MHT CET 2023 11th May Morning Shift
Paper was held on Thu, May 11, 2023 3:30 AM
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Chemistry

Name the accelerator used to introduce network of crosslink in elastomer.
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Which of the following is a property of alkali metals?
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The IUPAC name of following compound is:
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If $$\mathrm{K}_{\mathrm{b}}$$ denote molal elevation constant of water, then boiling point of an aqueous solution conta
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Which metal halide from following has lowest ionic character ( $$\mathrm{M}=$$ metal atom)?
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Which among the following reagents is called as Hinsberg's reagent?
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Which among the following amines has highest value of $$\mathrm{pK}_{\mathrm{b}}$$ ?
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What is vapour pressure of a solution containing $$1 \mathrm{~mol}$$ of a nonvolatile solute in $$36 \mathrm{~g}$$ of wa
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Identify the product obtained when phenol is reacted with dilute nitric acid at low temperature.
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For an elementary reaction $$2 \mathrm{~A}+\mathrm{B} \longrightarrow 3 \mathrm{C}$$ rate of appearance of $$\mathrm{C}$
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Which among the following alkenes is most stable?
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Identify a CORRECT formula for spin only magnetic moment.
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Which of the following salts turns red litmus blue in its aqueous solution?
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What is the value of increase in internal energy when system does $$8 \mathrm{~J}$$ of work on surrounding by supplying
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Benzonitrile on reduction with stannous chloride in presence of hydrochloric acid followed by acid hydrolysis forms:
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Which among the following is TRUE for isobaric process?
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Which among the following statements is TRUE about gammexane?
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Which of the following is primary allylic alcohol?
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Which of following is NOT correct about fructose?
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Which among following salts shows decrease in solubility with increase in temperature?
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Find the number of faradays of electricity required to produce $$45 \mathrm{~g}$$ of $$\mathrm{Al}$$ from molten $$\math
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Identify the reagent that confirms the presence of five $$-\mathrm{OH}$$ groups in glucose.
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What is the concentration of $$\mathrm{OH}^{-}$$ ion in a solution containing $$0.05 \mathrm{~M} \mathrm{~H}^{+}$$ ions?
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Which formula is used to calculate edge length in bcc structure?
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Identify the products of following reaction:
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What is the volume in $$\mathrm{dm}^3$$ occupied by $$3 \mathrm{~mol}$$ of ammonia gas at STP?
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Slope of the graph between $$\log \frac{[\mathrm{A}]_0}{[\mathrm{~A}]_{\mathrm{t}}}$$ (y axis) and time ( $$x$$ axis) fo
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What is total number of donor atoms in $$\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)\left(\mathrm{NH}_3\right)
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Which from following equations is used to express the angular momentum of an electron in a stationary state?
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Which emission transition series is obtained when electron jumps from $$\mathrm{n}_2=\infty$$ to $$\mathrm{n}_1=1$$ ?
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What is half life time of a first order reaction if initial conc. of reactant is $$0.01 \mathrm{~mol} \mathrm{~L}^{-1}$$
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Which among the following pairs of polymers contains both members as copolymers?
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What is atomic mass of an element with $$\mathrm{BCC}$$ structure and density $$10 \mathrm{~g} \mathrm{~cm}^{-3}$$ havin
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Oxidation state of manganese in potassium permanganate is:
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Which among following complexes is a neutral complex?
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Which among the following halogens combines readily with metals to form metal halides with highest ionic character?
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Which of the following compounds has highest boiling point?
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Identify physisorption from following.
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Identify the product of following reaction. Benzoyl chloride $$\stackrel{\mathrm{H}_2 \mathrm{O}}{\longrightarrow}$$ pro
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What is IUPAC name of the compound?
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Calculate the $$\mathrm{pH}$$ of $$1.36 \times 10^{-2} \mathrm{M}$$ solution of perchloric acid.
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Which of the following formulae is used to determine compressibility factor for measurement of deviation from ideal beha
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The molar conductivity of $$0.02 \mathrm{~M} \mathrm{~AgI}$$ at $$298 \mathrm{~K}$$ is $$142.3 \Omega^{-1} \mathrm{~cm}^
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What is IUPAC name of following compound?
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Identify a molecule with incomplete octet from following.
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What is the number of unit cells present in a cubic pack crystal lattice having 4 atoms per unit cell and weighing $$0.6
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Identify 'A' in the following reaction.
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Which among the following is CORRECT formula for determination of cell constant?
