How many amino acids are linked together by $(\mathrm{n}-1)$ amide bonds?

What is the percentage by mass of oxygen in NaOH ? (Atomic mass of $\mathrm{Na}=23 \mathrm{u}, \mathrm{O}=16 \mathrm{u}, \mathrm{H}=1 \mathrm{u}$ )

For the reaction

$$\begin{aligned} & 2 \mathrm{NO}_{(\mathrm{s})}+2 \mathrm{H}_{2(\mathrm{~g})} \longrightarrow \mathrm{N}_{2(\mathrm{~g})}+2 \mathrm{H}_2 \mathrm{O}_{(\mathrm{s})} \\\\ & \text { rate }=\mathrm{k}[\mathrm{NO}]^2\left[\mathrm{H}_2\right] . \end{aligned}$$

What is the order of reaction with respect to $\mathrm{H}_2$ and overall order of reaction respectively?

Identify the alloy used for construction of gas turbine engines.

Calculate the partial pressure exerted by dioxygen from a mixture of $32 \mathrm{~g} \mathrm{O}_2, 80 \mathrm{~g} \mathrm{Ar}$ (mol.mass 40 ) and 4 g dihydrogen $\left(\mathrm{P}_{\text {total }}=10 \mathrm{bar}\right)$.

What is IUPAC name of following compound?

Which among the following is ferromagnetic substance?

What is $\mathrm{O}-\mathrm{O}$ bond length in ozone molecule?

Find the number of electrons that generate 1 coulomb charge?

Which among the following statements is NOT true about rate constant?

Calculate the oxidation number of Cr in $\mathrm{CrO}_4^{2-}$ ion and $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ respectively.

Identify the monomer used to obtain a polymer that resembles the wool.

Which from following is a correct stability order of complex formed by metal ions if the ligand remains same?

Aldol condensation reaction is

What is the numerical difference in molar masses of second and third member of a homologous series?

What is the number of chiral carbon atoms present in 2-chloro-3,4-dimethylhexane?

Which of the following is a primary amine?

The $\mathrm{E}_{\text {cell }}^{+}$of $\mathrm{Cu}_{(\mathrm{s})}\left|\mathrm{Cu}_{(\mathrm{1M})}^{++} \| \mathrm{Ag}_{(\mathrm{1M})}^{+}\right| \mathrm{Ag}_{(\mathrm{s})}$ is 0.647 volt. Calculate the $\mathrm{E}_{\mathrm{Ag}}^{\circ}$ if $\mathrm{E}_{\mathrm{Cu}}^{\circ}$ is 0.153 V .

Conjugate acid of $\mathrm{NH}_2^{-}$and $\mathrm{NH}_3$ are respectively

Calculate the value of $\Delta G$ for the following reaction. $\mathrm{N}_2 \mathrm{O}_{4(\mathrm{~g})} \longrightarrow 2 \mathrm{NO}_{2(\mathrm{~g})}$ if $\Delta \mathrm{H}=57.44 \mathrm{~kJ}$ and $\Delta \mathrm{S}=176 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$.

Calculate the radius of first orbit of $\mathrm{Li}^{++}$.

Which from following polymers (trade name) is used to obtain paints?

What is the number of electrons lost by Cr in a complex $\left[\mathrm{Cr}(\mathrm{CO})_6\right]$ ?

Identify the reagent ' R ' used in the following reaction.

Ketone $\xrightarrow{\mathbf{R}}$ Semicarbazone

Identify alkadiene molecule from following.

Identify the product obtained in the following reaction.

$$\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Br}+\mathrm{CH}_3 \mathrm{COOAg} \xrightarrow{\Delta} \mathrm{x}+\mathrm{AgBr}$$

Identify the reagent R used in following conversion?

tert-butyl bromide $\xrightarrow{\mathrm{R}}$ Isobutylene

Calculate the mass of ' Ca ' deposited at cathode by passing 0.8 ampere current through molten $\mathrm{CaCl}_2$ in 60 minutes. [Molar mass of $\mathrm{Ca}=40 \mathrm{~g} \mathrm{~mol}^{-1}$ ]

What is the expected value of $\Delta T_f$ for $1.25 \mathrm{~m} \mathrm{CaCl}_2$ solution if 1.25 m sucrose solution has $\Delta \mathrm{T}_{\mathrm{f}}$ value x K ?

Calculate Henry's law constant if solubility of gas in water at $25^{\circ} \mathrm{C}$ is $5.14 \times 10^{-4} \mathrm{~mol} \mathrm{dm}^{-3}$ and partial pressure of the gas is 0.75 bar above solution.

