is flat.

(C) If both (A) and (B) are true, then $5+6=17$.

Then which of the following statements is correct?

If $\alpha+\beta=\frac{\pi}{2}$ and $\beta+\gamma=\alpha$, then $\tan \alpha$ equals

If $\mathrm{f}(x)=\frac{\log x}{x}(x>0)$, then it is increasing in

If $\overline{\mathrm{a}}, \overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ are three non-coplanar vectors, then $(\bar{a}+\bar{b}+\bar{c}) \cdot[(\bar{a}+\bar{b}) \times(\bar{a}+\bar{c})]$ equals

In a class of 300 students, every student reads 5 news papers and every news paper is read by 60 students. Then the number of newspapers is

The maximum value of $\frac{\log x}{x}$ is

Derivative of $\mathrm{e}^x$ w.r.t. $\sqrt{x}$ is

The curve satisfying the differential equation $y \mathrm{~d} x-\left(x+3 y^2\right) \mathrm{dy}=0$ and passing through the point $(1,1)$ also passes through the point

The maximum value of $z=x+y$, subjected to $x+y \leq 10,5 x+3 y \geq 15, x \leq 6, x, y \geq 0$

The distance of the point $(1,3,-7)$ from the plane passing through the point $(1,-1,-1)$ having normal perpendicular to both the lines $\frac{x-1}{1}=\frac{y+2}{-2}=\frac{z-4}{3}$ and $\frac{x-2}{2}=\frac{y+1}{-1}=\frac{z+7}{-1}$ is

Domain of definition of the real valued function $f(x)=\sqrt{\sin ^{-1}(2 x)+\frac{\pi}{6}}$ 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

Suppose that $\bar{p}, \bar{q}$ and $\overline{\mathrm{r}}$ are three non-coplanar vectors in $\mathbb{R}^3$. Let the components of a vector $\overline{\mathrm{s}}$ along $\overline{\mathrm{p}}, \overline{\mathrm{q}}$ and $\overline{\mathrm{r}}$ be 4,3 and 5 respectively. If the components of this vector $\overline{\mathrm{s}}$ along $(-\overline{\mathrm{p}}+\overline{\mathrm{q}}+\overline{\mathrm{r}}),(\overline{\mathrm{p}}-\overline{\mathrm{q}}+\overline{\mathrm{r}})$ and $(-\overline{\mathrm{p}}-\overline{\mathrm{q}}+\overline{\mathrm{r}})$ are $x$, $y$ and $z$ respectively, then the value of $2 x+y+z$ is

$\int \frac{x^4+x^2+1}{x^2-x+1} d x$ is equal to

If the curves $y^2=6 x, 9 x^2+\mathrm{b} y^2=16$ intersect each other at right angles, then the value of $b$ is

Let $\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$ and $\overline{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$ If $\bar{c}$ is a vector such that $\bar{a} \cdot \bar{c}=|\bar{c}|$, $|\overline{\mathrm{c}}-\overline{\mathrm{a}}|=2 \sqrt{2}$ and the angle between $(\overline{\mathrm{a}} \times \overline{\mathrm{b}})$ and $\bar{c}$ is $60^{\circ}$, then the value of $|(\bar{a} \times \bar{b}) \times \bar{c}|$ is

The mean and the standard deviation of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then reduced by $q$, where $p \neq 0$ and $q \neq 0$. If the new mean and new standard deviation (s.d.) become half of the original values, then $q$ is equal to

If Mean value theorem holds for the function $\mathrm{f}(x)=(x-1)(x-2)(x-3), x \in[0,4]$ then the values of $c$ as per the theorem are

The value of $\mathrm{I}=\mathrm{I}=\int_{\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{x^2 \cos x}{1+\mathrm{e}^{-x}} \mathrm{~d} x$ is equal to

If $\overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{a}} \cdot \overline{\mathrm{b}}=1$ and $\overline{\mathrm{a}} \times \overline{\mathrm{b}}=\hat{\mathrm{j}}-\hat{\mathrm{k}}$, then $\overline{\mathrm{b}}$ is

