MHT CET 2024 16th May Evening Shift
Paper was held on Thu, May 16, 2024 9:30 AM
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Chemistry

What is the number of moles of donor atoms present in one mole oxalate ion?
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Which from following substances acts as a base when reacted with water?
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Which from following polymers is classified as fibres?
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What type of solution is the iodine in air?
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Identify ' $Y$ ' in the following reaction. $$\mathrm{CH}_3 \mathrm{Br} \xrightarrow{\mathrm{KcN}} \mathrm{X} \xrightarr
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What is de Broglie's wavelength for a particle having mass $6.64 \times 10^{-27} \mathrm{~kg}$ moving with velocity of $
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Identify the product formed in the following reaction.
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What is the IUPAC name of the following compound?
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Calculate the pH of 0.02 M monobasic acid having $2 \%$ dissociation.
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Which of the following molecule can form hydrogen bonding with itself?
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Calculate the cell constant of conductivity cell containing 0.1 M KCl solution having resistance $60 \Omega$ and conduct
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Calculate standard internal energy change for $\mathrm{OF}_{2(\mathrm{~g})}+\mathrm{H}_2 \mathrm{O}_{(\mathrm{g})} \long
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Which of the following compounds is obtained by using Finkelstein reaction?
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In a first order reaction $60 \%$ of the reactant converts into product in 45 minute. Calculate rate constant of the rea
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Identify a compound having properties of tear gas.
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Which of the following series of emission spectral lines for hydrogen observed in visible region?
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What is the number of faraday required to produce 0.18 g aluminium at cathode during electrolysis of molten $\mathrm{AlC
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Which pair of metal ions from following have same number of unpaired electrons?
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Which from following compounds contains oxygen as a heteroatom?
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What type of glycosidic linkages are developed when excess glucose is to be stored for future use in animals?
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Calculate the relative lowering of vapour pressure if vapour pressure of pure solvent and vapour pressure of solution at
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Which from following ligands is neutral?
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Identify chiral molecule from following:
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Which from following polymers is a urea-formaldehyde resin?
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Which reagent is used in the conversion of phenol to picric acid?
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Identify the reactivity order for halogens towards alkanes.
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What is the total number of tetrahedral voids in 0.6 mole of compound that forms hcp structure?
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Identify name of reaction when aldehyde or ketone react with $\mathrm{Zn}-\mathrm{Hg} /$ conc. HCl to give alkane.
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What products are obtained when beryllium oxide is treated separately with aq. HCl and aq. NaOH solutions respectively?
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Calculate internal energy change of a system if work done by the system is 8 J and heat supplied to it is 40 J .
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Identify basic oxide from following.
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Calculate the solubility product of sparingly soluble salt BA at $27^{\circ} \mathrm{C}$ if its solubility is $1.8 \time
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Which of the following conversions is Hofmann Elimination reaction?
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 For the reaction, $$\mathrm{CH}_3 \mathrm{Br}_{(\mathrm{aq})}+\mathrm{OH}_{(\mathrm{aq})}^{-} \longrightarrow \mathrm{C
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Identify the product X in the following reaction. Ethanoyl chloride $\xrightarrow{\mathrm{H}_2 \mathrm{O}} \mathrm{X}$
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Which of the following is allylic alcohol?
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Identify positively charged sol from the following.
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Calculate the number of unit cells in 0.4 g metal if the product of density and volume of unit cell is $1.2 \times 10^{-
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What is the major product obtained when tert-butyl bromide is heated with silver fluoride?
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Which from following equations represents a correct relationship between standard cell potential and equilibrium constan
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What is the total number of particles present in base centred unit cell?
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Which of the following equation relates temperature of a reaction with $\Delta \mathrm{H}^{\circ}$ and $\Delta \mathrm{S
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Calculate the molality of solution if its depression in freezing point is 0.18 K . $\left[\mathrm{K}_{\mathrm{f}}=1.6 \m
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For the reaction, $$\mathrm{H}_{2(g)}+\mathrm{Br}_{2(8)} \longrightarrow 2 \mathrm{HBr}_{(\mathrm{g})}, \mathrm{r}=\math
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Identify an actinoid element from following.
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What is the oxidation number of Mn in $\mathrm{MnO}_4^{-}$?
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What is the number of electrons present in antibonding orbitals of $\mathrm{N}_2$ molecule according to molecular orbita
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Which from following is a largest size nanomaterial?