What is the total number of orbitals present in N shell?

What is value of percent atom economy when reactants having sum of formula weight 78 u results in the formation of a product with formula weight 65 u ?

Identify the product formed in the following reaction.

$\mathrm{CH_3CH_2MgBr}$ $$\mathrm{\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{ii)\,dil.\,HCl}^{i)\,dry\,ice/dry\,ether}}}$$ $\mathrm{product}$

Which from following is a mineral of copper?

Identify dispersed phase and dispersion medium in fog respectively.

Ethers when dissolved in cold concentrated sulfuric acid forms,

Calculate the total volume occupied by all atoms in simple cubic unit cell if radius of atom is $3 \times 10^{-8} \mathrm{~cm}$.

Under similar conditions enthalpy of freezing is exactly opposite to

A buffer solution is prepared by mixing $0.2 \mathrm{~M} \mathrm{~NH} \mathrm{O}_4 \mathrm{OH}$ and $1 \mathrm{~M} \mathrm{~NH}_4 \mathrm{Cl}$. What is the pH value of buffer solution? $\left(\right.$ Give $\left.\mathrm{pK}_{\mathrm{b}}=7.744\right)$

A solution of nonvolatile solute is obtained by dissolving 0.8 g in $0.3 \mathrm{dm}^3$ water has osmotic pressure 0.2 atm at 300 K . Calculate the molar mass of solute.

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

Which of the following molecules is an example of sp hybridization?

A first order reaction takes 40 minute for $20 \%$ decomposition. Calculate its rate constant.

What is the number of moles of water molecules present in a mole of carnallite?

What is the number of amino acids present in single turn of $\alpha$-helix of protein?

Which from following compounds is obtained as by product in synthesis of sodium carbonate by Solvay process?

Which of the following compounds is NOT a phenol?

A compound is formed by two elements A and B. The atoms of element B form ccp structure. The atoms of A occupy $\frac{1}{3}$ of tetrahedral voids. What is the formula of the compound?

Which of the following isomers of $\mathrm{C}_4 \mathrm{H}_9 \mathrm{Br}$ is a chiral molecule?

The dissociation constant of a weak monobasic acid is $3.2 \times 10^{-4}$. Calculate the degree of dissociation in its 0.04 M solution.

100 ml of $\mathrm{H}_{2(\mathrm{~g})}$ and 100 ml of $\mathrm{Cl}_{2(\mathrm{~g})}$ were allowed to react at 1 bar pressure as

$$\mathrm{H}_{2(\mathrm{~g})}+\mathrm{Cl}_{2(\mathrm{~g})} \longrightarrow 2 \mathrm{HCl}_{(\mathrm{g})}$$

What will be the PV type of work done during reaction?

If $$ y=[(x+1)(2 x+1)(3 x+1) \ldots \ldots \ldots(n x+1)]^2 $$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=0$ is

For the probability distribution

The expected value of X is

The value of $\int \frac{\mathrm{d} x}{7+6 x-x^2}$ is equal to

The value of $\begin{aligned} \cos \left(18^{\circ}-\mathrm{A}\right) \cos \left(18^{\circ}+\mathrm{A}\right) -\cos \left(72^{\circ}-\mathrm{A}\right) \cos \left(72^{\circ}+\mathrm{A}\right) \text { is equal to }\end{aligned}$

If $\int \frac{\mathrm{d} x}{1+3 \sin ^2 x}=\frac{1}{2} \tan ^{-1}(\mathrm{f}(x))+\mathrm{c}$, where c is a constant of integration, then $\mathrm{f}(x)$ is equal to

A random variable X has the following probability distribution

Then $\mathrm{p}(x \geq 2)$ is equal to

Let $f:[-1,3] \rightarrow \mathbb{R}$ be defined as

$$\left\{\begin{array}{lc} |x|+[x], & -1 \leqslant x<1 \\ x+|x|, & 1 \leqslant x<2 \\ x+[x], & 2 \leqslant x \leqslant 3 \end{array}\right.$$

where $[t]$ denotes the greatest integer function. Then $f$ is discontinuous at

Let $\overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{b}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overline{\mathrm{c}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}$ be three vectors. A vector $\bar{v}$ in the plane of $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$, whose projection on $\overline{\mathrm{c}}$ is $\frac{1}{\sqrt{3}}$, is given by

The differential equation, having general solution as $A x^2+B y^2=1$, where $A$ and $B$ are arbitrary constants, is