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Identify the catalyst (A) used in following reaction. $$\mathrm{CO}+\mathrm{H}_2 \mathrm{O} \stackrel{\mathrm{A}}{\right
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What is value of PV type of work for following reaction at 1 bar? $$\underset{(200 \mathrm{~mL})}{\mathrm{C}_2 \mathrm{H
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Mathematics

$$\int\limits_0^\pi \frac{d x}{4+3 \cos x}=$$
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If $$y=\log _{\sin x} \tan x$$, then $$\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)_{x=\frac{\pi}{4}}$$ has the value
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$$\lim _\limits{x \rightarrow 2}\left[\frac{1}{x-2}-\frac{2}{x^3-3 x^2+2 x}\right]$$ is equal to
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From a lot of 20 baskets, which includes 6 defective baskets, a sample of 2 baskets is drawn at random one by one withou
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If the angle between the lines represented by the equation $$x^2+\lambda x y-y^2 \tan ^2 \theta=0$$ is $$2 \theta$$, the
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Number of common tangents to the circles $$x^2+y^2-6 x-14 y+48=0$$ and $$x^2+y^2-6 x=0$$ are
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The left-hand derivative of $$\mathrm{f}(x)=[x] \sin (\pi x)$$, at $$x=\mathrm{k}, \mathrm{k}$$ is an integer and [.] is
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Let $$\mathrm{f}(x)=\int \frac{\sqrt{x}}{(1+x)^2} \mathrm{~d} x, x \geq 0$$, then $$\mathrm{f}(3)-\mathrm{f}(1)$$ is equ
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Value of $$c$$ satisfying the conditions and conclusions of Rolle's theorem for the function $$\mathrm{f}(x)=x \sqrt{x+6
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Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vert
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If the direction cosines $$l, \mathrm{~m}, \mathrm{n}$$ of two lines are connected by relations $$l-5 \mathrm{~m}+3 \mat
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Let $$\mathrm{f}(x)=\log (\sin x), 0
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Five students are to be arranged on a platform such that the boy $$B_1$$ occupies the second position and such that the
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If the volume of the parallelopiped is $$158 \mathrm{~cu}$$. units whose coterminus edges are given by the vectors $$\ba
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Let $$\mathrm{f}(x)$$ be positive for all real $$x$$. If $$\mathrm{I}_1=\int_\limits{1-\mathrm{h}}^{\mathrm{h}} x \mathr
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The mirror image of the point $$(1,2,3)$$ in a plane is $$\left(-\frac{7}{3},-\frac{4}{3},-\frac{1}{3}\right)$$. Thus, t
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If $$\alpha=3 \sin ^{-1} \frac{6}{11}$$ and $$\beta=3 \cos ^{-1}\left(\frac{4}{9}\right)$$, where the inverse trigonomet
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$$\text { The value of } \sec ^2\left(\tan ^{-1} 2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right) \text { is }$$
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The value of $$\tan \left(\frac{\pi}{8}\right)$$ is _________.
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A plane is parallel to two lines, whose direction ratios are $$1,0,-1$$ and $$-1,1,0$$ and it contains the point $$(1,1,
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The domain of the function given by $$2^x+2^y=2$$ is
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If $$\mathrm{f}(x)=x \mathrm{e}^{x(1-x)}, x \in \mathrm{R}$$, then $$\mathrm{f}(x)$$ is
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The solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{1+y^2}{1+x^2}$$ is
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If $$\bar{a}, \bar{b}, \bar{c}$$ are three vectors such that $$\overline{\mathrm{a}} \cdot(\overline{\mathrm{b}}+\overli
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Let $$\bar{a}=2 \hat{i}+\hat{j}-2 \hat{k}$$ and $$\bar{b}=\hat{i}+\hat{j}$$. If $$\bar{c}$$ is a vector such that $$\ove
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$$\int_\limits{-1}^3\left(\cot ^{-1}\left(\frac{x}{x^2+1}\right)+\cot ^{-1}\left(\frac{x^2+1}{x}\right)\right) \mathrm{d
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If $$P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$$ is the adjoint of a $$3 \tim
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If $$\mathrm{f}(x)=\left\{\begin{array}{ll}\frac{\sqrt{1+\mathrm{m} x}-\sqrt{1-\mathrm{m} x}}{x}, & -1 \leq x
