What is the calculated value of spin only magnetic moment in terms of BM if only one unpaired electron is present in a species?

Which of the following is tertiary allylic alcohol?

Identify the solvent used in bromination of phenol to obtain 2,4,6-tribromophenol.

How many moles of nitrogen atoms are present in $$8 \mathrm{~g}$$ of ammonium nitrate?

(Molar mass of ammonium nitrate $$=80$$ )

Identify the elements undergoing reduction and oxidation respectively in the following redox reaction.

$$3 \mathrm{H}_3 \mathrm{AsO}_{3(\mathrm{aq})}+\mathrm{BrO}_{3(\mathrm{aq})}^{-} \rightarrow \mathrm{Br}_{(\mathrm{aq})}^{-}+3 \mathrm{H}_3 \mathrm{AsO}_4$$

Which of the following is tricarboxylic acid?

Find the radius of an atom in fcc unit cell having edge length $$393 \mathrm{pm}$$.

Which from following is a CORRECT decreasing order of ionization enthalpies of different elements?

A gas absorbs $$200 \mathrm{~J}$$ heat and expands by $$500 \mathrm{~cm}^3$$ against a constant external pressure $$2 \times 10^5 \mathrm{~N} \mathrm{~m}^{-2}$$. What is the change in internal energy?

Identify a copolymer from following.

Find the average rate of formation of $$\mathrm{NO}_{2(\mathrm{~g})}$$, in following reaction.

$$\begin{aligned} & 2 \mathrm{~N}_2 \mathrm{O}_{5(\mathrm{~g})} \rightarrow 4 \mathrm{NO}_{2(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})} \\ & {\left[-\frac{\Delta\left[\mathrm{N}_2 \mathrm{O}_5\right]}{\Delta \mathrm{t}}\right]=x \mathrm{~mol} \mathrm{~dm}^{-3} \mathrm{~s}^{-1}} \end{aligned}$$

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

Identify the product obtained when benzonitrile is reduced by stannous chloride in presence of hydrochloric acid followed by acid hydrolysis.

Find solubility in terms of $$\mathrm{mol} \mathrm{~L}^{-1}$$ if solubility product of silver bromide is $$6.4 \times 10^{-13}$$.

What happens when solution of an electrolyte is diluted?

The solubility of a gas in a liquid is directly proportional to the pressure of the gas over the solution. Identify the law for this statement.

Weak acid HX has dissociation constant $$1 \times 10^{-5}$$. Calculate the percent dissociation in its $$0.1 \mathrm{M}$$ solution.

Calculate the $$\mathrm{pH}$$ of a buffer solution containing $$0.01 ~\mathrm{M}$$ salt and $$0.004 \mathrm{~M}$$ weak acid.

$$\left(\mathrm{pK}_{\mathrm{a}}=4.762\right)$$

Which among the following is vinylic halide?

Which from following compounds is obtained when carbon dioxide gas bubbled through slaked lime solution?

Calculate the number of atoms present in unit cell of an element having molar mass $$190 \mathrm{~g} \mathrm{~mol}^{-1}$$ and density $$20 \mathrm{~g} \mathrm{~cm}^{-3}$$.

$$\left[\mathrm{a}^3 \cdot \mathrm{N}_{\mathrm{A}}=38 \mathrm{~cm}^3 \mathrm{~mol}^{-1}\right]$$

What is the solubility of a gas in water at $$25^{\circ} \mathrm{C}$$ if partial pressure is $$0.18 \mathrm{~atm}$$ ?

$$\left(\mathrm{K}_{\mathrm{H}}=0.16 \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~atm}^{-1}\right)$$

What is the radius of fourth orbit of $$\mathrm{Be}^{+++}$$ ?

What is the number of unpaired electrons in $$\mathrm{NO}$$ molecule?

Identify the glycosidic linkage present in lactose.

Which from following statements is TRUE about $$\mathrm{CH}_3 \mathrm{CH}\left(\mathrm{NH}_2\right) \mathrm{CH}_2 \mathrm{COOH}$$ molecule?