Let $z$ be a complex number such that $|z|+z=2+i$, where $i=\sqrt{-1}$, then $|z|$ is equal to

If $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$ are two unit vectors such that $5 \overline{\mathrm{a}}+4 \overline{\mathrm{~b}}$ and $\overline{\mathrm{a}}-2 \overline{\mathrm{~b}}$ are perpendicular to each other, then the angle between $\bar{a}$ and $\bar{b}$ is

The value of $\int \frac{\sec x \cdot \tan x}{9-16 \tan ^2 x} \mathrm{dx}$ is equal to

If $n(A)=4, n(B)=2$. Then the number of subsets of the set $\mathrm{A} \times \mathrm{B}$ each having at least 3 elements are

A radio active substance has half-life of $h$ days, then its initial decay rate is given by Note that at $\mathrm{t}=0, \mathrm{M}=\mathrm{m}_{\mathrm{o}}$

If $(a+\sqrt{2} b \cos x)(a-\sqrt{2} b \cos y)=a^2-b^2$, where $\mathrm{a}>\mathrm{b}>0$, then $\frac{\mathrm{d} x}{\mathrm{~d} y}$ at $\left(\frac{\pi}{4}, \frac{\pi}{4}\right)$ is

Contrapositive of the statement. 'If two numbers are equal, then their squares are equal' is

Let A and B be $3 \times 3$ real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations $\left(A^2 B^2-B^2 A^2\right) X=O$. where $X$ is $3 \times 1$ column matrix of unknown variables and $O$ is a $3 \times 1$ null matrix, has

If $\mathrm{f}(x)=x^3-10 x^2+200 x-10$, then

The number of common tangents to the circles $x^2+y^2-x=0$ and $x^2+y^2+x=0$ is /are

Let $\bar{a}=2 \hat{i}+\hat{j}-2 \hat{k}$ and $\bar{b}=\hat{i}+\hat{j}$. If $\bar{c}$ is a vector such that $\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}=|\overline{\mathrm{c}}|,|\overline{\mathrm{c}}-\overline{\mathrm{a}}|=2 \sqrt{2}$ and the angle between $(\overline{\mathrm{a}} \times \overline{\mathrm{b}})$ and $\overline{\mathrm{c}}$ is $30^{\circ}$, then $|(\overline{\mathrm{a}} \times \overline{\mathrm{b}}) \times \overline{\mathrm{c}}|$ is equal to

The equation $\mathrm{e}^{\sin x}-\mathrm{e}^{-\sin x}=4$ has ̱_________ solutions.

The value of $\int \frac{d x}{5+4 \sin x}$ is equal to

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

The area of the region bounded by curves $y=3 x+1, y=4 x+1$ and $x=2$ is

The region represented by the inequations $2 x+3 y \leqslant 18, x+y \geqslant 10, x \geqslant 0, y \geqslant 0$ is

Let $\mathrm{f}(x)=(x+1)^2-1, x \geqslant-1$, then the set $\left\{x / f(x)=f^{-1}(x)\right\}$ is

The probability, that a year selected at random will have 53 Mondays, is

Let $\mathrm{L}_1: \frac{x+2}{5}=\frac{y-3}{2}=\frac{\mathrm{z}-6}{1}$ and $\mathrm{L}_2: \frac{x-3}{4}=\frac{y+2}{3}=\frac{z-3}{5}$ be the given lines. Then the unit vector perpendicular to both $\mathrm{L}_1$ and $\mathrm{L}_2$ is

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

The perpendicular distance from the origin to the plane containing the two lines $\frac{x+2}{3}=\frac{y-2}{5}=\frac{z+5}{7}$ and $\frac{x-1}{1}=\frac{y-4}{4}=\frac{z+4}{7}$, is

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

The value of integral $\int_\limits{-2}^0\left(x^3+3 x^2+3 x+5+(x+1) \cos (x+1)\right) d x$ is equal to

If $x=2 \cos \theta-\cos 2 \theta$ and $y=2 \sin \theta-\sin 2 \theta$, then $\frac{\mathrm{d}^2 y}{d x^2}$ is equal to

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

If two sides of a square are $4 x+3 y-20=0$ and $4 x+3 y+15=0$, then the area of the square is

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq.m) of the flowerbed is

Let $a, b, c$ be three non-zero real numbers such that the equation $\sqrt{3} \mathrm{a} \cos x+2 b \sin x=c$, $x \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ has two distinct real roots $\alpha$ and $\beta$ with $\alpha+\beta=\frac{\pi}{3}$. Then the value of $\frac{b}{a}$ is

