Which of the following molecules has no lone pair of electrons on central atom?

Calculate $$\Delta \mathrm{G}^{\circ}$$ for the cell:

$$\mathrm{Sn}_{(\mathrm{s})}\left|\mathrm{Sn}_{(\mathrm{1M})}^{2+}\right|\left|\mathrm{Ag}_{(\mathrm{1M})}^{+}\right| \mathrm{Ag}_{(\mathrm{s})}$$ at $$25^{\circ} \mathrm{C}\left(\mathrm{E}_{\text {cell }}^{\circ}=0.90 \mathrm{~V}\right)$$

Which from following statements is NOT correct?

A compound made of elements $$\mathrm{A}$$ and $$\mathrm{B}$$ form fcc structure. Atoms of A are at the corners and atoms of B are present at the centres of faces of cube. What is the formula of the compound?

What are different possible oxidation states exhibited by scandium?

Which from following is the slope of the graph of rate versus concentration of the reactant for first order reaction?

What is the packing efficiency of silver metal in its unit cell?

Which from following polymers is obtained from $$\mathrm{C}_2 \mathrm{~F}_4$$ ?

Calculate current in ampere required to deposit $$4.8 \mathrm{~g} ~\mathrm{Cu}$$ from it's salt solution in 30 minutes. [Molar mass of $$\mathrm{Cu}=63.5 \mathrm{~g} \mathrm{~mol}^{-1}$$ ]

Identify number of moles of donor atoms in $$2 \mathrm{n}$$ mole of $$\mathrm{SCN}^{-}$$.

$$0.2 ~\mathrm{M}$$ aqueous solution of glucose has osmotic pressure 4.9 atm at $$300 \mathrm{~K}$$. What is the concentration of glucose if it has osmotic pressure $$1.5 \mathrm{~atm}$$ at same temperature?

Identify the product when phenol is heated with zinc dust.

Identify the product '$$\mathrm{B}$$' in the following reaction.

Dry ice $$\mathrm{\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{Dry\,ether}^{C{H_3}MgBr}}}$$ A $$\mathrm{\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{dil.\,HCl}^{{H_2}O}}}$$ B

Which among the following reactions exhibits $$\Delta \mathrm{H}=\Delta \mathrm{U}$$ ?

A buffer solution is prepared by mixing 0.2 M sodium acetate and 0.1 M acetic acid. If pK$$_a$$ for acetic acid is 4.7, find the pH.

A solution of nonvolatile solute is obtained by dissolving $$3.5 \mathrm{~g}$$ in $$100 \mathrm{~g}$$ solvent has boiling point elevation $$0.35 \mathrm{~K}$$. Calculate the molar mass of solute.

(Molal elevation constant $$=2.5 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$$ )

At $$0{ }^{\circ} \mathrm{C}$$ a gas occupies 22.4 liters. What is the temperature in Kelvin to reach the volume of 224 liters?

Which from following rule / principle states that "No two electrons in an atom can have the same set of four quantum numbers"?

Which from following molecules exhibits highest acidic nature?

What is the number of moles of $$\mathrm{sp}^2$$ hybrid carbon atoms in one mole of hexa-1,4-diyne?

Which of the following is NOT obtained when a mixture of methyl chloride and n-propyl chloride is treated with sodium metal in dry ether?

Which carbon atoms (numbered from $$C_1$$ to $$C_6$$ ) are involved in the formation of ring structure of glucose?

Calculate the amount of reactant in percent that remains after 60 minutes involved in first order reaction. $$\left(\mathrm{k}=0.02303\right.$$ minute $$\left.^{-1}\right)$$

Which salt from following forms aqueous solution having $$\mathrm{pH}$$ less than 7 ?

Identify neutral ligand from following

Identify the product 'B' in following reaction.

Ethyl phenyl ketone $$\mathrm{\buildrel {{H_2}N - N{H_2}} \over \longrightarrow}$$ A $$\mathrm{\mathrel{\mathop{\kern0pt\longrightarrow} \limits_\Delta ^{KOH,HO - {{(C{H_2})}_2} - OH}}}$$

Which of the following amines undergoes acylation reaction?

What is the IUPAC name of following compound?

What is the number of unit cells when one mole atom of a metal that forms simple cubic structure?

Identify the gas produced due to reduction of $$\mathrm{NH}_4^{+}$$ ions at cathode during working of dry cell.