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The area of the region bounded by the parabola $$y=x^2$$ and the curve $$y=|x|$$ is
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Derivative of $$\tan ^{-1}\left(\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\right)$$ w.r.t. $$\cos ^{-1}
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A binomial random variable $$\mathrm{X}$$ satisfies $$9. p(X=4)=p(X=2)$$ when $$n=6$$. Then $$p$$ is equal to
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If in $$\triangle \mathrm{ABC}$$, with usual notations, $$a \cdot \cos ^2 \frac{C}{2}+c \cos ^2 \frac{A}{2}=\frac{3 b}{2
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The lines $$\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-1}{5} \quad$$ and $$\frac{x+2}{4}=\frac{y-1}{3}=\frac{z+1}{2}$$
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A curve passes through the point $$\left(1, \frac{\pi}{6}\right)$$. Let the slope of the curve at each point $$(x, y)$$
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For the following shaded area, the linear constraints except $$x,y \ge 0$$ are
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Let $$\omega \neq 1$$ be a cube root of unity and $$S$$ be the set of all non-singular matrices of the form $$\left[\beg
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The value of $$2 \tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{7}$$
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$$\int \frac{\mathrm{e}^x(1+x)}{\cos ^2\left(\mathrm{e}^x \cdot x\right)} \mathrm{d} x=$$
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In a triangle $$\mathrm{ABC}$$, with usual notations, if $$\mathrm{m} \angle \mathrm{A}=60^{\circ}, \mathrm{b}=8, \mathr
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If variance of $$x_1, x_2 \ldots \ldots, x_n$$ is $$\sigma_x^2$$, then the variance of $$\lambda x_1, \lambda x_2, \ldot
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If $$\quad \overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}, \quad \overline{\mathrm{b}}=2 \hat{\mathrm{j}}-\hat{
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If $$\mathrm{z}=x+\mathrm{i} y$$ and $$\mathrm{z}^{1 / 3}=\mathrm{p}+\mathrm{iq}$$, where $$x, y, \mathrm{p}, \mathrm{q}
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If $$\int \frac{\mathrm{d} x}{x \sqrt{1-x^3}}=\mathrm{k} \log \left(\frac{\sqrt{1-x^3}-1}{\sqrt{1-x^3}+1}\right)+\mathrm
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The statement pattern $$\mathrm{p} \rightarrow \sim(\mathrm{p} \wedge \sim \mathrm{q})$$ is equivalent to
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$$\mathrm{a}$$ and $$\mathrm{b}$$ are the intercepts made by a line on the co-ordinate axes. If $$3 \mathrm{a}=\mathrm{b
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Let $$\bar{a}, \bar{b}$$ and $$\bar{c}$$ be three unit vectors such that $$\bar{a} \times(\bar{b} \times \bar{c})=\frac{
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The vector equation of the line $$2 x+4=3 y+1=6 z-3$$ is
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If $$\overline{\mathrm{a}}$$ and $$\overline{\mathrm{b}}$$ are two unit vectors such that $$\overline{\mathrm{a}}+2 \ove
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$$\int \frac{\log (\cot x)}{\sin 2 x} d x=$$
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$$\text { If } y=\sqrt{\frac{1-\sin ^{-1}(x)}{1+\sin ^{-1}(x)}} \text {, then } \frac{\mathrm{d} y}{\mathrm{~d} x} \text
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Physics

A coil of radius '$$r$$' is placed on another coil (whose radius is $$\mathrm{R}$$ and current flowing through it is cha
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Two capillary tubes of the same diameter are kept vertically in two different liquids whose densities are in the ratio $
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Two spherical black bodies of radii '$$r_1$$' and '$$r_2$$' at temperature '$$\mathrm{T}_1$$' and '$$\mathrm{T}_2$$' res
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For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at certain displacement '$$x$$' from
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The maximum kinetic energies of photoelectrons emitted are $$\mathrm{K}_1$$ and $$\mathrm{K}_2$$ when lights of waveleng
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A particle moves along a circular path with decreasing speed. Hence
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Identify the correct circuit diagrams for the normal operation from the following.