Let $P(2,1,5)$ be a point in space and $Q$ be a point on the line $\bar{r}=(\hat{i}-\hat{j}+2 \hat{k})+\mu(-3 \hat{i}+\hat{j}+5 \hat{k})$. Then the value of $\mu$ for which the vector $\overline{\mathrm{PQ}}$ is parallel to the plane $3 x-y+4 z=1$ is

$$\lim _\limits{x \rightarrow \frac{\pi}{2}} \frac{\left(1-\tan \left(\frac{x}{2}\right)\right)(1-\sin x)}{\left(1+\tan \left(\frac{x}{2}\right)\right)(\pi-2 x)^3}$$ is

A ladder 5 m in length is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall, at the rate of $2 \mathrm{~m} / \mathrm{sec}$. How fast is the height on the wall decreasing when the foot of the ladder is 4 m away from the wall?

If the equation $\cos ^4 \theta+\sin ^4 \theta+\lambda=0$ has real solutions for $\theta$, then $\lambda$ lies in the interval

The equation of the tangent to the parabola $y^2=8 x$, which is parallel to the line $4 x-y+3=0$ is

The centroid of tetrahedron with vertices $\mathrm{P}(5,-7,0), \mathrm{Q}(\mathrm{a}, 5,3), \mathrm{R}(4,-6, b)$ and $\mathrm{S}(6, \mathrm{c}, 2)$ is $(4,-3,2)$, then the value of $2 a+3 b+c$ is equal to

The approximate value of $3^{2.001}$, if $\log 3=1.0986$ is

If the vectors $\overline{\mathrm{a}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{b}}=2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overline{\mathrm{c}}=\mathrm{pi}+\hat{\mathrm{j}}+\mathrm{q} \hat{\mathrm{k}}$ are mutually orthogonal, then $(p, q)$ is equal to

If $\bar{u}, \bar{v}$ and $\bar{w}$ are three non-coplanar vectors, then $(\bar{u}+\bar{v}-\bar{w}) \cdot[(\bar{u}-\bar{v}) \times(\bar{v}-\bar{w})]$ is equal to

The value of $k$, if the slope of one of the lines given by $4 x^2+k x y+y^2=0$ is four times that of the other, is given by

The differential equation of $y=\mathrm{e}^x\left(\mathrm{a}+\mathrm{bx}+x^2\right)$ is

The mean of the numbers $a, b, 8,5,10$ is 6 and the variance is $6.8$ . Then which of the following gives possible values of $a$ and $b$ ?

Let $\overline{\mathrm{u}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}, \overline{\mathrm{v}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}$ and $\overline{\mathrm{w}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$. If $\hat{\mathrm{n}}$ is a unit vector such that $\overline{\mathbf{u}} \cdot \hat{\mathrm{n}}=0$ and $\overline{\mathrm{v}} \cdot \hat{\mathrm{n}}=0$, then $|\overline{\mathrm{w}} \cdot \hat{\mathrm{n}}|$ is equal to

A thin uniform metal rod of mass ' $M$ ' and length ' $L$ ' is swinging about a horizontal axis passing through its end. Its maximum angular velocity is ' $\omega$ '. Its centre of mass rises to a maximum height of ( $\mathrm{g}=$ Acceleration due to gravity)

When the number of turns in a coil are made 3 times without any change in the length of the coil, its self inductance becomes

When a system is taken from state ' $a$ ' to state ' $c$ ' along a path abc, it is found that $\mathrm{Q}=80 \mathrm{cal}$ and $\mathrm{W}=35 \mathrm{cal}$. Along path adc $\mathrm{Q}=65 \mathrm{cal}$ the work done W along path adc is

The driver of a car travelling with a speed ' $V_1$ ' $\mathrm{m} / \mathrm{s}$ towards a wall sounds a siren of frequency ' $n$ ' Hz. If the velocity of sound in air is $\mathrm{V} \mathrm{m} / \mathrm{s}$, then the frequency of sound reflected from the wall and as heard by the driver, in Hz , is

When a mercury drop of radius ' $R$ ' splits up into 1000 droplets of radius ' $r$ ', the change in surface energy is ( $T=$ surface tension of mercury)

Two different logic gates giving output ' 1 ' for the inputs $(1,0)$ and then for $(0,1)$ are

An open organ pipe of length ' $l$ ' is sounded together with another open organ pipe of length $\left(l+l_1\right)$ in their fundamental modes. Speed of sound in air is ' $V$ '. The beat frequency heard will be ( $\left.l_1< < l\right)$

When a coil is connected to a d.c. source of e.m.f. 12 volt; then the current of 4 A flows in it . If the same coil is connected to a 12 volt, 50 Hz a.c. source, then the current flowing in it is 2.4 A . Then self-inductance of the coil will be

The ratio of work done by an ideal rigid diatomic gas to the heat supplied by the gas in an isobaric process is

A galvanometer has resistance $80 \Omega$ and it is shunted with resistance $20 \Omega$. If $20 \%$ of the main current flows through galvanometer, then what is the value of main current?

