MHT CET 2023 13th May Morning Shift
Paper was held on Sat, May 13, 2023 3:30 AM
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Chemistry

Identify cationic sphere complex from following.
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Identify substrate '$$\mathrm{A}$$' in the following conversion. $$\mathrm{A}+\underset{\text { (excess) }}{\mathrm{CH}_
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Identify FALSE statement regarding adsorption from following.
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Find the rate of formation of $$\mathrm{NO}_{2(\mathrm{~g})}$$ in the following reaction. $$\begin{aligned} & 2 \mathrm{
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Which from following properties is exhibited by group 2 elements?
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Calculate the rate constant of the first order reaction if $$20 \%$$ of the reactant decomposes in 15 minutes.
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Which from following methods of structural formula representation uses conventionally a point for front carbon and a cir
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Identify substrate '$$\mathrm{A}$$' in the following sequence of reactions. A $$\mathrm{\mathrel{\mathop{\kern0pt\longri
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Which of the following is tertiary benzylic alcohol?
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Which among the following is a feature of $$\mathrm{S}_{\mathrm{N}} 1$$ mechanism?
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The volume of a gas is $$4 \mathrm{~dm}^3$$ at $$0^{\circ} \mathrm{C}$$. Calculate new volume at constant pressure when
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Which following reagent is used in Etard reaction?
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Which of the following processes exhibits increase in internal energy?
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Calculate $$\mathrm{E}_{\text {cell }}^0$$ if the equilibrium constant for following reaction is $$1.2 \times 10^6$$. $$
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Which from following alloys is used to make statues?
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Which of the following molecules does NOT obey octet rule?
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Calculate van't Hoff factor of $$\mathrm{K}_2 \mathrm{SO}_4$$ if $$0.1 \mathrm{~m}$$ aqueous solution of $$\mathrm{K}_2
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Find the radius of fourth orbit of hydrogen atom if its radius of first orbit is $$\mathrm{R}$$ pm.
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Which noble gas element from following exhibits highest number of different oxidation states?
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Which among the following is a pair of monocarboxylic acids?
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Identify the overall oxidation reaction that occurs in lead storage cell during discharge.
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What is the change in oxidation number of selenium in the following redox reaction? $$\mathrm{SeO}_{3(\text { (a) })}^{2
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A buffer solution is prepared by mixing equimolar acetic acid and sodium acetate. If '$$\mathrm{K}_d$$' of acetic acid i
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What is the number of moles of nascent hydrogen required to prepare 1 mole of methane from iodomethane?
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Which from following metal has hcp crystal structure?
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One mole of an ideal gas performs $$900 \mathrm{~J}$$ of work on surrounding. If internal energy increases by $$625 \mat
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Which of the following temperature values in Fahrenheit $$\left({ }^{\circ} \mathrm{F}\right)$$ is equal to $$50^{\circ}
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Which from following formulae is of trioxalatocobaltate(III) ion?
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Which of the following pair of nuclides is an example of isotones?
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Identify FALSE statement from following.
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What is IUPAC name of crotonyl alcohol?
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A solution of $$5.6 \mathrm{~g}$$ non-volatile solute in $$50 \mathrm{~g}$$ solvent has elevation in boiling point $$1.7
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What is the common name of benzene-1,3-diol?
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Identify the CORRECT decreasing order of basic strength of compounds from following.
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Calculate the work done in the following reaction at $$300 \mathrm{~K}$$ and at constant pressure. $$\left(\mathrm{R}=8.
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The solubility product of $$\mathrm{Mg}(\mathrm{OH})_2$$ is $$1.8 \times 10^{-11}$$ at $$298 \mathrm{~K}$$. What is its
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If $$\mathrm{K}_{\mathrm{sp}}$$ is solubility product of $$\mathrm{Al}(\mathrm{OH})_3$$, its solubility is expressed by
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Which from following is the slope of the graph of $$[\mathrm{A}]_{\mathrm{t}}$$ versus time for zero order reaction?
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Which from following statements is NOT true about natural rubber?
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What is the molal elevation constant if one gram mole of a nonvolatile solute is dissolved in $$1 \mathrm{~kg}$$ of ethy
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Which from following elements exhibits ferromagnetic properties?
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Which of the following is NOT a globular protein?
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Calculate the time required in second to deposit $$6.35 \mathrm{~g}$$ copper from its salt solution by passing 5 ampere
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Which from following nanomaterial has one dimension less than $$100 \mathrm{~nm}$$ ?
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Which among the following compounds has highest boiling point?
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Calculate the radius of metal atom in bcc unit cell having edge length $$287 \mathrm{~pm}$$.