Which of the following is secondary benzylic alcohol?

Find the value of spin only magnetic moment for chromium cation in +2 state.

An ideal gas expands by performing $$200 \mathrm{~J}$$ of work, during this internal energy increases by $$432 \mathrm{~J}$$. What is enthalpy change?

Calculate the wavenumber of the photon emitted during transition from the orbit of $$n=2$$ to $$n=1$$ in hydrogen atom. $$\left[R_H=109677 \mathrm{~cm}^{-1}\right]$$

Calculate the value of $$\Delta G$$ for following reaction at $$300 \mathrm{~K}$$.

$$\begin{aligned} & \mathrm{H}_2 \mathrm{O}_{(\mathrm{s})} \longrightarrow \mathrm{H}_2 \mathrm{O}_{(l)} \\ & \left(\Delta \mathrm{H}=7 \mathrm{~kJ}, \Delta \mathrm{S}=24.8 \mathrm{~J} \mathrm{~K}^{-1}\right) \end{aligned}$$

What is the oxidation state of carbon in $$\mathrm{CaC}_2$$ and $$\mathrm{K}_2 \mathrm{C}_2 \mathrm{O}_4$$ respectively?

What is the number of moles of water molecules required to prepare n moles of methane from n moles of methyl magnesium iodide?

Which of the following metals is used as catalyst in manufacture of sulphuric acid by contact process?

The rate for reaction $$\mathrm{A}+\mathrm{B} \rightarrow$$ product, is $$1.8 \times 10^{-2} \mathrm{~mol} \mathrm{~dm}^{-3} \mathrm{~s}^{-1}$$. Calculate the rate constant if the reaction is second order in $$\mathrm{A}$$ and first order in $$\mathrm{B}$$. ($$[\mathrm{A}]=0.2 \mathrm{M} ;[\mathrm{B}]=0.1 \mathrm{M}$$)

Which of the following concentration terms depends on temperature?

What type of reaction is the formation of aldol from aldehyde?

Identify homopolymer from following.

Identify the chiral molecule from following.

What is the mass in gram of 1 atom of an element if its atomic mass is $$10 ~\mathrm{u}$$ ?

Solubility of a salt $$\mathrm{A}_2 \mathrm{~B}_3$$ is $$1 \times 10^{-3} \mathrm{~mol} \mathrm{~dm}^{-3}$$. What is the value of its solubility product?

Identify the element having general electronic configuration $$\mathrm{ns}^2 \mathrm{np}^4$$ from following.

Identify the product $$\mathrm{A}$$ obtained in the following reaction.

Phenol + Conc. Nitric acid $$\stackrel{\text { conc, } \mathrm{H}_2 \mathrm{SO}_4}{\longrightarrow} \mathrm{A}$$

What is the value of specific rotation exhibited by glucose molecule?

What type of information is collected using scanning electron microscopy?

Identify the reagent $$\mathrm{A}$$ in the following conversion.

Alkyl halide $$\stackrel{A}{\longrightarrow}$$ Alkyl nitrite

If two vertices of a triangle are $$\mathrm{A}(3,1,4)$$ and $$\mathrm{B}(-4,5,-3)$$ and the centroid of the triangle is $$G(-1,2,1)$$, then the third vertex $$C$$ of the triangle is

In a Binomial distribution with $$\mathrm{n}=4$$, if $$2 \mathrm{P}(\mathrm{X}=3)=3 \mathrm{P}(\mathrm{X}=2)$$, then the variance is

Let two non-collinear vectors $$\hat{a}$$ and $$\hat{b}$$ form an acute angle. A point $$\mathrm{P}$$ moves, so that at any time $$t$$ the position vector $$\overline{\mathrm{OP}}$$, where $$\mathrm{O}$$ is origin, is given by $$\hat{a} \sin t+\hat{b} \cos t$$, when $$P$$ is farthest from origin $$O$$, let $$M$$ be the length of $$\overline{\mathrm{OP}}$$ and $$\hat{\mathrm{u}}$$ be the unit vector along $$\overline{\mathrm{OP}}$$, then

The number of solutions in $$[0,2 \pi]$$ of the equation $$16^{\sin ^2 x}+16^{\cos ^2 x}=10$$ is

The differential equation of all parabolas, whose axes are parallel to $$\mathrm{Y}$$-axis, is