Which of the following is obtained as product when ethylene reacts with oxygen in presence of $$\mathrm{Pd} / \mathrm{Al}_2 \mathrm{O}_3$$ ?

What is the position of transition elements from $$\mathrm{Sc}$$ to $$\mathrm{Zn}$$ in long form of periodic table?

Which from following elements is most abundant on earth?

What is the volume of 1 mole real gas at STP $$\left(V_0=22.4 \mathrm{~dm}^3\right)$$, if compressibility factor of real gas is 1.1 at STP?

Identify the product obtained when isopropyl bromide is reacted with metallic sodium in dry ether.

Which of the following is general representation of Grignard reagent?

Which among the following statements is NOT true about high density polythene?

What is osmotic pressure of solution of $$1.7 \mathrm{~g} \mathrm{~CaCl}_2$$ in $$1.25 \mathrm{~dm}^3$$ water at $$300 \mathrm{~K}$$ if van't Hoff factor and molar mass of $$\mathrm{CaCl}_2$$, are 2.47 and $$111 \mathrm{~g} \mathrm{~mol}^{-1}$$ respectively?

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

Which among the following pair of properties is intensive?

Identify the molecular formula of an alkane that exhibits only two different structural isomers.

An organic compound '$$\mathrm{A}$$' on reaction with $$\mathrm{PCl}_3$$ gives an alkyl chloride having formula $$\mathrm{C}_3 \mathrm{H}_7 \mathrm{Cl}$$. '$$\mathrm{A}$$' on oxidation with $$\mathrm{PCC}$$ forms an aldehyde having formula $$\mathrm{C}_3 \mathrm{H}_6 \mathrm{O}$$. Identify '$$\mathrm{A}$$'.

Identify tetrasaccharide from following.

What type of ligand does the ethylenediamine is?

What is angular momentum of an electron in fourth orbit of hydrogen atom?

Which from following complexes is heteroleptic?

Calculate $$E_{\text {cell }}^{\circ}$$ in which following reaction occurs. $$\mathrm{Mg}_{(\mathrm{s})}+2 \mathrm{Ag}_{(\mathrm{IM})}^{+} \rightarrow \mathrm{Mg}_{(1 \mathrm{M})}^{+}+2 \mathrm{Ag}_{(\mathrm{s})}$$ if $$\mathrm{E}_{\mathrm{Ag}}^{\circ}=0.8 \mathrm{~V}$$ and $$\mathrm{E}_{\mathrm{Mg}}^{\circ}=-2.37 \mathrm{~V}$$

Identify CORRECT decreasing order of solubilities of alcohols, alkanes and amines in water having comparable molar mass.

Which of the following characteristic properties is NOT true for crystalline solid?

Time required for $$90 \%$$ completion of a first order reaction is '$$x$$' minute. Calculate the time required to complete $$99.9 \%$$ of the reaction at same temperature.

Identify '$$A$$' in the following reaction:

A $$\mathrm{\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{ether}^{LiAl{H_4}}}}$$ Ethanamine

Which of the following reagents is used in Gatterman-Koch formylation of arene?

Identify the last step in wet chemical synthesis of nanomaterial.

Calculate the conductivity of $$0.02 \mathrm{~M}$$ electrolyte solution if its molar conductivity $$407.2 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$$ ?

If $$8.84 \mathrm{~kJ}$$ heat is liberated for formation of $$3 \mathrm{~g}$$ ethane, calculate its $$\triangle_{\mathrm{f}} \mathrm{H}^{\circ}$$.