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Identify A in the following reaction. $$\mathrm{{C_6}{H_{12}}{O_6}\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{dil
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Which of the following is formed when propene is heated with chlorine at high temperature?
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Identify the monomer used to prepare Teflon.
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Calculate the number of atoms present in unit cell if an element having molar mass $$23 \mathrm{~g} \mathrm{~mol}^{-1}$$
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Mathematics

If $$\mathrm{f}(x)=x^3+\mathrm{b} x^2+\mathrm{c} x+\mathrm{d}$$ and $$0
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Differentiation of $$\tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$$ w.r.t. $$\cos ^{-1}\left(\sqrt{\frac{1+\sqrt{1+x^
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The function $$\mathrm{f}(\mathrm{t})=\frac{1}{\mathrm{t}^2+\mathrm{t}-2}$$ where $$\mathrm{t}=\frac{1}{x-1}$$ is discon
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A random variable $$X$$ has the following probability distribution .tg {border-collapse:collapse;border-spacing:0;} .t
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If $$\mathrm{I}=\int \frac{2 x-7}{\sqrt{3 x-2}} \mathrm{~d} x$$, then $$\mathrm{I}$$ is given by
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Let $$\mathrm{X}$$ be random variable having Binomial distribution $$B(7, p)$$. If $$P[X=3]=5 P[X=4]$$, then variance of
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The scalar product of vectors $$\overline{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$$ and a unit
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$$\int \frac{\log \left(x^2+a^2\right)}{x^2} d x=$$
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The parametric equations of the curve $$x^2+y^2+a x+b y=0$$ are
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The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one, then the
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$$x, y, z$$ are in G.P. and $$\tan ^{-1} x, \tan ^{-1} y, \tan ^{-1} z$$ are in A.P., then
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In $$\triangle A B C$$ with usual notation, $$\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$$ and $$a=\frac{1}{\sqr
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If $$\hat{\mathrm{a}}$$ and $$\hat{\mathrm{b}}$$ are unit vectors and $$\overline{\mathrm{c}}=\hat{\mathrm{b}}-(\hat{\ma
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Angles of a triangle are in the ratio $$4: 1: 1$$. Then the ratio of its greatest side to its perimeter is
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If a continuous random variable $$\mathrm{X}$$ has probability density function $$\mathrm{f}(x)$$ given by $$f(x)=\left\
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The value of $$\begin{aligned} \cos \left(18^{\circ}-\mathrm{A}\right) \cdot \cos ( & \left.18^{\circ}+\mathrm{A}\right)
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If $$\int x^5 e^{-4 x^3} \mathrm{~d} x=\frac{1}{48} \mathrm{e}^{-4 x^3} \mathrm{f}(x)+\mathrm{c}$$, where $$\mathrm{c}$$
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The solution of the differential equation $$\mathrm{e}^{-x}(y+1) \mathrm{d} y+\left(\cos ^2 x-\sin 2 x\right) y \mathrm{
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If $$A=\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$$ and $$A_{i j}$$ is a cofactor of
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Rate of increase of bacteria in a culture is proportional to the number of bacteria present at that instant and it is fo
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The slope of the normal to the curve $$x=\sqrt{t}$$ and $$y=t-\frac{1}{\sqrt{t}}$$ at $$t=4$$ is
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If $$3 \mathrm{f}(x)-\mathrm{f}\left(\frac{1}{x}\right)=8 \log _2 x^3, x>0$$, then $$\mathrm{f}(2), \mathrm{f}(4)$$, $$f
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If the angle between the lines given by $$x^2-3 x y+\lambda y^2+3 x-5 y+2=0 ; \lambda \geq 0$$ is $$\tan ^{-1}\left(\fra
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A line drawn from the point $$\mathrm{A}(1,3,2)$$ parallel to the line $$\frac{x}{2}=\frac{y}{4}=\frac{z}{1}$$, intersec
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The value of $$\frac{\mathrm{i}^{248}+\mathrm{i}^{246}+\mathrm{i}^{244}+\mathrm{i}^{242}+\mathrm{i}^{240}}{\mathrm{i}^{2
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If $$\mathrm{f}(x)=\int \frac{x^2 \mathrm{~d} x}{\left(1+x^2\right)\left(1+\sqrt{1+x^2}\right)}$$ and $$\mathrm{f}(0)=0$
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A line $$\mathrm{L}_1$$ passes through the point, whose p. v. (position vector) $$3 \hat{i}$$, is parallel to the vector
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If $$y=\tan ^{-1}\left(\frac{4 \sin 2 x}{\cos 2 x-6 \sin ^2 x}\right)$$, then $$\left(\frac{\mathrm{d} y}{\mathrm{~d} x}
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The expression $$(p \wedge \sim q) \vee q \vee(\sim p \wedge q)$$ is equivalent to
