MHT CET 2023 10th May Evening Shift

Paper was held on
Wed, May 10, 2023 9:30 AM

## Chemistry

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

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Which of the following is tertiary allylic alcohol?

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

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

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Identify the elements undergoing reduction and oxidation respectively in the following redox reaction.
$$3 \mathrm{H}_3

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Which of the following is tricarboxylic acid?

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

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

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A gas absorbs $$200 \mathrm{~J}$$ heat and expands by $$500 \mathrm{~cm}^3$$ against a constant external pressure $$2 \t

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Identify a copolymer from following.

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

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Calculate the rate constant for the first order reaction, $$\mathrm{A} \rightarrow \mathrm{B}$$ if the rate of reaction

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

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

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What happens when solution of an electrolyte is diluted?

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

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

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

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Which among the following is vinylic halide?

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

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

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

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

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

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Identify the glycosidic linkage present in lactose.

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

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

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

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Which from following elements is most abundant on earth?

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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

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

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Which of the following is general representation of Grignard reagent?

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

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What is osmotic pressure of solution of $$1.7 \mathrm{~g} \mathrm{~CaCl}_2$$ in $$1.25 \mathrm{~dm}^3$$ water at $$300 \

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Which among the following pair of properties is intensive?

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

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An organic compound '$$\mathrm{A}$$' on reaction with $$\mathrm{PCl}_3$$ gives an alkyl chloride having formula $$\mathr

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Identify tetrasaccharide from following.

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What type of ligand does the ethylenediamine is?

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

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Which from following complexes is heteroleptic?

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Calculate $$E_{\text {cell }}^{\circ}$$ in which following reaction occurs. $$\mathrm{Mg}_{(\mathrm{s})}+2 \mathrm{Ag}_{

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

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

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Time required for $$90 \%$$ completion of a first order reaction is '$$x$$' minute. Calculate the time required to compl

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Identify '$$A$$' in the following reaction:
A $$\mathrm{\mathrel{\mathop{\kern0pt\longrightarrow}
\limits_{ether}^{LiAl{

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

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Identify the last step in wet chemical synthesis of nanomaterial.

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

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

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## Mathematics

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

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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:

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If $$\mathrm{p}$$ and $$\mathrm{q}$$ are true statements and $$\mathrm{r}$$ and $$\mathrm{s}$$ are false statements, the

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

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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 $

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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

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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

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Let $$f$$ be a differentiable function such that $$\mathrm{f}(1)=2$$ and $$\mathrm{f}^{\prime}(x)=\mathrm{f}(x)$$, for a

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The joint equation of a pair of lines passing through the origin and making an angle of $$\frac{\pi}{4}$$ with the line

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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

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

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$$\int \frac{5 \tan x}{\tan x-2} \mathrm{~d} x=x+\mathrm{a} \log |\sin x-2 \cos x|+\mathrm{c},$$
(where $$c$$ is a const

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Let $$\mathrm{S}=\left\{\mathrm{t} \in \mathrm{R} / \mathrm{f}(x)=|x-\pi|\left(\mathrm{e}^{|x|}-1\right) \sin |x|\right.

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

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

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

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Let $$\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$$ and $$\mathrm{g}: \mathrm{R} \rightarrow \mathrm{R}$$ be continuou

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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

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The value of $$\frac{{ }^{10} \mathrm{C}_{\mathrm{r}}}{{ }^{11} \mathrm{C}_{\mathrm{r}}}$$, when both the numerator and

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

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

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

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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 perp

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

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

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

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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]

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Two lines $$\frac{x-3}{1}=\frac{y+1}{3}=\frac{z-6}{-1}$$ and $$\frac{x+5}{7}=\frac{y-2}{-6}=\frac{z-3}{4} \quad$$ inters

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

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The shaded area in the figure given below is a solution set of a system of inequations. The minimum value of objective f

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If $$\overline{\mathrm{a}}=\mathrm{m} \overline{\mathrm{b}}+\mathrm{nc}$$, where $$\overline{\mathrm{a}}=4 \hat{\mathrm{

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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

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

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

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

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

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If $$B=\left[\begin{array}{ccc}3 & \alpha & -1 \\ 1 & 3 & 1 \\ -1 & 1 & 3\end{array}\right]$$ is the adjoint of a $$3 \t

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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

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

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

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If the volume of tetrahedron, whose vertices are with position vectors $$\hat{i}-6 \hat{j}+10 \hat{k},-\hat{i}-3 \hat{j}

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

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If $$y=\tan ^{-1}\left(\frac{\log \left(\frac{\mathrm{e}}{x^2}\right)}{\log \left(e x^2\right)}\right)+\tan ^{-1}\left(\

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If the surface area of a spherical balloon of radius $$6 \mathrm{~cm}$$ is increasing at the rate $$2 \mathrm{~cm}^2 / \