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

The value of $I=\int \frac{(x-1) \mathrm{e}^x}{(x+1)^3} \mathrm{dx}$ is

If $Z=\frac{-2}{1+\sqrt{3} i}, i=\sqrt{-1}$, then the value of $\arg Z$ is

In $(0,2 \pi)$, the number of solutions of $\tan \theta+\sec \theta=2 \cos \theta$ are

If the area of the parallelogram with $\bar{a}$ and $\bar{b}$ as two adjacent sides is 15 square units, then the area (in square units) of the parallelogram, having $3 \bar{a}+2 \bar{b}$ and $\bar{a}+3 \bar{b}$ as two adjacent sides, is

If an equation $h x y+g x+f y+c=0$ represents a pair of lines, then

The general solution of $\sin x-3 \sin 2 x+\sin 3 x=\cos x-3 \cos 2 x+\cos 3 x$ is

The length of the perpendicular from the point $\mathrm{A}(1,-2,-3)$ on the line $\frac{x-1}{2}=\frac{y+3}{-1}=\frac{z+1}{-2}$ is

The straight line, $2 x-3 y+17=0$ is perpendicular to the line passing through the points $(7,17)$ and $(15, \beta)$, then $\beta$ equals

If $\mathrm{f}(x)=\frac{x^2-x}{x^2+2 x}$ then $\frac{\mathrm{d}}{\mathrm{d} x}\left(\mathrm{f}^{-1}(x)\right)$ at $x=2$ is

For the triangle ABC , with usual notations, if the angles $A, B, C$ are in A.P. and $\mathrm{m} \angle \mathrm{A}=30^{\circ}, \mathrm{c}=3$, then the values of a and b are respectively

Let $p, q, r$ be three statements such that the truth value of $(p \wedge q) \rightarrow(\sim q \vee r)$ is $F$. Then the truth values of $p, q, r$ are respectively

Let k be a non-zero real number. If $f(x)=\left\{\begin{array}{cl}\frac{\left(\mathrm{e}^x-1\right)^2}{\sin \left(\frac{x}{k}\right) \log \left(1+\frac{x}{4}\right)} & , x \neq 0 \\ 12 & , x=0\end{array}\right.$ is a continuous function, then the value of $k$ is

The gyromagnetic ratio and Bohr magneton are given respectively by [Given $\rightarrow \mathrm{e}=$ charge on electron, $\mathrm{m}=$ mass of electron, $\mathrm{h}=$ Planck's constant]

Two satellites A and B having ratio of masses $3: 1$ are revolving in circular orbits of radii ' $r$ ' and ' 4 r '. The ratio of total energy of satellites A to that of B is

The current amplification factor of a transistor is 50 . The input resistance when used in common emitter mode is $1 \mathrm{k} \Omega$. The peak value for an a.c. input voltage of 0.01 V peak is

Average power associated with an ideal inductor and ideal capacitor over a complete cycle of a.c. is respectively

A metal rod of length ' $l$ ' rotates about one of its ends in a plane perpendicular to a magnetic field of induction ' $B$ '. If the e.m.f. induced between the ends of the rod is ' $e$ ', then the number of revolutions made by the rod per second is

In S.H.M. the displacement of a particle at an instant is $Y=A \cos 30^{\circ}$, where $A=40 \mathrm{~cm}$ and kinetic energy is 200 J . If force constant is $1 \times 10^{\times} \mathrm{N} / \mathrm{m}$, then x will be $\left(\cos 30^{\circ}=\sqrt{3} / 2\right)$

Two sound waves having same amplitude ' $A$ ' and angular frequency ' $\omega$ ' but having a phase difference of $\left(\frac{\pi}{2}\right)^c$ are superimposed then the maximum amplitude of the resultant wave is

Out of the following musical instruments, which is 'NOT' a percussion instrument?