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The raw data $$x_1, x_2, \ldots \ldots, x_{\mathrm{n}}$$ is an A.P. with common difference $$\mathrm{d}$$ and first term
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The particular solution of differential equation $$\mathrm{e}^{\frac{d y}{d x}}=(x+1), y(0)=3$$ is
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A card is drawn at random from a well shuffled pack of 52 cards. The probability that it is black card or face card is
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If $$\bar{a}=2 \hat{i}+3 \hat{j}-4 \hat{k}$$ and $$\bar{b}=\hat{i}-\hat{j}-\hat{k}$$, then the projection of $$\bar{b}$$
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If $$\mathrm{f}(x)=\left\{\begin{array}{ll}\mathrm{e}^{\cos x} \sin x & , \text { for }|x| \leq 2 \\ 2, & \text { otherw
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The equation of the line passing through the point $$(-1,3,-2)$$ and perpendicular to each of the lines $$\frac{x}{1}=\f
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Let $$\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$$ be a function such that $$\mathrm{f}(x)=x^3+x^2 \mathrm{f}^{\prime
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If $$A(1,4,2)$$ and $$C(5,-7,1)$$ are two vertices of triangle $$A B C$$ and $$G\left(\frac{4}{3}, 0, \frac{-2}{3}\right
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The base of an equilateral triangle is represented by the equation $$2 x-y-1=0$$ and its vertex is $$(1,2)$$, then the l
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Five persons $$\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$$ and $$\mathrm{E}$$ are seated in a circular arrangement.
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The distance of the point $$(-1,-5,-10)$$ from the point of intersection of the line $$\frac{x-2}{3}=\frac{y+1}{4}=\frac
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Negation of inverse of the following statement pattern $$(p \wedge q) \rightarrow(p \vee \sim q)$$ is
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If $$\mathrm{f}(x)=3 x^{10}-7 x^8+5 x^6-21 x^3+3 x^2-7$$, then $$\lim _\limits{\alpha \rightarrow 0} \frac{f(1-\alpha)-f
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The area (in sq. units) of the region bounded by curves $$y=3 x+1, y=4 x+1$$ and $$x=3$$ is
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Values of $$c$$ as per Rolle's theorem for $$f(x)=\sin x+\cos x+6$$ on $$[0,2 \pi]$$ are
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A vector $$\bar{a}$$ has components 1 and $$2 p$$ with respect to a rectangular Cartesian system. This system is rotated
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A line is drawn through the point $$(1,2)$$ to meet the co-ordinate axes at $$\mathrm{P}$$ and $$\mathrm{Q}$$ such that
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If feasible region is as shown in the figure, then related inequalities are
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The general solution of the equation $$3 \sec ^2 \theta=2 \operatorname{cosec} \theta$$ is
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A right circular cone has height $$9 \mathrm{~cm}$$ and radius of base $$5 \mathrm{~cm}$$. It is inverted and water is p
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If $$\theta$$ is angle between the vectors $$\bar{a}$$ and $$\bar{b}$$ where $$|\bar{a}|=4,|\bar{b}|=3$$ and $$\theta \i
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Physics

Select the 'WRONG' statement out of the following.
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Two cells $$E_1$$ and $$E_2$$ having equal EMF '$$E$$' and internal resistances $$r_1$$ and $$r_2\left(r_1>r_2\right)$$
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Which one of the following represents correctly the variation of volume (V) of an ideal gas with temperature $$(\mathrm{
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Using variation of force and time given below, final velocity of a particle of mass $$2 \mathrm{~kg}$$ moving with initi
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$$\mathrm{dQ}$$ is the heat energy supplied to an ideal gas under isochoric conditions. If $$\mathrm{dU}$$ and $$\mathrm
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A black body at temperature $$127^{\circ} \mathrm{C}$$ radiates heat at the rate of $$5 \mathrm{~cal} / \mathrm{cm}^2 \m
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The following graph represents
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A rigid body rotates with an angular momentum L. If its rotational kinetic energy is made four times, its angular moment
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A radioactive sample has half-life of 5 years. The percentage of fraction decayed in 10 years will be
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Three coils of inductance $$\mathrm{L}_1=2 \mathrm{H}, \mathrm{L}_2=3 \mathrm{H}$$ and $$\mathrm{L}_3=6 \mathrm{H}$$ are
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A Carnot engine has the same efficiency between (i) $$100 \mathrm{~K}$$ and $$600 \mathrm{~K}$$ and (ii) $$\mathrm{T} \m
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For which of the following substances, the magnetic susceptibility is independent of temperature?