The value of $$c$$ of Lagrange's mean value theorem for $$f(x)=\sqrt{25-x^2}$$ on $$[1,5]$$ is

$$\int \frac{x+1}{x\left(1+x \mathrm{e}^x\right)^2} \mathrm{~d} x=$$

If $$Z_1=4 i^{40}-5 i^{35}+6 i^{17}+2, Z_2=-1+i$$, where $$i=\sqrt{-1}$$, then $$\left|Z_1+Z_2\right|=$$

The approximate value of $$\log _{10} 998$$ is (given that $$\log _{10} \mathrm{e}=0.4343$$ )

If $$\sin ^{-1} x+\cos ^{-1} y=\frac{3 \pi}{10}$$, then the value of $$\cos ^{-1} x+\sin ^{-1} y$$ is

The area (in sq. units) of the region $$\mathrm{A}=\left\{(x, y) / \frac{y^2}{2} \leq x \leq y+4\right\}$$ is

$$\mathrm{A}, \mathrm{B}, \mathrm{C}$$ are three events, one of which must and only one can happen. The odds in favor of $$\mathrm{A}$$ are $$4: 6$$, the odds against $$B$$ are $$7: 3$$. Thus, odds against $$\mathrm{C}$$ are

The value of $$\alpha$$, so that the volume of the parallelopiped formed by $$\hat{i}+\alpha \hat{j}+\hat{k}, \hat{j}+\alpha \hat{k}$$ and $$\alpha \hat{i}+\hat{k}$$ becomes maximum, is

Two sides of a triangle are $$\sqrt{3}+1$$ and $$\sqrt{3}-1$$ and the included angle is $$60^{\circ}$$, then the difference of the remaining angles is

The standard deviation of the following distribution

is

The maximum value of xy when x + 2y = 8 is

If truth values of statements $$\mathrm{p}, \mathrm{q}$$ are true, and $$\mathrm{r}$$, $$s$$ are false, then the truth values of the following statement patterns are respectively

$$\begin{aligned} & \mathrm{a}: \sim(\mathrm{p} \wedge \sim \mathrm{r}) \vee(\sim \mathrm{q} \vee \mathrm{s}) \\ & \mathrm{b}:(\sim \mathrm{q} \wedge \sim \mathrm{r}) \leftrightarrow(\mathrm{p} \vee \mathrm{s}) \\ & \mathrm{c}:(\sim \mathrm{p} \vee \mathrm{q}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{s}) \end{aligned}$$

The rate of change of $$\sqrt{x^2+16}$$ with respect to $$\frac{x}{x-1}$$ at $$x=5$$ is

If $$x^2+y^2=\mathrm{t}+\frac{1}{\mathrm{t}}$$ and $$x^4+y^4=\mathrm{t}^2+\frac{1}{\mathrm{t}^2}$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ is equal to

Two tangents to the circle $$x^2+y^2=4$$ at the points $$\mathrm{A}$$ and $$\mathrm{B}$$ meet at the point $$\mathrm{P}(-4,0)$$. Then the area of the quadrilateral $$\mathrm{PAOB}, \mathrm{O}$$ being the origin, is

$$\mathrm{f}: \mathbb{R}-\left(-\frac{3}{5}\right) \rightarrow \mathbb{R}$$ is defined by $$f(x)=\frac{3 x-2}{5 x+3}$$, then $$f \circ f(1)$$ is

The value of $$\cot \left(\sum_\limits{n=1}^{23} \cot ^{-1}\left(1+\sum_\limits{k=1}^n 2 k\right)\right)$$ is

An object is moving in the clockwise direction around the unit circle $$x^2+y^2=1$$. As it passes through the point $$\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$$, its $$y$$-co-ordinate is decreasing at the rate of 3 units per sec. The rate at which the $$x$$-co-ordinate changes at this point is

If feasible region is as shown in the figure, then the related inequalities are

$$\int \frac{\mathrm{e}^{\tan ^{-1} x}}{1+x^2}\left[\left(\sec ^{-1} \sqrt{1+x^2}\right)^2+\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right] \mathrm{d} x, x > 0=$$