The function of dielectric in a capacitor is

Three identical metal spheres (of same surface area) have red, black and white colors and they are heated up to same temperature. They are allowed to cool. Arrange them from maximum rate of cooling to minimum rate of cooling

In an ammeter, $4 \%$ of the main current is passing through the galvanometer, If shunt resistance is $5 \Omega$, then resistance of galvanometer will be

LC series resonant circuit produces resonant frequency ' $f$ '. If ' $L$ ' is tripled and ' $C$ ' is increased by $3 C$, the resonant frequency will be

A wavefront is a surface

When the tension in string is increased by $3 \mathrm{~kg} \omega \mathrm{t}$, the frequency of the fundamental mode increases in the ratio $2: 3$. The initial tension in the string is

In the system of two particles of masses ' $\mathrm{m}_1$ ' and ' $\mathrm{m}_2$ ', the first particle is moved by a distance 'd' towards the centre of mass. To keep the centre of mass unchanged, the second particle will have to be moved by a distance

The potential energy of a long spring when it is stretched by 3 cm is ' $U$ '. If the spring is stretched by 9 cm , potential energy stored in it will be

A thin uniform rod of length ' $L$ ' and mass ' $M$ ' is swinging freely along a horizontal axis passing through its centre. Its maximum angular speed is ' $\omega$ '. Its centre of mass rises to a maximum height of [ $\mathrm{g}=$ gravitational acceleration]

Three immiscible transparent liquids with uniform refractive indices $\frac{3}{2}, \frac{4}{3}$ and $\frac{6}{5}$ are arranged one on top of another. The depths of the liquids are 3 cm 4 cm and 6 cm respectively. The apparent depth of the vessel is

When a hydrogen atom is raised from the ground state to the excited state

In the logic circuit diagram, when all the four inputs $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ are one, the outputs $\mathrm{Y}_1, \mathrm{Y}_2, \mathrm{Y}_3$ are respectively $(1,1,0)$. When all the inputs $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ are changed to 'zero', the outputs $\mathrm{Y}_1, \mathrm{Y}_2, \mathrm{Y}_3$ respectively change to

Two coils have a mutual inductance $5 \times 10^{-3} \mathrm{H}$. The current changes in the first coil according to the equation $I_1=I_0 \sin \omega t$ where $I_0=10 \mathrm{~A}$ and $\omega=100 \pi \mathrm{rad} / \mathrm{s}$. What is the value of the maximum e.m.f. in the coil?

When an air bubble rises from the bottom of lake to the surface, its radius is doubled. The atmospheric pressure is equal to that of a column of water of height ' $H$ '. The depth of the lake is

The period of a planet around the sun is 8 times that of earth. The ratio of radius of planet's orbit to the radius of the earth's orbit is

The magnetic induction due to an ideal solenoid is independent of

The moment of inertia of thin square plate PQRS of uniform thickness, about an axis passing through centre ' O ' and perpendicular to the plane of the plate is $\left(\mathrm{I}_1, \mathrm{I}_2, \mathrm{I}_3, \mathrm{I}_4\right.$ are respectively the moments of inertia about axis $1,2,3,4$ which are in the plane of the plate as shown in figure)

In hydrogen atom, ratio of the shortest wavelength in the Balmer series to that in the Paschen series is

At certain temperature, $\operatorname{rod} \mathrm{A}$ and $\operatorname{rod} \mathrm{B}$ of different materials have lengths $\mathrm{L}_{\mathrm{A}}$ and $\mathrm{L}_{\mathrm{B}}$ respectively. Their coefficients of linear expansion are $\alpha_A$ and $\alpha_B$ respectively. It is observed that the difference between their lengths remains constant at all temperatures. The ratio $\mathrm{L}_{\mathrm{A}}: \mathrm{L}_{\mathrm{B}}$ is given by

Velocity of light in diamond is $\left(\frac{5}{12}\right)^{\text {th }}$ times that in air. Velocity of light in water is $\left(\frac{3}{4}\right)^{\text {th }}$ times that in air. The angle of incidence of ray of light travelling from water to diamond is (angle of refraction $\left.(\mathrm{r})=30^{\circ}\right)\left[\right.$ Given $\left.\rightarrow \sin 30^{\circ}=\frac{1}{2}\right]$

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

The internal energy of a gas will increase when it

A sonometer wire is stretched by hanging a metal bob, the fundamental frequency of the wire is ' $n_1$ '. When the bob is completely immersed in water, the frequency of vibration of wire becomes ' $n_2$ '. The relative density of the metal of the bob is