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Which from following nitrogen bases of nucleic acids is derived from purine?
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Calculate mass in kg of 2.5 mole ammonia.
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Mathematics

If $\mathrm{g}(x)=[\mathrm{f}(2 \mathrm{f}(x)+2)]^2$ and $\mathrm{f}(0)=-1, \mathrm{f}^{\prime}(0)=1$ then $g^{\prime}(0
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If $\tan ^{-1}\left(\frac{1}{4}\right)+\tan ^{-1}\left(\frac{2}{9}\right)=\frac{1}{2} \cos ^{-1} x$, then $x$ is
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The shaded area in the given figure is a solution set for some system of inequalities. The maximum value of the function
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If $z_1=5-2 i$ and $z_2=3+i$, where $i=\sqrt{-1}$, then $\arg \left(\frac{z_1+z_2}{z_1-z_2}\right)$ is
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The co-ordinates of the foot of the perpendicular from the point $(0,2,3)$ on the line $\frac{x+3}{5}=\frac{y+1}{2}=\fra
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The slope of tangent at $(x, y)$ to a curve passing through $\left(1, \frac{\pi}{4}\right)$ is $\frac{y}{x}-\cos ^2 \fra
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If $\cos ^{-1}\left(\frac{12}{13}\right)+\sin ^{-1}\left(\frac{3}{5}\right)=\sin ^{-1} \mathrm{P}$, then the value of $P
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The rate of change of the volume of a sphere with respect to its surface area, when its radius is 2 cm , is _________ $\
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In a triangle $\mathrm{ABC}, l(\mathrm{AB})=\sqrt{23}$ units, $l(\mathrm{BC})=3$ units, $l(\mathrm{CA})=4$ units, then $
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Truth values of $\mathrm{p} \rightarrow \mathrm{r}$ is F and $\mathrm{p} \leftrightarrow \mathrm{q}$ is F . Then the tru
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Water is being poured at the rate of $36 \mathrm{~m}^3 / \mathrm{min}$ into a cylindrical vessel, whose circular base is
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A line having direction ratios $1,-4,2$ intersects the lines $\frac{x-7}{3}=\frac{y-1}{-1}=\frac{z+2}{1}$ and $\frac{x}{
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$\int \frac{x^2-4}{x^4+9 x^2+16} \mathrm{dx}=\tan ^{-1}(\mathrm{f}(x))+\mathrm{c}$ (where c is a constant of integration
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If $\overline{\mathrm{a}}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ and $\overline{\mathrm{b}}=2 \hat{i}+3
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Let $A=\left[\begin{array}{cc}1 & 2 \\ -1 & 4\end{array}\right]$ and $A^{-1}=\alpha \mathrm{I}+\beta \mathrm{A}, \alpha,
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$$\lim _\limits{y \rightarrow 0} \frac{\sqrt{1+\sqrt{1+y^4}}-\sqrt{2}}{y^4}=$$
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If $\overline{\mathrm{a}}$ is perpendicular to $\bar{b}$ and $\bar{c},|\bar{a}|=2$, $|\overline{\mathrm{b}}|=3,|\overlin
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The mean and variance of seven observations are 8 and 16 respectively. If five of the observations are $2,4,10,12,14$, t
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If $y=\tan ^{-1}\left(\frac{2+3 x}{3-2 x}\right)+\tan ^{-1}\left(\frac{4 x}{1+5 x^2}\right)$, then $\frac{d y}{d x}=$
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If $\mathrm{f}(x)=\frac{a \sin x+b \cos x}{c \sin x+d \cos x}$ is decreasing for all $x$ then
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If a discrete random variable X is defined as follows $\mathrm{P}[\mathrm{X}=x]=\left\{\begin{array}{cl}\frac{\mathrm{k}
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If $\bar{a}=2 \hat{i}-\hat{j}+\hat{k}, \bar{b}=\hat{i}+\hat{j}-2 \hat{k}$ and $\bar{c}=4 \hat{i}-2 \hat{j}+\hat{k}$, the
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Numbers are selected at random, one at a time from two digit numbers $10,11,12 \ldots ., 99$ with replacement. An event
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The function $y(x)$ represented by $x=\sin t$, $y=a e^{t \sqrt{2}}+b e^{t \sqrt{2}}, t \in\left(\frac{-\pi}{2}, \frac{\p
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The value of $\cos 20^{\circ}+2 \sin ^2 55^{\circ}-\sqrt{2} \sin 65^{\circ}$ is
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If $[x]$ denotes the greatest integer function, then $$\int_\limits0^5 x^2[x] d x=$$
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If the function $f$ defined on $\left(\frac{\pi}{6}, \frac{\pi}{3}\right)$ by $$f(x)=\left\{\begin{array}{cc} \frac{\sqr
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$$\int \cos ^{\frac{-3}{7}} x \cdot \sin ^{\frac{-11}{7}} x d x=$$
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If $\bar{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k}, \quad \bar{b}=b_1 \hat{i}+b_2 \hat{j}+b_3 \hat{k}$, $\bar{c}=c_1 \hat{i
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The domain of the function $\mathrm{f}(x)=\frac{\sin ^{-1}(x-3)}{\sqrt{9-x^2}}$ is
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If $\bar{a}=2 \hat{i}+2 \hat{j}+3 \hat{k}, \quad \bar{b}=-\hat{i}+2 \hat{j}+\hat{k}$ and $\bar{c}=3 \hat{i}+\hat{j}$ are
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The area (in sq. units) bounded between the parabolas $x^2=\frac{y}{4}$ and $x^2=9 y$ and the line $y=2$ is