If $$\mathrm{f}(x)$$ is a function satisfying $$\mathrm{f}^{\prime}(x)=\mathrm{f}(x)$$ with $$\mathrm{f}(0)=1$$ and $$\mathrm{g}(x)$$ is a function that satisfies $$\mathrm{f}(x)+\mathrm{g}(x)=x^2$$. Then the value of the integral $$\int_\limits0^1 f(x) g(x) d x$$ is

The foot of the perpendicular drawn from the origin to the plane is $$(4,-2,5)$$, then the Cartesian equation of the plane is

$$\lim _\limits{x \rightarrow \frac{\pi}{2}} \frac{\cot x-\cos x}{(\pi-2 x)^3}$$ equals

If the distance between the parallel lines given by the equation $$x^2+4 x y+p y^2+3 x+q y-4=0$$ is $$\lambda$$, then $$\lambda^2=$$

The particular solution of the differential equation $$\left(1+y^2\right) \mathrm{d} x-x y \mathrm{~d} y=0$$ at $$x=1, y=0$$, represents

If at the end of certain meeting, everyone had shaken hands with everyone else, it was found that 45 handshakes were exchanged, then the number of members present at the meeting, are

If $$\sin 18^{\circ}=\frac{\sqrt{5}-1}{4}$$, then $$\cos ^2 48^{\circ}-\sin ^2 12^{\circ}$$ has the value

If $$A=\left[\begin{array}{cc}2 & -1 \\ -1 & 3\end{array}\right]$$, then the inverse of $$\left(2 A^2+5 A\right)$$ is

If $$ I=\int \frac{\sin x+\sin ^3 x}{\cos 2 x} d x=P \cos x+Q \log \left|\frac{\sqrt{2} \cos x-1}{\sqrt{2} \cos x+1}\right| $$ (where $$c$$ is a constant of integration), then values of $$\mathrm{P}$$ and $$\mathrm{Q}$$ are respectively

The negation of the statement $$(p \wedge q) \rightarrow(\sim p \vee r)$$ is

The probability mass function of random variable X is given by

$$P[X=r]=\left\{\begin{array}{ll} \frac{{ }^n C_r}{32}, & n, r \in \mathbb{N} \\ 0, & \text { otherwise } \end{array} \text {, then } P[X \leq 2]=\right.$$

The distance of a point $$(2,5)$$ from the line $$3 x+y+4=0$$ measured along the line $$L_1$$ and $$L_1$$ are same. If slope of line $$L_1$$ is $$\frac{3}{4}$$, then slope of the line $$\mathrm{L}_2$$ is

The distance of the point having position vector $$\hat{i}-2 \hat{j}-6 \hat{k}$$, from the straight line passing through the point $$(2,-3,-4)$$ and parallel to the vector $$6 \hat{i}+3 \hat{j}-4 \hat{k}$$ is units.

A vector $$\overrightarrow{\mathrm{n}}$$ is inclined to $$\mathrm{X}$$-axis at $$45^{\circ}$$, $$\mathrm{Y}$$-axis at $$60^{\circ}$$ and at an acute angle to Z-axis If $$\overrightarrow{\mathrm{n}}$$ is normal to a plane passing through the point $$(-\sqrt{2}, 1,1)$$, then equation of the plane is

If $$\cos ^{-1} x-\cos ^{-1} \frac{y}{3}=\alpha$$, where $$-1 \leq x \leq 1, -3 \leq y \leq 3, x \leq \frac{y}{3}$$, then for all $$x, y$$ $$9 x^2-6 x y \cos \alpha+y^2$$ is equal to

If $$\mathrm{f}(1)=1, \mathrm{f}^{\prime}(1)=3$$, then the derivative of $$\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f}(x))^2$$ at $$x=1$$ is

Three fair coins numbered 1 and 0 are tossed simultaneously. Then variance Var (X) of the probability distribution of random variable $$\mathrm{X}$$, where $$\mathrm{X}$$ is the sum of numbers on the uppermost faces, is

$$\int \frac{1}{\sin (x-a) \sin x} d x=$$

The derivative of $$\mathrm{f}(\sec x)$$ with respect to $$g(\tan x)$$ at $$x=\frac{\pi}{4}$$, where $$f^{\prime}(\sqrt{2})=4$$ and $$g^{\prime}(1)=2$$, is

The scalar product of the vector $$\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$$ with a unit vector along the sum of the vectors $$2 \hat{i}+4 \hat{j}-5 \hat{k}$$ and $$\lambda \hat{i}+2 \hat{j}+3 \hat{k}$$ is equal to 1 , then value of $$\lambda$$ is