The magnetic field intensity inside current carrying solenoid is $\mathrm{H}=2.4 \times 10^3 \mathrm{~A} / \mathrm{m}$. If length and number of turns of a solenoid is 15 cm and 60 turns respectively. The current flowing in the solenoid is

If the electric flux entering and leaving an enclosed surface is $\phi_1$ and $\phi_2$ then charge enclosed in the surface is ($\varepsilon_0=$ permittivity of free space)

A gas is contained in closed vessel. The initial temperature of the gas is $100^{\circ} \mathrm{C}$. If the pressure of the gas is increased by $4 \%$, the increase in the temperature of the gas is

According to Bohr's theory of hydrogen atom, the ratio of the maximum and minimum wavelength of Lyman series will be

In the given circuit diagram, in the steady state the current through the battery and the charge on the capacitor respectively are

Water is flowing in a conical tube as shown in figure. Velocity of water at area ' $\mathrm{A}_2$ ' is $60 \mathrm{~cm} / \mathrm{s}$. The value of ' $\mathrm{A}_1$ ' and ' $\mathrm{A}_2$ ' is $10 \mathrm{~cm}^2$ and $5 \mathrm{~cm}^2$ respectively. The pressure difference at both the cross-section is

A point object kept at P in front of a glass sphere of radius ' $R$ ' has its image formed at $Q$ such that $\mathrm{PO}=\mathrm{QO}$. The refractive index of material of glass sphere is 1.4. The distance PO is equal to

The magnetic flux through a coil of resistance ' $R$ ' changes by an amount ' $\Delta \phi$ ' in time ' $\Delta t$ '. The amount of induced current and induced charge in the coil are respectively

A circular disc of radius ' $R$ ' and thickness $\frac{R}{8}$ has moment of inertia 'I' about an axis passing through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere then moment of inertia of sphere about an axis passing through diameter is

When the two known resistance ' $R$ ' and ' $S$ ' are connected in the left and right gaps of a meter bridge respectively, the null point is found at a distance ' $l_1$ ' from the zero end of a meter bridge wire. An unknown resistance ' X ' is now connected in parallel with ' S ' and null point is found at a distance ' $l_2$ ' form zero end of meter bridge wire. The unknown resistance ' X ' is

For an ideal gas, in an isobaric process, the ratio of heat supplied ' $Q$ ' to the work done ' $w$ ' by the system is ( $\gamma=$ ratio of specific heat at constant pressure to that at constant volume)

A particle is performing S.H.M. with an amplitude 4 cm . At the mean position the velocity of the particle is $12 \mathrm{~cm} / \mathrm{s}$. When the speed of the particle becomes $6 \mathrm{~cm} / \mathrm{s}$, the distance of the particle from mean position is

A velocity - time graph of a body is shown below. The distance covered by the body from 6 second to 9 second is

Two identical photocathodes receive light of frequencies ' $\mathrm{n}_1$ ' and ' $\mathrm{n}_2$ '. If the velocities of the emitted photoelectrons of mass ' $m$ ' are ' $\mathrm{V}_1$ ' and ' V , respectively, then ( $\mathrm{h}=$ Planck's constant )

The temperature of a gas is $-80^{\circ} \mathrm{C}$. To what temperature the gas should be heated so that the r.m.s. speed is increased by 2 times?

Two wavelength 590 nm and 596 nm of sodium light are used one after other, to study the diffraction taking place at a single slit of aperture 2.4 mm . The distance between the slit and screen is 2 m . The separation between the positions of first secondary maximum of the diffraction pattern obtained in the two cases is

For the diagram shown, the resistance between points A and B when the ideal diode ' $D$ ' is forward biased is ' $R_1$ ' and that when reverse biased is ' $R_2$ '. The ratio $\frac{R_1}{R_2}$ is

A parallel plate capacitor of capacitance ' $C$ ' is connected to a battery and charged to a potential difference ' $V$ '. Another capacitor of capacitance 3 C is similarly charged to a potential difference 3 V . The charging battery is then disconnected and capacitors are connected in parallel to each other in such a way that positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is

A tuning fork of frequency 340 Hz is vibrated just above a tube of 120 cm height. Water is slowly poured in the tube. What is the minimum height of water necessary for resonance?