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A plane makes positive intercepts of unit length on each of $X$ and $Y$ axis. If it passes through the point $(-1,1,2)$
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The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is
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One end of the diameter of the circle $x^2+y^2-6 x-5 y-1=0$ is $(-1,3)$, then the equation of the tangent at the other e
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If $\tan ^{-1}\left(\frac{x+1}{x-1}\right)+\tan ^{-1}\left(\frac{x-1}{x}\right)=\tan ^{-1}(-7)$, then $x$ is equal to
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The equation of the normal to the curve $y=x \log x$ parallel to $2 x-2 y+3=0$ is
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$$\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}{
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The equation of plane through the point $(2,-1,-3)$ and parallel to lines $\frac{x-1}{3}=\frac{y+2}{2}=\frac{z}{-4}$ and
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The co-ordinates of the foot of perpendicular, drawn from the point $(-2,3)$ on the line $3 x-y-1=0$ are
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The value of $\tan ^{-1}(-\sqrt{3})-\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)+\cos ^{-1}\left(\frac{-1}{2}\right)$ is
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The general solution of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}=y \tan x-y^2 \sec x$ is
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If $\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$ are three vectors such that $\overline{\mathrm{
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Two friends A and B apply for a job in the same company. The probabilities of A getting selected is $\frac{2}{5}$ and th
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If $P_1$ and $P_2$ are perpendicular distances (in units) from point $(2,-1)$ to the pair of lines $2 x^2-5 x y+2 y^2=0$
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$$\int \frac{x^3-7 x+6}{x^2+3 x} \mathrm{~d} x=$$
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The cumulative distribution function of a discrete random variable X is given by .tg {border-collapse:collapse;border-
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A five digit number divisible by 3 is to be formed using the digits $0,1,2,3,4,5$ without repetition, then the total num
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The statement $\sim(p \leftrightarrow \sim q)$ is
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If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha \log |x|+\beta x^2+x$, then
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Physics

A circular coil of resistance ' $R$ ', area ' $A$ ', number of turns ' N ' is rotated about its vertical diameter with a
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The linear speed of a particle at the equator of the earth due to its spin motion is ' V '. The linear speed of the part
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Three point masses, each of mass ' $m$ ' are placed at the corners of an equilateral triangle of side ' $L$ '. The momen
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In the second orbit of hydrogen atom, the energy of an electron is ' $E$ '. In the third orbit of helium atom, the energ
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The graph shows the variation of voltage ' V ' across the plates of two capacitors $A$ and $B$ versus increase in charge
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The bob of a pendulum of length ' $l$ ' is pulled aside from its equilibrium position through an angle ' $\theta$ ' and
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On the surface of the liquid in equilibrium, molecules of the liquid possess
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An optician makes spectacles having a combination of a convex lens of focal length 40 cm in contact with a concave lens
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A ray of light travelling through a rarer medium is incident at very small angle ' $i$ ' on a glass slab and after refra
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Kinetic energy of a proton is equal to energy $E$ of a photon. Let ' $\lambda_1$ ' be the de-Broglie wavelength of proto
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An inductance of 2 mH , a condenser of $20 \mu \mathrm{~F}$ and a resistance of $50 \Omega$ are connected in series to a
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Two sound waves having frequencies 250 Hz and 256 Hz superimpose to produce beat wave. The resultant beat wave has inten
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A body travelling with uniform acceleration crosses two points A and B with velocities $20 \mathrm{~m} / \mathrm{s}$ and
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During an experiment, an ideal gas is found to obey an additional law $\mathrm{VP}^2=$ constant. The gas is initially at
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To get the truth table shown from the following logic circuit, the logic gate G should be
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In an $L C R$ circuit, if ' $V$ ' is the effective value of the applied voltage, $V_R$ is the voltage across ' $R$ ', '
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Two objects of masses ' $m_1$ ' and ' $m_2$ ' are moving in the circles of radii ' $r_1$ ' and ' $r_2$ ' respectively. T