The value of $$\mathrm{c}$$ for the function $$\mathrm{f}(x)=\log x$$ on [$$1$$, e] if LMVT can be applied, is

The three ships namely A, B and C sail from India to Africa. If the odds in favour of the ships reaching safely are $$2: 5,3: 7$$ and $$6: 11$$ respectively, then probability of all of them arriving safely is

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

If the sum of mean and variance of a Binomial Distribution is $$\frac{15}{2}$$ for 10 trials, then the variance is

If $$(\bar{a} \times \bar{b}) \times \bar{c}=-5 \bar{a}+4 \bar{b}$$ and $$\bar{a} \cdot \bar{b}=3$$, then the value of $$\bar{a} \times(\bar{b} \times \bar{c})$$ is

The plane through the intersection of planes $$x+y+z=1$$ and $$2 x+3 y-z+4=0$$ and parallel to $$\mathrm{Y}$$-axis also passes through the point

Let $$\mathrm{f}(x)=\mathrm{e}^x-x$$ and $$\mathrm{g}(x)=x^2-x, \forall x \in \mathrm{R}$$, then the set of all $$x \in \mathrm{R}$$, where the function $$\mathrm{h}(x)=(\mathrm{fog})(x)$$ is increasing is

Let $$f$$ be a differentiable function such that $$\mathrm{f}(1)=2$$ and $$\mathrm{f}^{\prime}(x)=\mathrm{f}(x)$$, for all $$x \in \mathrm{R}$$. If $$\mathrm{h}(x)=\mathrm{f}(\mathrm{f}(x))$$, then $$\mathrm{h}^{\prime}(1)$$ is equal to

The joint equation of a pair of lines passing through the origin and making an angle of $$\frac{\pi}{4}$$ with the line $$3 x+2 y-8=0$$ is

Two sides of a square are along the lines $$5 x-12 y+39=0$$ and $$5 x-12 y+78=0$$, then area of the square is

The value of $$\int \frac{\mathrm{d} x}{x^2\left(x^4+1\right)^{\frac{3}{4}}}$$ is

$$\int \frac{5 \tan x}{\tan x-2} \mathrm{~d} x=x+\mathrm{a} \log |\sin x-2 \cos x|+\mathrm{c},$$ (where $$c$$ is a constant of integration), then the value of $$a$$ is

Let $$\mathrm{S}=\left\{\mathrm{t} \in \mathrm{R} / \mathrm{f}(x)=|x-\pi|\left(\mathrm{e}^{|x|}-1\right) \sin |x|\right.$$ is not differentiable at $$\mathrm{t}\}$$, then $$\mathrm{S}$$ is

The domain of the function $$\mathrm{f}(x)=\sin ^{-1}\left(\frac{|x|+5}{x^2+1}\right)$$ is $$(-\infty,-a] \cup[a, \infty)$$. Then a is equal to

The perpendicular distance of the origin from the plane $$x-3 y+4 z-6=0$$ is

The area bounded by the $$\mathrm{X}$$-axis and the curve $$y=x(x-2)(x+1)$$ is

Let $$\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$$ and $$\mathrm{g}: \mathrm{R} \rightarrow \mathrm{R}$$ be continuous functions. Then the value of the integral $$\int_\limits{\frac{-\pi}{2}}^{\frac{\pi}{2}}[\mathrm{f}(x)+\mathrm{f}(-x)][\mathrm{g}(x)-\mathrm{g}(-x)] \mathrm{d} x$$ is

If $$\bar{p}=\hat{i}+\hat{j}+\hat{k}$$ and $$\bar{q}=\hat{i}-2 \hat{j}+\hat{k}$$. Then a vector of magnitude $$5 \sqrt{3}$$ units perpendicular to the vector $$\bar{q}$$ and coplanar with $$\bar{p}$$ and $$\bar{q}$$ is

The value of $$\frac{{ }^{10} \mathrm{C}_{\mathrm{r}}}{{ }^{11} \mathrm{C}_{\mathrm{r}}}$$, when both the numerator and denominator are at their greatest values, is

The general solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}+\left(\frac{3 x^2}{1+x^3}\right) y=\frac{1}{x^3+1}$$ is

If $$y$$ is a function of $$x$$ and $$\log (x+y)=2 x y$$, then $$\frac{d y}{d x}$$ at $$x=0$$ is

The displacement '$$\mathrm{S}$$' of a moving particle at a time $$t$$ is given by $$S=5+\frac{48}{t}+t^3$$. Then its acceleration when the velocity is zero, is

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

The value of $$\tan ^{-1}(1)+\cos ^{-1}\left(-\frac{1}{2}\right)+\sin ^{-1}\left(-\frac{1}{2}\right)$$ is

$$\int_\limits 0^\pi \frac{x \tan x}{\sec x+\cos x} d x= $$

If $$\tan ^{-1} a+\tan ^{-1} b+\tan ^{-1} c=\pi$$, then which of the following statement is true?

