MHT CET 2021 21th September Evening Shift

Paper was held on
Tue, Sep 21, 2021 8:30 AM

## Chemistry

When 1 mole of gas is heated at constant volume, the temperature rises form $$273 \mathrm{~K}$$ to $$546 \mathrm{~K}$$.

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Oxidation state of iodine in I$$_3^-$$ is

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What is the total number of atoms in BCC crystal lattice having $$1.8 \times 10^{20}$$ unit cells?

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Identify the product B in the following sequence of reactions?

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What is the volume occupied by 16 g methane gas at STP?

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The $$\left[\mathrm{OH}^{-}\right]$$ in a solution is $$1 \times 10^{-12} \mathrm{~mol} \mathrm{~dm}{ }^{-3}$$. What is

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Which among the following statements is true for Galvanic cell?

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Identify the product $$(\mathrm{X})$$ formed in the following reaction.
$$\mathrm{C}_6 \mathrm{H}_5 \mathrm{OH}+\mathrm{

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Which of the following is NOT true for alkaline earth metals?

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Which of the following is NOT formed when a mixture of methyl bromide and n-propyl bromide is treated with sodium metal

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Which element among the following is ferromagnetic?

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Which of following enzymes is useful in conversion of glucose to fructose?

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Which of the following reagents is used in the reaction shown below?
Benzoyl chloride $$\stackrel{?}{\longrightarrow}$$

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What is vapour pressure of a solution when $$2 \mathrm{~mol}$$ of a non-volatile solute are dissolved in $$20 \mathrm{~m

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Which among following amines has lowest $$\mathrm{pK}_{\mathrm{b}}$$ values?

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Which of following elements forms crosslinks in vulcanization of SBR rubber?

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What will be the concentration of solution of electrolyte if it's molar conductivity and conductivity are respectively 2

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Identify cationic complex from following.

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Which property from following is NOT exhibited by interstitial compounds?

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Which among the following salt solution in water shows pH greater than 7?

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What is the percentage of unoccupied volume in BCC structure?

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What type of isomers are the ethoxy ethane and methoxy propane?

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What is the value of $$\mathrm{\Delta H-\Delta U}$$ for the formation of 2 moles of ammonia from $$\mathrm{H_{2(g)}}$$ a

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What is the density of an element (At mass 100 g mol$$^{-1}$$) having BCC structure with edge length 400 pm?

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In which of the following salts, the solubility increases appreciably with increase in temperature?

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What is effective atomic number of cobalt in [Co(NH$$_3$$)$$_6$$]$$^{3+}$$ if Co(Z = 27) ?

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Which among the following is NOT an example of one-dimensional nanostructure?

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For a first order reaction, intercept of the graph between $$\mathrm{\log\frac{[A]_o}{[A]_t}}$$(Y-axis) and conc. (X-axi

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The pH of 0.005 M KOH is 9.95. Calculate the [OH$$^-$$] ?

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Which of the following reactions is a Wurtz - Fittig reaction?

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Which among the following noble gases reacts with fluorine to give crystalline fluorides?

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Identify the name of following reaction.
Toluene + chromyl chloride $$\stackrel{\mathrm{CS}_2}{\longrightarrow}$$ comple

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What is the half-life of a first order reaction if time required to decrease concentration of reactant from 1.0 M to 0.2

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Which among the following is obtained as major product $$\mathrm{x}$$ in the reaction stated below?
Anisole $$\mathrm{\m

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Which among the following statements about ozone depletion is NOT true?

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Which free radical initiator is used for polymerization of tetrafluoro ethylene?

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Chlorobenzene on heating with concentrated HNO$$_3$$ in presence of concentrated H$$_2$$SO$$_4$$ gives

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What is the boiling point of 0.5 molal aqueous solution of sucrose if 0.1 molal aqueous solution of glucose boils at 100

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Identify the product formed when tertiary butyl bromide reacts with alcoholic NH$$_3$$ solution?

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Which among the following gases is adsorbed to greater extent at similar conditions of temperature and pressure if the a

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What is the rate of disappearance of B in following reaction? $$2 \mathrm{A}+\mathrm{B} \rightarrow 3 \mathrm{C}$$, if r

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Which reagent oxidizes glucose to saccharic acid?