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When a light of wavelength $$300 \mathrm{~nm}$$ fall on a photoelectric emitter, photo electrons are emitted. For anothe
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In a given meter bridge, the current flowing through $$40 \Omega$$ resistor is
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A body of mass $$0.04 \mathrm{~kg}$$ executes simple harmonic motion (SHM) about $$\mathrm{x}=0$$ under the influence of
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A large number of water droplets each of radius '$$t$$' combine to form a large drop of Radius '$$R$$'. If the surface t
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In resonance tube, first and second resonance are obtained at depths $$22.7 \mathrm{~cm}$$ and $$70.2 \mathrm{~cm}$$ res
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Twenty seven droplets of water each of radius $$0.1 \mathrm{~mm}$$ merge to form a single drop then the energy released
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If two inputs of a NAND gate are shorted, the resulting gate is
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Venturimeter is used to
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Which of the following statements is 'WRONG' for the conductors?
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A circular coil of radius '$$r$$' and number of turns ' $n$ ' carries a current '$$I$$'. The magnetic fields at a small
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A spherical surface of radius of curvature '$$R$$' separates air from glass of refractive index 1.5. The centre of curva
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The rotational kinetic energy and translational kinetic energy of a rolling body are same, the body is
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Two concentric circular coils A and B have radii $$20 \mathrm{~cm}$$ and $$10 \mathrm{~cm}$$ respectively lie in the sam
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A charged spherical conductor of radius '$$R$$' is connected momentarily to another uncharged spherical conductor of rad
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The magnet is moved towards the coil with speed '$$\mathrm{V}$$'. The induced e.m.f. in the coil is '$$\mathrm{e}$$'. Th
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A uniform wire $$20 \mathrm{~m}$$ long and weighing $$50 \mathrm{~N}$$ hangs vertically. The speed of the wave at mid po
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A large number of bullets are fired in all directions with same speed '$$U$$'. The maximum area on the ground on which t
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A transformer has 20 turns in the primary and 100 turns in the secondary coil. An ac voltage of $$\mathrm{V}_{\text {in
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On increasing the reverse bias to a large value in a P-N junction diode, current
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For an ideal gas the density of the gas is $$\rho_0$$ when temperature and pressure of the gas are $$T_0$$ and $$P_0$$ r
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The temperature gradient in a rod of length $$75 \mathrm{~cm}$$ is $$40^{\circ} \mathrm{C} / \mathrm{m}$$. If the temper
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In an oscillating LC circuit, the maximum charge on the capacitor is '$$Q$$'. When the energy is stored equally between
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A body of mass '$$\mathrm{m}$$' is raised through a height above the earth's surface so that the increase in potential e
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With increase in frequency of a.c. supply, the impedance of an L-C-R series circuit
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A passenger is sitting in a train which is moving fast. The engine of the train blows a whistle of frequency '$$n$$'. If
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If the magnitude of intensity of electric field at a distance '$$r_1$$' on an axial line and at a distance '$$r_2$$' on
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In an a.c. circuit the instantaneous current and emf are represented as $$\mathrm{I}=\mathrm{I}_0, \sin [\omega \mathrm{
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In a biprism experiment, monochromatic light of wavelength '$$\lambda$$' is used. The distance between two coherent sour
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Three charges each of value $$+q$$ are placed at the corners of an isosceles triangle $$\mathrm{ABC}$$ of sides $$\mathr
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Light of frequency 1.5 times the threshold frequency is incident on photosensitive material. If the frequency is halved
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A solid cylinder of mass $$3 \mathrm{~kg}$$ is rolling on a horizontal surface with velocity $$4 \mathrm{~m} / \mathrm{s
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Which one of the following statements is Wrong?
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The fundamental frequency of a sonometer wir carrying a block of mass '$$M$$' and density '$$\rho$$' is '$$n$$' Hz. When
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A simple pendulum has a time period '$$T$$' in air. Its time period when it is completely immersed in a liquid of densit
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Array of light is incident at an angle of incidence '$$i$$' on one surface of a prism of small angle $$\mathrm{A}$$ and
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An isotope of the original nucleus can be formed in a radioactive decay, with the emission of following particles.
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If two identical spherical bodies of same material and dimensions are kept in contact, the gravitational force between t
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$$\mathrm{A}$$ and $$\mathrm{B}$$ are two interfering sources where $$\mathrm{A}$$ is ahead in phase by $$54^{\circ}$$ r
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