The number of discontinuities of the greatest integer function $$\mathrm{f}(x)=[x], x \in\left(-\frac{7}{2}, 100\right)$$

If $$[(\bar{a}+2 \bar{b}+3 \bar{c}) \times(\bar{b}+2 \bar{c}+3 \bar{a})] \cdot(\bar{c}+2 \bar{a}+3 \bar{b})=54$$ then the value of $$\left[\begin{array}{lll}\bar{a} & \bar{b} & \bar{c}\end{array}\right]$$ is

A spherical raindrop evaporates at a rate proportional to its surface area. If originally its radius is $$3 \mathrm{~mm}$$ and 1 hour later it reduces to $$2 \mathrm{~mm}$$, then the expression for the radius $$R$$ of the raindrop at any time $$t$$ is

If the Cartesian equation of a line is $$6 x-2=3 y+1=2 z-2$$, then the vector equation of the line is

The volume of parallelopiped, whose coterminous edges are given by $$\overline{\mathrm{u}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}, \vec{v}=\hat{i}+\hat{j}+3 \hat{k}, \bar{w}=2 \hat{i}+\hat{j}+\hat{k}$$ is 1 cu. units. If $$\theta$$ is the angle between $$\bar{u}$$ and $$\bar{w}$$, then the value of $$\cos \theta$$ is

A rubber ball filled with water, having a small hole is used as the bob of a simple pendulum. The time period of such a pendulum

The ratio of wavelengths for transition of electrons from $$2^{\text {nd }}$$ orbit to $$1^{\text {st }}$$ orbit of Helium $$\left(\mathrm{He}^{++}\right)$$ and Lithium $$\left(\mathrm{Li}^{++1}\right)$$ is (Atomic number of Helium $$=2$$, Atomic number of Lithium $$=3$$ )

For an intrinsic semiconductor $$\left(\mathrm{n}_{\mathrm{h}}\right.$$ and $$\mathrm{n}_{\mathrm{e}}$$ are the number of holes per unit volume and number of electrons per unit volume respectively)

A $$5.0 \mathrm{~V}$$ stabilized power supply is required to be designed using a $$12 \mathrm{~V}$$ DC power supply as input source. The maximum power rating of zener diode is $$2.0 \mathrm{~W}$$. The minimum value of resistance $$R_{\mathrm{s}}$$ in $$\Omega$$ connected in series with zener diode will be

A jar '$$\mathrm{P}$$' is filled with gas having pressure, volume and temperature $$\mathrm{P}, \mathrm{V}, \mathrm{T}$$ respectively. Another gas jar $$Q$$ filled with a gas having pressure $$2 \mathrm{P}$$, volume $$\frac{\mathrm{V}}{4}$$ and temperature $$2 \mathrm{~T}$$. The ratio of the number of molecules in jar $$\mathrm{P}$$ to those in jar $$Q$$ is

The magnetic flux through a loop of resistance $$10 ~\Omega$$ varying according to the relation $$\phi=6 \mathrm{t}^2+7 \mathrm{t}+1$$, where $$\phi$$ is in milliweber, time is in second at time $$\mathrm{t}=1 \mathrm{~s}$$ the induced e.m.f. is

A thin rod of length '$$L$$' is bent in the form of a circle. Its mass is '$$M$$'. What force will act on mass '$$m$$' placed at the centre of this circle?

( $$\mathrm{G}=$$ constant of gravitation)

The coil of an a.c. generator has 100 turns, each of cross-sectional area $$2 \mathrm{~m}^2$$. It is rotating at constant angular speed $$30 ~\mathrm{rad} / \mathrm{s}$$, in a uniform magnetic field of $$2 \times 10^{-2} \mathrm{~T}$$. If the total resistance of the circuit is $$600 ~\Omega$$ then maximum power dissipated in the circuit is

A beam of unpolarized light passes through a tourmaline crystal A and then it passes through a second tourmaline crystal B oriented so that its principal plane is parallel to that of A. The intensity of emergent light is $$I_0$$. Now B is rotated by $$45^{\circ}$$ about the ray. The emergent light will have intensity $$\left(\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right)$$

The materials suitable for making electromagnets should have

A body falls on a surface of coefficient of restitution 0.6 from a height of $$1 \mathrm{~m}$$. Then the body rebounds to a height of