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A hollow cylinder has charge ' $q$ ' $C$ within it. If ' $\phi$ ' is the electric flux associated with the curved
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A water drop is divided into 8 equal droplets. The pressure difference between the inner and outer side of the big drop
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An arc of a circle of radius ' $R$ ' subtends an angle $\frac{\pi}{2}$ at the centre. It carries a current $I$. The magn
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The Boolean expression for the given combination of logic gates is
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A body performing uniform circular motion of radius ' $R$ ' has frequency ' $n$ '. Its centripetal acceleration per unit
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A solenoid having 400 turns per metre has a core of a material with relative permeability 400. When a current of 0.5 A i
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Three identical metal balls each of radius ' $r$ ' are placed such that an equilateral triangle is formed when centres o
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Two identical galvanometers are converted into an ammeter and into milliammeter. For the same current, the value of shun
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A boy weighs 72 N on the surface of earth. The gravitational force on a body due to earth at a height equal to half the
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In a single slit diffraction experiment, for a wavelength of light ' $\lambda$ ', half-angular width of the principle ma
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The first operation involved in a Carnot cycle is
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Temperature remaining constant, the pressure of gas is decreased by $20 \%$. The percentage change in volume
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A plane mirror is placed at the bottom of a tank containing a liquid of refractive index ' $\mu$ ', ' $p$ ' is a small o
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A light bulb connected in series with a capacitor and an a.c. source is glowing with a certain brightness. On reducing t
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A pipe 60 cm long and open at both the ends produces harmonics. Which harmonic mode of pipe resonates a 2.2 KHz source?
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A point source of light is used in a photoelectric effect. If the source is removed farther from the emitting metal, the
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The kinetic energy of a particle, executing simple harmonic motion is 16 J when it is in mean position. If amplitude of
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At certain temperature, $\operatorname{rod} \mathrm{A}$ and $\operatorname{rod} \mathrm{B}$ of different materials have
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A liquid drop having surface energy ' $E$ ' is spread into 512 droplets of same size. The final surface energy of the dr
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Two radioactive substances A and B have decay constants ' $5 \lambda$ ' and ' $\lambda$ ' respectively. At $\mathrm{t}=0
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A monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in changing the internal energy
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A source and listener are both moving towards each other with speed $\frac{\mathrm{V}}{10}$. (where V is speed of sound)
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The ratio of the specific heats $\frac{C_p}{C_v}=\gamma$, in terms of degrees of freedom ( n ) is
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In a double slit experiment, the distance between slits is increased 10 times, whereas their distance from screen is hal
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If a transformer of an audio amplifier has output impedance $8000 \Omega$ and the speaker has input impedance $8 \Omega$
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A particle performs linear S.H.M. At a particular instant, velocity of the particle is ' $u$ ' and acceleration is ' $\a
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Two uniform strings A and B made of steel are made to vibrate under the same tension. If first overtone of A is equal to
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 ' $n$ ' small drops of same size are charged to ' $V$ ' volt each. If they coalesce to form a single large drop, then i
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Air capacitor has capacitance ' $\mathrm{C}_1$ '. The space between two plates of capacitor is filled with two dielectri
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A coil is wound on a core of rectangular crosssection. If all the linear dimensions of the core are increased by a facto
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When a small amount of impurity atoms are added to semiconductor, then generally its resistivity
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 A current 'I' flows in anticlockwise direction in a circular arc of a wire having $\left(\frac{3}{4}\right)^{\text {th
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When a resistance of $200 \Omega$ is connected in series with a galvanometer of resistance ' $G$ ', its range is ' $V$ '
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