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With the gradual increase in frequency of an a. c. source, the impedance of an LCR series circuit
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In energy band diagram of insulators, a band gap and the conduction band is respectively
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Two positively charged identical spheres separated by a distance 'd' exert some force (F) on each other when they are ke
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A string fixed at both the ends forms standing wave with node separation of $$5 \mathrm{~cm}$$. If the velocity of the w
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A ball of mass '$$\mathrm{m}$$' is attached to the free end of a string of length '$$l$$'. The ball is moving in horizon
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Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its pl
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When a current of $$1 \mathrm{~A}$$ is passed through a coil of 100 turns, the flux associated with it is $$2.5 \times 1
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A spherical liquid drop of radius $$\mathrm{R}$$ is divided into 8 equal droplets. If surface tension is $$\mathrm{S}$$,
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The rate of flow of heat through a metal rod with temperature difference $$40^{\circ} \mathrm{C}$$ is $$1600 \mathrm{~ca
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Two charges of equal magnitude '$$q$$' are placed in air at a distance '$$2 r$$' apart and third charge '$$-2 \mathrm{q}
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The size of the real image produced by a convex lens of focal length $$F$$ is '$$m$$' times the size of the object. The
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A double slit experiment is immersed in water of refractive index 1.33. The slit separation is $$1 \mathrm{~mm}$$, dista
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Potential difference between the points P and Q is nearly
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An electron in the hydrogen atom jumps from the first excited state to the ground state. What will be the percentage cha
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In series LCR circuit, the voltage across the inductance and the capacitance are not
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If the temperature of a hot body is increased by $$50 \%$$, then the increase in the quantity of emitted heat radiation
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The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe of length '$$L$$'. The
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The radius of earth is $$6400 \mathrm{~km}$$ and acceleration due to gravity $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$. For th
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A car sounding a horn of frequency $$1000 \mathrm{~Hz}$$ passes a stationary observer. The ratio of frequencies of the h
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The time period of a simple pendulum inside a stationary lift is '$$T$$'. When the lift starts accelerating upwards with
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The mutual inductance of a pair of coils, each of '$$N$$' turns, is '$$M$$' henry. If a current of '$$I$$' ampere in one
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To manufacture a solenoid of length $$1 \mathrm{~m}$$ and inductance $$1 \mathrm{~mH}$$, the length of thin wire require
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In a radioactive disintegration, the ratio of initial number of atoms to the number of atoms present at time $$t=\frac{1
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A bullet is fired on a target with velocity '$$\mathrm{V}$$'. Its velocity decreases from '$$\mathrm{V}$$' to '$$\mathrm
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In the experiment of diffraction due to a single slit, if the slit width is decreased, the width of the central maximum
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A cylindrical magnetic rod has length $$5 \mathrm{~cm}$$ and diameter $$1 \mathrm{~cm}$$. It has uniform magnetization $
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In biprism experiment, if $$5^{\text {th }}$$ bright band with wavelength $$\lambda_1^{\prime}$$ coincides with $$6^{\te
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A body of mass '$$\mathrm{m}$$' kg starts falling from a distance 3R above earth's surface. When it reaches a distance '
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In the case of NAND gate, if A and B are the inputs and $$\mathrm{Y}$$ is the output then
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A monoatomic gas at pressure '$$\mathrm{P}$$', having volume '$$\mathrm{V}$$' expands isothermally to a volume '$$2 \mat
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In potentiometer experiments, two cells of e. m. f. '$$E_1$$' and '$$E_2$$' are connected in series $$\left(E_1>E_2\righ
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A diatomic gas $$\left(\gamma=\frac{7}{5}\right)$$ is compressed adiabatically to volume $$\frac{V_i}{32}$$ where $$V_i$
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A disc has mass $$M$$ and radius $$R$$. How much tangential force should be applied to the rim of the disc, so as to rot
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An electron moving with velocity $$1.6 \times 10^7 \mathrm{~m} / \mathrm{s}$$ has wavelength of $$0.4 \mathop A\limits^o
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The prism has refracting angle '$$\mathrm{A}$$'. The second refracting surface of the prism is silvered. Light ray falli
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Two parallel wires of equal lengths are separated by a distance of $$3 \mathrm{~m}$$ from each other. The currents flowi
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Three point charges $$+\mathrm{q},+2 \mathrm{q}$$ and $$+\mathrm{Q}$$ are placed at the three vertices of an equilateral
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If a gas is compressed isothermally then the r.m.s. velocity of the molecules
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The bob of a simple pendulum of length '$$L$$' has a mass '$$\mathrm{m}$$' and charge '$$\mathrm{q}$$'. The pendulum is
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An electron is projected along the axis of circular conductor carrying current I. Electron will experience
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Two identical capacitors have the same capacitance '$$C$$'. One of them is charged to a potential $$V_1$$ and the other
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A transverse wave $$\mathrm{Y}=2 \sin (0.01 \mathrm{x}+30 \mathrm{t})$$ moves on a stretched string from one end to anot
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A body of density '$$\rho$$' is dropped from rest at a height '$$h$$' into a lake of density '$$\sigma' (\sigma>\rho)$$.
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