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

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In a certain culture of bacteria, the rate of increase is proportional to the number of bacteria present at that instant

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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

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

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

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

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## Physics

Two trains, each $$30 \mathrm{~m}$$ long are travelling in opposite directions with velocities $$5 \mathrm{~m} / \mathrm

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The fundamental frequency of air column in pipe 'A' closed at one end is in unison with second overtone of an air column

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In Young's double slit experiment, the two slits are 'd' distance apart. Interference pattern is observed on a screen at

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A black body radiates maximum energy at wavelength '$$\lambda$$' and its emissive power is 'E' Now due to change in temp

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In meter bridge experiment, null point was obtained at a distance '$$l$$' from left end. The values of resistances in th

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The magnetic field at the centre of a circular coil of radius '$$R$$', carrying current $$2 A$$ is '$$B_1$$'. The magnet

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

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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 '$

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With an alternating voltage source of frequency '$$f$$', inductor '$$L$$', capacitor '$$C$$' and resistance '$$R$$' are

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A pure $$\mathrm{Si}$$ crystal has $$4 \times 10^{28}$$ atoms per $$\mathrm{m}^3$$. It is doped by 1 ppm concentration o

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A mass '$$\mathrm{M}$$' moving with velocity '$$\mathrm{V}$$' along $$\mathrm{X}$$-axis collides and sticks to another m

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

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

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'$$n$$' number of liquid drops each of radius '$$r$$' coalesce to form a single drop of radius '$$R$$'. The energy relea

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What is the moment of inertia of the electron moving in second Bohr orbit of hydrogen atom? [ $$\mathrm{h}=$$ Planck's c

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At critical temperature, the surface tension of liquid is

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Two wires $$2 \mathrm{~mm}$$ apart supply current to a $$100 \mathrm{~V}, 1 \mathrm{~kW}$$ heater. The force per metre b

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

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

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The capacitive reactance of a capacitor '$$C$$' is $$\mathrm{X} \Omega$$. Both, the frequency of a.c. supply and capacit

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

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A metal rod $$2 \mathrm{~m}$$ long increases in length by $$1.6 \mathrm{~mm}$$, when heated from $$0^{\circ} \mathrm{C}$

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Assume that an electric field $$\mathrm{E}=30 \mathrm{x}^2 \hat{\mathrm{i}}$$ exists in space. If '$$\mathrm{V}_0$$' is

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Two dielectric slabs having dielectric constant '$$\mathrm{K}_1$$' and '$$\mathrm{K}_2$$' of thickness $$\frac{\mathrm{d

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

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

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A hollow metal pipe is held vertically and bar magnet is dropped through it with its length along the axis of the pipe.

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A metal sphere of mass '$$m$$' and density '$$\sigma_1$$' falls with terminal velocity through a container containing li

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Two uniform wires of same material are vibrating under the same tension. If the first overtone of first wire is equal to

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A body is projected vertically from earth's surface with velocity equal to half the escape velocity. The maximum height

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A ball of mass '$$\mathrm{m}$$' is dropped from a height '$$\mathrm{s}$$' on a horizontal platform fixed at the top of a

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In the circuit given below, the current through inductor is $$0.9 \mathrm{~A}$$ and through the capacitor is $$0.6 \math

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A body is executing a linear S.H.M. Its potential energies at the displacement '$$\mathrm{x}$$' and '$$\mathrm{y}$$' are

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We have a jar filled with gas characterized by parameters $$\mathrm{P}, \mathrm{V}, \mathrm{T}$$ and another jar B fille

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Two spheres each of mass '$$M$$' and radius $$\frac{R}{2}$$ are connected at the ends of massless rod of length '$$2 R$$

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If the potential difference used to accelerate electrons is doubled, by what factor does the de-Broglie wavelength assoc

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A simple harmonic progressive wave is represented by $$y=A \sin (100 \pi t+3 x)$$. The distance between two points on th

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An insulated container contains a monoatomic gas of molar mass '$$\mathrm{m}$$'. The container is moving with velocity '

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

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

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For the diagram shown, the resistances between points A and B when ideal diode D is forward biased is '$$R_1$$' and that

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The maximum kinetic energy of the photoelectrons varies

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Light waves from two coherent sources arrive at two points on a screen with path difference of zero and $$\frac{\lambda^

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A uniform rope of length '$$L$$' and mass '$$m_1$$' hangs vertically from a rigid support. A block of mass '$$m_2$$' is

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

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Two concentric circular coils having radii $$r_1$$ and $$r_2\left(r_2

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A system consists of three particles each of mass '$$m_1$$' placed at the corners of an equilateral triangle of side '$$

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The moment of inertia of a uniform square plate about an axis perpendicular to its plane and passing through the centre

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

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A particle performing uniform circular motion of radius $$\frac{\pi}{2} \mathrm{~m}$$ makes '$$\mathrm{x}$$' revolutions

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