If $$\mathrm{f}(x)=\frac{4}{x^4}\left[1-\cos \frac{x}{2}-\cos \frac{x}{4}+\cos \frac{x}{2} \cdot \cos \frac{x}{4}\right]$$ is continuous at $$x=0$$, then $$\mathrm{f}(0)$$ is

Two lines $$\frac{x-3}{1}=\frac{y+1}{3}=\frac{z-6}{-1}$$ and $$\frac{x+5}{7}=\frac{y-2}{-6}=\frac{z-3}{4} \quad$$ intersect at the point R. Then reflection of $$\mathrm{R}$$ in the $$x y$$-plane has co-ordinates

The value of $$\int \frac{\left(x^2-1\right) d x}{x^3 \sqrt{2 x^4-2 x^2+1}}$$ is

The shaded area in the figure given below is a solution set of a system of inequations. The minimum value of objective function $$3 x+5 y$$, subject to the linear constraints given by this system of inequations is

If $$\overline{\mathrm{a}}=\mathrm{m} \overline{\mathrm{b}}+\mathrm{nc}$$, where $$\overline{\mathrm{a}}=4 \hat{\mathrm{i}}+13 \hat{\mathrm{j}}-18 \hat{\mathrm{k}}, \overline{\mathrm{b}}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}, \overline{\mathrm{c}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}}$$, then $$\mathrm{m}+\mathrm{n}=$$

In a game, 3 coins are tossed. A person is paid ₹ 7 /-, if he gets all heads or all tails; and he is supposed to pay ₹ 3 /-, if he gets one head or two heads. The amount he can expect to win on an average per game is ₹

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

The parametric equations of the circle $$x^2+y^2+2 x-4 y-4=0$$ are

In a triangle $$\mathrm{ABC}$$, with usual notations, if $$\mathrm{c}=4$$, then value of $$(a-b)^2 \cos ^2 \frac{C}{2}+(a+b)^2 \sin ^2 \frac{C}{2}$$ is

$$\lim _\limits{x \rightarrow a} \frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}}=$$

If $$B=\left[\begin{array}{ccc}3 & \alpha & -1 \\ 1 & 3 & 1 \\ -1 & 1 & 3\end{array}\right]$$ is the adjoint of a $$3 \times 3$$ matrix $$\mathrm{A}$$ and $$|\mathrm{A}|=4$$, then $$\alpha$$ is equal to

If $$x=3 \tan \mathrm{t}$$ and $$y=3 \sec \mathrm{t}$$, then the value of $$\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}$$ at $$\mathrm{t}=\frac{\pi}{4}$$ is

A fair die is tossed twice in succession. If $$\mathrm{X}$$ denotes the number of sixes in two tosses, then the probability distribution of $$\mathrm{X}$$ is given by

The negation of the statement pattern $$\sim s \vee(\sim r \wedge s)$$ is equivalent to

If the volume of tetrahedron, whose vertices are with position vectors $$\hat{i}-6 \hat{j}+10 \hat{k},-\hat{i}-3 \hat{j}+7 \hat{k}, 5 \hat{i}-\hat{j}+\lambda \hat{k}$$ and $$7 \hat{i}-4 \hat{j}+7 \hat{k}$$ is 11 cubic units, then value of $$\lambda$$ is

The argument of $$\frac{1+i \sqrt{3}}{\sqrt{3}+i}, i=\sqrt{-1}$$ is

If $$y=\tan ^{-1}\left(\frac{\log \left(\frac{\mathrm{e}}{x^2}\right)}{\log \left(e x^2\right)}\right)+\tan ^{-1}\left(\frac{4+2 \log x}{1-8 \log x}\right)$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ is