The weights of an object are measured in a coal mine of depth ' $h_1$ ', then at sea level of height ' $h_2$ ' and lastly at the top of a mountain of height ' $h_3$ ' as $W_1, W_2$ and $W_3$ respectively. Which one of the following relation is correct? [h $h_1 \ll R, h_3 \gg h_2=R, R=$ radius of the earth ]

The angle of contact between glass and water is $0^{\circ}$ and water rises in a glass capillary upto 6 cm (Surface tension of water is T). Another liquid of surface tension ' $2 \mathrm{~T}^{\prime}$ ', angle of contact $60^{\circ}$ and relative density 2 will rise in the same capillary up to $\left(\cos 0^{\circ}=1, \cos 60^{\circ}=0.5\right)$

In double slit experiment, instead of taking slits of equal widths, one slit is made twice as wide as the other. Then in interference pattern

Two parallel wires separated by distance 'b' are carrying equal current ' $I$ ' in the same direction. The force per unit length of the wire is

In an a.c. circuit, the reactance of a coil is $\sqrt{3}$ times its resistance. The phase difference between the voltage across the coil to the current through the coil will be

Three thin rods, each of mass ' $M$ ' and length ' $L$ ' are placed along $\mathrm{X}, \mathrm{Y}$ and Z axes which are mutually perpendicular. One end of each rod is at origin. M. I. of the system about Z axis is

For a symmetric (equilateral) prism, the prism formula can be written as

The internal energy of an ideal diatomic gas corresponding to volume ' $V$ ' and pressure ' P ' is 2.5 PV. The gas expands from 1 litre to 2 litre at a constant pressure of $10^5 \mathrm{~N} / \mathrm{m}^2$. The heat supplied to a gas is

Two photons having energies twice and thrice the work function of metal are incident one after another on the metal surface. Then the ratio of maximum velocities of the photoelectrons emitted in the two cases is respectively

If a unit positive charge is shifted from a region of low potential to a region of high potential, then the electric potential energy of the system

Magnetic induction produced at the centre of a circular loop of radius ' $R$ ' carrying a current is ' B '. The magnetic moment of the loop is ( $\mu_0=$ permeability of free space)

The pulleys and strings shown in figure are smooth and of negligible mass. For the system to remain in equilibrium, angle $\theta$ should be

In biprism experiment, the fringe width is 0.6 mm . The distance between $6^{\text {th }}$ dark fringe and $8^{\text {th }}$ bright fringe on the same side of central bright fringe is

A radioactive substance has half-life of 60 minute. During 3 hour, the amount of substance decayed would be

A horizontal platform with a small object placed on it executes a linear S.H.M. in the vertical direction. The amplitude of oscillation is 40 cm . What should be the least period of these oscillations, so that the object is not detached from the platform? [Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$]

In Young's double slit experiment, 'I' is the minimum intensity and ' $I_1$ ' is the intensity at a point where the path difference is $\frac{\lambda}{4}$ where ' $\lambda$ ' is the wavelength of light used. The ratio $I_1 \mathrm{I}_1$ is (Intensities of the two interfering waves are same) $\left(\cos 0^{\circ}=1, \cos 90^{\circ}=0\right)$

For a ray of light, the critical angle is minimum, when it travels from

Four moles of hydrogen, two moles of helium and one mole of water vapour form an ideal gas mixture. $\left[C_{\mathrm{v}}\right.$ for hydrogen $=\frac{5}{2} R, C_v$ for helium $=\frac{3}{2} R, \quad C_{\mathrm{v}}$ for water vapour $\left.=3 \mathrm{R}\right]$ What is the molar specific heat at constant pressure of the mixture?