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Two moles of an ideal gas are expanded isothermally from $$15 \mathrm{dm}^3$$ to $$20 \mathrm{dm}^3$$. If the amount of

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Which from following statements is NOT correct for heterolysis?

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Which among the following molecules exhibits strong London forces?

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What is the number of moles of electrons passed when current of 5 ampere is passed through a solution of FeCl$$_3$$ for

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What is the formal charge of oxygen atom in carbon monoxide?

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Which isomer of C$$_6$$H$$_{14}$$ has highest boiling point?

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What is the wavelength for a wave having frequency 50 Hz?

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Identify the product formed when benzoyl chloride is reduced by hydrogen using palladium catalyst poisoned with barium s

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## Mathematics

If $$\mathrm{(m+3 n)(3 m+n)=4 h^2}$$, then the acute angle between the lines represented by $$\mathrm{m x^2+2 h x y+n y^

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$$\text{I} : y^{\prime}=\frac{y+x}{x} ; \quad \text { II }: y^{\prime}=\frac{x^2+y}{x^3} ; \quad \text { III }: y^{\prim

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The differential equation of the family of circles touching $$y$$-axis at the origin is

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The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2 and 6, then the ot

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If $$\overline{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}, \overline{\mathrm{b}}=3 \hat{\mathrm{

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If $$\mathrm{p}$$ is the length of the perpendicular from origin to the line whose intercepts on the axes are a and $$b$

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The abscissa of the points, where the tangent to the curve $$y=x^3-3 x^2-9 x+5$$ is parallel to $$X$$ axis are

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$$\int \frac{1}{x^{\frac{1}{2}}+x^{\frac{1}{3}}} d x=$$

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If $$A=\left[\begin{array}{ccc}\cos \theta & -\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\r

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$$\int[\sin |\log x|+\cos |\log x|] d x=$$

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$$\int\limits_5^{10} \frac{d x}{(x-1)(x-2)}=$$

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The direction cosines $$\ell, \mathrm{m}, \mathrm{n}$$ of the line $$\frac{\mathrm{x}+2}{2}=\frac{2 \mathrm{y}-5}{3} ; \

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an urn contains 9 balls of which 3 are red, 4 are blue and 2 are green. Three balls are drawn at random from the urn. Th

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If $${\pi \over 2}

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Equation of the plane passing through the point (2, 0, 5) and parallel to the vectors $$\widehat i - \widehat j + \wideh

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If $$A=\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1\end{array}\right]$$ and $$A^{-1}=\frac{1}{2}\left[\be

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For all real $$x$$, the minimum value of the function $$f(x)=\frac{1-x+x^2}{1+x+x^2}$$ is

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The objective function $$z=4 x+5 y$$ subjective to $$2 x+y \geq 7 ; 2 x+3 y \leq 15 ; y \leq 3, x \geq 0 ; y \geq 0$$ ha

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The co-ordinates of the point $$\mathrm{P} \equiv(1,2,3)$$ and $$\mathrm{O} \equiv(0,0,0)$$, then the direction cosines

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$$\int\limits_{{{ - \pi } \over 2}}^{{\pi \over 2}} {{{\cos x} \over {1 + {e^x}}}dx = } $$

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The equation of the plane containing the line $$\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$$ and the point $$(0,7,-7)$$

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If the lines $$x^2-4xy+y^2=0$$ make angles $$\alpha$$ and $$\beta$$ with positive direction X-axis, then $$\cot^2\alpha+

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It is observed that $$25 \%$$ of the cases related to child labour reported to the police station are solved. If 6 new c

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For X ~ B(n, p), if p = 0.6, E(X) = 6, then Var(X) =

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The equation of a line passing through $$(3,-1,2)$$ and perpendicular to the lines $$\bar{r}=(\hat{i}+\hat{j}-\hat{k})+\

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$$\begin{aligned}
& \text { } f(x)=\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x} \text {, if } 1 \leq x
is continuous in the inter

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The function $$f(x)=\log (1+x)-\frac{2 x}{2+x}$$ is increasing on

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If $$A=\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right]$$, then $$A^{-1}=$$

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The equation of circle with centre at $$(2,-3)$$ and the circumference $$10 \pi$$ units is

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If y = 2 sin x + 3 cos x and y + A$$\mathrm{\frac{d^2y}{dx^2}}$$ = B, then the values of A, B are respectively

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The number of solutions of cos2$$\theta$$ = sin$$\theta$$ in (0, 2$$\pi$$) are