If the surface area of a spherical balloon of radius $$6 \mathrm{~cm}$$ is increasing at the rate $$2 \mathrm{~cm}^2 / \mathrm{sec}$$, then the rate of increase in its volume in $$\mathrm{cm}^3 / \mathrm{sec}$$ is

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

In a certain culture of bacteria, the rate of increase is proportional to the number of bacteria present at that instant. It is found that there are 10,000 bacteria at the end of 3 hours and 40,000 bacteria at the end of 5 hours, then the number of bacteria present in the beginning are

If $$x, y, z$$ are in A.P. and $$\tan ^{-1} x, \tan ^{-1} y$$ and $$\tan ^{-1} z$$ are also in A.P., then

Mean and variance of six observations are 8 and 16 respectively. If each observation is multiplied by 3, then new variance of the resulting observations is

The differential equation of all circles, passing through the origin and having their centres on the $$\mathrm{X}$$-axis, is

$$\int_\limits0^1 \cos ^{-1} x d x=$$

Two trains, each $$30 \mathrm{~m}$$ long are travelling in opposite directions with velocities $$5 \mathrm{~m} / \mathrm{s}$$ and $$10 \mathrm{~m} / \mathrm{s}$$. They will cross after

The fundamental frequency of air column in pipe 'A' closed at one end is in unison with second overtone of an air column in pipe 'B' open at both ends. The ratio of length of air column in pipe '$$\mathrm{A}$$' to that of air column in pipe '$$\mathrm{B}$$' is

In Young's double slit experiment, the two slits are 'd' distance apart. Interference pattern is observed on a screen at a distance 'D' from the slits. A dark fringe is observed on a screen directly opposite to one of the slits. The wavelength of light is

A black body radiates maximum energy at wavelength '$$\lambda$$' and its emissive power is 'E' Now due to change in temperature of that body, it radiates maximum energy at wavelength $$\frac{2 \lambda}{3}$$. At that temperature emissive power is

In meter bridge experiment, null point was obtained at a distance '$$l$$' from left end. The values of resistances in the left and right gap are doubled and then interchanged. The new position of the null point is

The magnetic field at the centre of a circular coil of radius '$$R$$', carrying current $$2 A$$ is '$$B_1$$'. The magnetic field at the centre of another coil of radius '$$3 R$$' carrying current $$4 A$$ is '$$B_2$$'. The ratio $$B_1:B_2$$ is

If a capacitor of capacity $$900 ~\mu \mathrm{F}$$ is charged to $$100 \mathrm{~V}$$ and its total energy is transferred to a capacitor of capacity $$100 ~\mu \mathrm{F}$$, then its potential will be

The equation of wave is $$Y=6 \sin$$ $$\left(12 \pi t-0.02 \pi x+\frac{\pi}{3}\right)$$ where '$$x$$' is in $$m$$ and '$$t$$' in $$\mathrm{s}$$. The velocity of the wave is

With an alternating voltage source of frequency '$$f$$', inductor '$$L$$', capacitor '$$C$$' and resistance '$$R$$' are connected in series. The voltage leads the current by $$45^{\circ}$$. The value of '$$L$$' is $$\left(\tan 45^{\circ}=1\right)$$

A pure $$\mathrm{Si}$$ crystal has $$4 \times 10^{28}$$ atoms per $$\mathrm{m}^3$$. It is doped by 1 ppm concentration of antimony. The number of free electrons available will be

A mass '$$\mathrm{M}$$' moving with velocity '$$\mathrm{V}$$' along $$\mathrm{X}$$-axis collides and sticks to another mass $$2 \mathrm{M}$$ which is moving along $$\mathrm{Y}$$-axis with velocity '$$3 \mathrm{~V}$$'. The velocity of the combination after collision is

Which of the following graphs between pressure (P) and volume (V) correctly shows isochoric changes?

A galvanometer has resistance '$$\mathrm{G}$$' and range '$$\mathrm{V} g$$'. How much resistance is required to read voltage upto '$$\mathrm{V}$$' volt?