Electrons are accelerated through a potential difference of 16 kV . If the potential difference is increased to 64 kV , then de-Broglie wavelength associated with electron will

Starting from mean position, a body oscillates simple harmonically with a period ' $T$ '. After what time will its kinetic energy be $75 \%$ of the total energy? $\left(\sin 30^{\circ}=0.5\right)$

Two solenoids of equal number of turns have their lengths as well as radii in the same ratio $1: 3$. The ratio of their self inductance will be

In an extrinsic n-type semiconductor, the free electrons donated by the impurity atoms occupy energy levels in

If the angular velocity of a body rotating about the given axis increases by $20 \%$, then its kinetic energy of rotation will increase by

Two progressive waves $Y_1=\sin 2 \pi\left(\frac{t}{0 \cdot 4}-\frac{x}{4}\right)$ and $Y_2=\sin 2 \pi\left(\frac{t}{0 \cdot 4}+\frac{x}{4}\right)$ superpose to form a standing wave. ' $x$ ' and ' $y$ ' are in SI system. Amplitude of the particle at $x=0.5 \mathrm{~m}$ is $\left[\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right]$

The strength of magnetic field at a perpendicular distance ' $x$ ' near a long straight conductor carrying current ' I ' is ' B '. The magnetic field at a distance $\frac{x}{3}$ from straight conductor will be

The ratio of the areas of the electron orbits for the second excited state to the first excited state for the hydrogen atom is

Two point charges $+8 q$ and $-2 q$ are located at $\mathrm{X}=0$ (origin) and $\mathrm{X}=\mathrm{L}$ respectively. The net electric field due to these two charges is zero at point $P$ on $X$-axis. The location of point $P$ from the origin is

A series $\mathrm{L}-\mathrm{C}-\mathrm{R}$ circuit containing a resistance ' $R$ ' has angular frequency ' $\omega$ '. At resonance the voltage across resistance and inductor are ' $V_R$ ' and ' $\mathrm{V}_{\mathrm{L}}$ ' respectively, then value of capacitance will be

Consider a long uniformly charged cylinder having constant volume charge density ' $\lambda$ ' and radius ' $R$ '. A Gaussian surface is in the form of a cylinder of radius ' $r$ ' such that vertical axis of both the cylinders coincide. For a point inside the cylinder $(r< R)$, electric field is directly proportional to

Two capillary tubes A and B of the same internal diameter are kept vertically in two different liquids whose densities are in the ratio $4: 3$. If the surface tensions of these two liquids are in the ratio $6: 5$, then the ratio of rise of liquid in capillary A to that in B is (assume their angles of contact are nearly equal)

For a transistor, current gain $(\beta)=50$. To change the collector current by $350 \mu \mathrm{~A}$, the base current should be changed by

A sheet of steel is 40 cm long and 5 cm broad at $0^{\circ} \mathrm{C}$. The surface area of the sheet increases by $1.4 \mathrm{~cm}^2$ at $100^{\circ} \mathrm{C}$. Coefficient of linear expansion of steel is

When a sonometer wire vibrates in third overtone there are

Alternating current of peak value $\left(\frac{2}{\pi}\right)$ A flows through the primary coil of a transformer. The coefficient of mutual inductance between primary and secondary coils is 1 H . The peak e.m.f. induced in secondary coil (Frequency of a.c. $=50 \mathrm{~Hz}$ )

Three condensers of capacities ' $\mathrm{C}_1$ ', ' $\mathrm{C}_2$ ', ' $\mathrm{C}_3$ ' are connected in series with a source of e.m.f. ' $V$ '. The potentials across the three condensers are in the ratio

The maximum velocity of a particle, executing S.H.M. with an amplitude 7 mm is $4.4 \mathrm{~ms}^{-1}$ The period of oscillation is $\left[\pi=\frac{22}{7}\right]$

A satellite of mass ' $m$ ' is revolving around the earth of mass ' $M$ ' in an orbit of radius ' $r$ ' with constant angular velocity ' $\omega$ '. The angular momentum of satellite is ( $\mathrm{G}=$ Universal constant of gravitation)

A cell balances against a length of 150 cm on a potentiometer wire when it is shunted by a resistance of $5 \Omega$. But when it is shunted by a resistance of $10 \Omega$, then balancing length increases by 25 cm . The balancing length when the cell is in an open circuit is

A quantity of heat ' $Q$ ' is supplied to monoatomic ideal gas which expands at constant pressure. The fraction of heat converted into work is $\left[\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{5}{3}\right]$

A body of mass 1 kg starts from rest and moves with uniform acceleration. In 2 seconds, its velocity is $10 \mathrm{~m} / \mathrm{s}$. The power exerted on the body in one second is