In a diffraction pattern due to single slit of width '$$a$$', the first minimum is observed at an angle of $$30^{\circ}$$ when the light of wavelength $$5400 \mathop A\limits^o$$ is incident on the slit. The first secondary maximum is observed at an angle of $$\left(\sin 30^{\circ}=\frac{1}{2}\right)$$

A stone is projected vertically upwards with speed '$$v$$'. Another stone of same mass is projected at an angle of $$60^{\circ}$$ with the vertical with the same speed '$$v$$'. The ratio of their potential energies at the highest points of their journey is $$\left[\sin 30^{\circ}=\cos 60^{\circ}=0.5, \cos 30^{\circ}=\sin 60^{\circ}=\frac{\sqrt{3}}{2}\right]$$

An electron (mass $$\mathrm{m}$$ ) is accelerated through a potential difference of '$$V$$' and then it enters in a magnetic field of induction '$$B$$' normal to the lines. The radius of the circular path is ($$\mathrm{e}=$$ electronic charge)

A capacitor, an inductor and an electric bulb are connected in series to an a.c. supply of variable frequency. As the frequency of the supply is increased gradually, then the electric bulb is found to

When both source and listener are approaching each other the observed frequency of sound is given by $$\left(V_L\right.$$ and $$V_S$$ is the velocity of listener and source respectively, $$\mathrm{n}_0=$$ radiated frequency)

Water is flowing through a horizontal pipe in stream line flow. At the narrowest part of the pipe

The angle of prism is $$A$$ and one of its refracting surface is silvered. Light rays falling at an angle of incidence '$$2 \mathrm{A}$$' on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index of the material of the prism is

The maximum velocity of a particle performing S.H.M. is '$$\mathrm{V}$$'. If the periodic time is made $$\left(\frac{1}{3}\right)^d$$ and the amplitude is doubled, then the new maximum velocity of the particle will be

A conducting wire of length $$2500 \mathrm{~m}$$ is kept in east-west direction, at a height of $$10 \mathrm{~m}$$ from the ground. If it falls freely on the ground then the current induced in the wire is (Resistance of wire $$=25 \sqrt{2} \Omega$$, acceleration due to gravity $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \mathrm{~B}_{\mathrm{H}}=2 \times 10^{-5} \mathrm{~T}$$ )

For an electron moving in the $$\mathrm{n}^{\text {th }}$$ Bohr orbit the deBroglie wavelength of an electron is

A square lamina of side '$$b$$' has same mass as a disc of radius '$$R$$' the moment of inertia of the two objects about an axis perpendicular to the plane and passing through the centre is equal. The ratio $$\frac{b}{R}$$ is

A body weighs $$300 \mathrm{~N}$$ on the surface of the earth. How much will it weigh at a distance $$\frac{R}{2}$$ below the surface of earth? ( $$R \rightarrow$$ Radius of earth)

To get the truth table shown, from the following logic circuit, the Gate G should be

For a gas having '$$\mathrm{X}$$' degrees of freedom, '$$\gamma$$' is ($$\gamma=$$ ratio of specific heats $$=\mathrm{C_P / C_V}$$)

A galvanometer of resistance $$\mathrm{G}$$ is shunted with a resistance of $$10 \%$$ of $$\mathrm{G}$$. The part of the total current that flows through the galvanometer is

If an electron in a hydrogen atom jumps from an orbit of level $$n=3$$ to orbit of level $$n=2$$, then the emitted radiation frequency is (where R = Rydberg's constant, C = Velocity of light)

Self inductance of solenoid is

The capacitance of a parallel plate capacitor is $$2.5 ~\mu \mathrm{F}$$. When it is half filled with a dielectric as shown in figure, its capacitance becomes $$5 ~\mu \mathrm{F}$$. The dielectric constant of the dielectric is

Equation of simple harmonic progressive wave is given by $$y=\frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \cos \omega t$$ then the resultant amplitude of the wave is $$\left(\cos 90^{\circ}=0\right)$$

Two uniform brass rods $$A$$ and $$B$$ of length '$$l$$' and '$$2 l$$' and their radii '$$2 r$$' and '$$r$$' respectively are heated to same temperature. The ratio of the increase in the volume of $$\operatorname{rod} \mathrm{A}$$ to that of $$\operatorname{rod} \mathrm{B}$$ is

In a single slit experiment, the width of the slit is doubled. Which one of the following statements is correct?