'$$n$$' number of liquid drops each of radius '$$r$$' coalesce to form a single drop of radius '$$R$$'. The energy released in the process is converted into the kinetic energy of the big drop so formed. The speed of the big drop is

$$[\mathrm{T}=$$ surface tension of liquid, $$\rho=$$ density of liquid.]

What is the moment of inertia of the electron moving in second Bohr orbit of hydrogen atom? [ $$\mathrm{h}=$$ Planck's constant, $$\mathrm{m}=$$ mass of electron, $$\varepsilon_0=$$ permittivity of free space, $$\mathrm{e}=$$ charge on electron]

At critical temperature, the surface tension of liquid is

Two wires $$2 \mathrm{~mm}$$ apart supply current to a $$100 \mathrm{~V}, 1 \mathrm{~kW}$$ heater. The force per metre between the wires is ( $$\mu_0=4 \pi \times 10^{-27}$$ SI unit)

A solenoid of 500 turns/m is carrying a current of 3 A. Its core is made of iron which has relative permeability 5001. The magnitude of magnetization is

The ratio of the velocity of the electron in the first Bohr orbit to that in the second Bohr orbit of hydrogen atom is

The capacitive reactance of a capacitor '$$C$$' is $$\mathrm{X} \Omega$$. Both, the frequency of a.c. supply and capacitance of the above capacitor are doubled. The new capacitive reactance will be

A $$100 \mathrm{~mH}$$ coil carries a current of $$1 \mathrm{~A}$$. Energy stored in the form of magnetic field is

A metal rod $$2 \mathrm{~m}$$ long increases in length by $$1.6 \mathrm{~mm}$$, when heated from $$0^{\circ} \mathrm{C}$$ to $$60^{\circ} \mathrm{C}$$. The coefficient of linear expansion of metal rod is

Assume that an electric field $$\mathrm{E}=30 \mathrm{x}^2 \hat{\mathrm{i}}$$ exists in space. If '$$\mathrm{V}_0$$' is the potential at the origin and '$$V_A$$' is the potential at $$x=2 \mathrm{~m}$$, then the potential difference $$\left(\mathrm{V}_{\mathrm{A}}-\mathrm{V}_0\right)$$ is

Two dielectric slabs having dielectric constant '$$\mathrm{K}_1$$' and '$$\mathrm{K}_2$$' of thickness $$\frac{\mathrm{d}}{4}$$ and $$\frac{3 \mathrm{~d}}{4}$$ are inserted between the plates as shown in figure. The net capacitance between $$A$$ and $$B$$ is $$\left[\varepsilon_0\right.$$ is permittivity of free space]

The output of an 'OR' gate is connected to both the inputs of a 'NAND' gate. The combination will serve as

Which one of the operations of $$\mathrm{n}-\mathrm{p}-\mathrm{n}$$ transistor differs from that of $$p-n-p$$ transistor?

A hollow metal pipe is held vertically and bar magnet is dropped through it with its length along the axis of the pipe. The acceleration of the falling magnet is ( $$\mathrm{g}=$$ acceleration due to gravity)

A metal sphere of mass '$$m$$' and density '$$\sigma_1$$' falls with terminal velocity through a container containing liquid. The density of liquid is '$$\sigma_2$$'. The viscous force acting on the sphere is

Two uniform wires of same material are vibrating under the same tension. If the first overtone of first wire is equal to the $$2^{\text {nd }}$$ overtone of $$2^{\text {nd }}$$ wire and radius of the first wire is twice the radius of the $$2^{\text {nd }}$$ wire then the ratio of length of first wire to $$2^{\text {nd }}$$ wire is

A body is projected vertically from earth's surface with velocity equal to half the escape velocity. The maximum height reached by the satellite is ( $$R$$ = radius of earth)

A ball of mass '$$\mathrm{m}$$' is dropped from a height '$$\mathrm{s}$$' on a horizontal platform fixed at the top of a vertical spring. The platform is depressed by a distance '$$h$$'. The spring constant is ( $$\mathrm{g}=$$ acceleration due to gravity)

In the circuit given below, the current through inductor is $$0.9 \mathrm{~A}$$ and through the capacitor is $$0.6 \mathrm{~A}$$. The current drawn from the a.c. source is

A body is executing a linear S.H.M. Its potential energies at the displacement '$$\mathrm{x}$$' and '$$\mathrm{y}$$' are '$$\mathrm{E}_1$$' and '$$E_2$$' respectively. Its potential energy at displacement $$(\mathrm{x}+\mathrm{y})$$ will be

We have a jar filled with gas characterized by parameters $$\mathrm{P}, \mathrm{V}, \mathrm{T}$$ and another jar B filled with gas having parameters $$2 \mathrm{P}, \frac{\mathrm{V}}{4}, 2 \mathrm{~T}$$, where symbols have their usual meaning. The ratio of number of molecules in jar A to those in jar B is

Two spheres each of mass '$$M$$' and radius $$\frac{R}{2}$$ are connected at the ends of massless rod of length '$$2 R$$'. What will be the moment of inertia of the system about an axis passing through centre of one of the spheres and perpendicular to the rod?

If the potential difference used to accelerate electrons is doubled, by what factor does the de-Broglie wavelength associated with electrons change?

A simple harmonic progressive wave is represented by $$y=A \sin (100 \pi t+3 x)$$. The distance between two points on the wave at a phase difference of $$\frac{\pi}{3}$$ radian is

An insulated container contains a monoatomic gas of molar mass '$$\mathrm{m}$$'. The container is moving with velocity '$$\mathrm{V}$$'. If it is stopped suddenly, the change in temperature of a gas is [R is gas constant]

To get three images of a single object, the angle between the two plane mirrors should be

A parallel beam of monochromatic light falls normally on a single narrow slit. The angular width of the central maximum in the resulting diffraction pattern

For the diagram shown, the resistances between points A and B when ideal diode D is forward biased is '$$R_1$$' and that when reverse biased is '$$R_2$$'. The ratio $$R_1: R_2$$ is

The maximum kinetic energy of the photoelectrons varies

Light waves from two coherent sources arrive at two points on a screen with path difference of zero and $$\frac{\lambda^{\prime}}{2}$$. The ratio of intensities at the points is $$\left(\cos 0^{\circ}=1, \cos \pi=-1\right)$$

A uniform rope of length '$$L$$' and mass '$$m_1$$' hangs vertically from a rigid support. A block of mass '$$m_2$$' is attached to the free end of the rope. A transverse wave of wavelength '$$\lambda_1$$' is produced at the lower end of the rope. The wavelength of the wave when it reaches the top of the rope is '$$\lambda_2$$'. The ratio $$\frac{\lambda_1}{\lambda_2}$$ is

In a vessel, the ideal gas is at a pressure $$\mathrm{P}$$. If the mass of all the molecules is halved and their speed is doubled, then resultant pressure of the gas will be

Two concentric circular coils having radii $$r_1$$ and $$r_2\left(r_2 << r_1\right)$$ are placed co-axially with centres coinciding. The mutual induction of the arrangement is (Both coils have single turn, $$\mu_0=$$ permeability of free space)

A system consists of three particles each of mass '$$m_1$$' placed at the corners of an equilateral triangle of side '$$\frac{\mathrm{L}}{3}$$', A particle of mass '$$\mathrm{m}_2$$' is placed at the mid point of any one side of the triangle. Due to the system of particles, the force acting on $$\mathrm{m}_2$$ is

The moment of inertia of a uniform square plate about an axis perpendicular to its plane and passing through the centre is $$\frac{\mathrm{Ma}^2}{6}$$, where '$$M$$' is the mass and '$$a$$' is the side of square plate. Moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

Two lenses of power $$-15 \mathrm{D}$$ and $$+5 \mathrm{D}$$ are in contact with each other. The focal length of the combination is

A particle performing uniform circular motion of radius $$\frac{\pi}{2} \mathrm{~m}$$ makes '$$\mathrm{x}$$' revolutions in time '$$t$$'. Its tangential velocity is