A gas at N.T.P. is suddenly compressed to $$\left(\frac{1}{4}\right)^{\text {th }}$$ of its original volume. The final pressure in (Given $$\gamma=$$ ratio of sp. heats $$=\frac{3}{2}$$ ) atmosphere is ( $$\mathrm{P}=$$ original pressure)

The excess of pressure in a first soap bubble is three times that of other soap bubble. Then the ratio of the volume of first bubble to other is

In a meter bridge experiment null point is obtained at $$l \mathrm{~cm}$$ from the left end. If the meter bridge wire is replaced by a wire of same material but twice the area of across-section, then the null point is obtained at a distance

A long straight wire carrying a current of $$25 \mathrm{~A}$$ rests on the table. Another wire PQ of length $$1 \mathrm{~m}$$ and mass $$2.5 \mathrm{~g}$$ carries the same current but in the opposite direction. The wire PQ is free to slide up and down. To what height will wire PQ rise? ($$\mu_0=4 \pi \times 10^{-7}$$ SI unit)

In a thermodynamic process, there is no exchange of heat between the system and surroundings. Then the thermodynamic process is

According to kinetic theory of gases, which one of the following statements is wrong?

The radii of two soap bubbles are $$r_1$$ and $$r_2$$. In isothermal condition they combine with each other to form a single bubble. The radius of resultant bubble is

The rays of different colours fail to converge at a point after passing through a thick converging lens. This defect is called

The ratio of potential difference that must be applied across parallel and series combination of two capacitors $$C_1$$ and $$C_2$$ with their capacitance in the ratio $$1: 2$$ so that energy stored in these two cases becomes same is

The potential energy of charged parallel plate capacitor is $$v_0$$. If a slab of dielectric constant $$\mathrm{K}$$ is inserted between the plates, then the new potential energy will be

A solid sphere rolls without slipping on an inclined plane at an angle $$\theta$$. The ratio of total kinetic energy to its rotational kinetic energy is

Two discs of same mass and same thickness (t) are made from two different materials of densities '$$d_1$$' and '$$d_2$$' respectively. The ratio of the moment of inertia $$I_1$$ to $$I_2$$ of two discs about an axis passing through the centre and perpendicular to the plane of disc is

When a string of length '$$l$$' is divided into three segments of length $$l_1, l_2$$ and $$l_3$$. The fundamental frequencies of three segments are $$\mathrm{n}_1, \mathrm{n}_2$$ and $$\mathrm{n}_3$$ respectively. The original fundamental frequency '$$n$$' of the string is

A seconds pendulum is placed in a space laboratory orbiting round the earth at a height '$$3 \mathrm{R}$$' from the earth's surface. The time period of the pendulum will be ( $$R=$$ radius of earth)

A solid metallic sphere has a charge $$+3 Q$$. Concentric with this sphere is a conducting spherical shell having charge $$-\mathrm{Q}$$. The radius of the sphere is '$$A$$' and that of the spherical shell is '$$B$$'. $$(B > A)$$. The electric field at a distance '$$\mathrm{R}$$' $$(\mathrm{A} < \mathrm{R} < \mathrm{B})$$ from the centre is ( $$\varepsilon_0=$$ permittivity of vacuum)

A closed organ pipe of length '$$L_1$$' and an open organ pipe contain diatomic gases of densities '$$\rho_1$$' and '$$\rho_2$$' respectively. The compressibilities of the gases are same in both pipes, which are vibrating in their first overtone with same frequency. The length of the open organ pipe is (Neglect end correction)

From a metallic surface photoelectric emission is observed for frequencies $$v_1$$ and $$v_2\left(v_1 > v_2\right)$$ of the incident light. The maximum values of the kinetic energy of the photoelectrons emitted in the two cases are in the ratio $$1: \mathrm{x}$$. Hence the threshold frequency of the metallic surface is

In an $$\mathrm{AC}$$ circuit, the current is $$\mathrm{i}=5 \sin \left(100 \mathrm{t}-\frac{\pi}{2}\right) \mathrm{A}$$ and voltage is $$\mathrm{e}=200 \sin (100 \mathrm{t})$$ volt. Power consumption in the circuit is $$\left(\cos 90^{\circ}=0\right)$$