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If $$y=\tan ^{-1}\left[\frac{1}{1+x+x^2}\right]+\tan ^{-1}\left[\frac{1}{x^2+3 x+3}\right], x>0$$, then $$\frac{d y}{d x

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If $$z(2-i)=(3+i)$$, then $$z^{38}=$$, ( where $$z=x+i y$$)

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The area bounded by the parabola $$y^2=x$$, the straight line $$y=4$$ and $$Y$$ axis is

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If $$\sin ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)=\sin ^{-1} \alpha$$, then $$\alpha=$$

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If $$\lim _\limits{x \rightarrow 5} \frac{x^k-5^k}{x-5}=500$$, then the value of $$k$$, where $$k \in N$$ is

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The logical statement (p $$\to$$ q) $$\wedge$$ (q $$\to$$ ~p) is equivalent to

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For a set of five true or false questions, no student has written the all correct answers and no two students have given

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The general solution of the differential equation. $$\left(\frac{y}{x}\right) \cos \left(\frac{y}{x}\right) d x-\left[\l

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If the half life period of a substance is 5 years, then the total amount of the substance left after 15 years, when init

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A bakerman sells 5 types of cakes. Profit due to sale of each type of cake is respectively ₹ 2.5, ₹ 3 , ₹ 1.5 and ₹ 1. T

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If $$m$$ is order and $$n$$ is degree of the differential equation $$\left(\frac{d^2 y}{d x^2}\right)^5+4 \frac{\left(\f

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If $$\theta+\phi=\alpha$$ and $$\tan \theta=k \tan \phi($$ where $$K>1)$$, then the value of $$\sin (\theta-\phi)$$ is

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With usual notations, perimeter of a triangle $$A B C$$ is 6 times the arithmetic mean of sine of its angles. If $$\math

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If p $$\to$$ (~p $$\vee$$ q) is false, then the truth values of p and q are, respectively

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If $$|\bar{a} \times \bar{b}|^2+(\bar{a} \cdot \bar{b})^2=144$$ and $$|\bar{a}|=4$$, then $$|\bar{b}|=$$

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Let A = {10, 11, 12, 14, 26} and let f : A $$\to$$ N be such that f(a) = highest prime factor of a, where a $$\in$$ A, t

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If $$\int {{{5\tan x} \over {\tan x - 2}}dx = x + a\log |\sin x - 2\cos x| + c} $$, then a = (Where c is constant of int

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The area of the parallelogram with vertices A(1, 2, 3), B(1, 3, a), C(3, 8, 6) and D(3, 7, 3) is $$\sqrt{265}$$ sq. unit

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If $$y = {\tan ^{ - 1}}\left\{ {{{a\cos x - b\sin x} \over {b\cos x + a\sin x}}} \right\}$$, then $${{dy} \over {dx}}$$

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## Physics

Under isothermal conditions, two soap bubbles of radii '$$r_1$$' and '$$r_2$$' combine to form a single soap bubble of

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Two identical parallel plate air capacitors are connected in series to a battery of emf '$$\mathrm{V}$$'. If one of the

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In LCR series resonant circuit, at resonance, voltage across 'L' and 'C' will cancel each other because they are

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Two coherent sources of wavelength '$$\lambda$$' produce steady interference pattern. The path difference corresponding

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In a capillary tube having area of cross-section A, water rises to a height 'h'. If cross-sectional area is reduced to $

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Water rises upto a height $$10 \mathrm{~cm}$$ in a capillary tube. It will rise to a height which is much more than $$10

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A moving coil galvanometer is converted into an ammeter, reading upto $$0.04 \mathrm{~A}$$ by connecting a shunt of resi

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The inductive reactance of a coil is R$$\Omega$$. If the inductance of a coil is doubled and frequency of a.c. supply is

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For a body of mass '$$m$$', the acceleration due to gravity at a distance '$$R$$' from the surface of the earth is $$\le

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What is the ratio of the velocity of sound in hydrogen $$\left(\gamma=\frac{7}{5}\right)$$ to that in helium $$\left(\ga

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A particle performs rotational motion with an angular momentum 'L'. If frequency of rotation is doubled and its kinetic

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Equation of two simple harmonic waves are given by $${Y_1} = 2\sin 8\pi \left( {{t \over {0.2}} - {x \over 2}} \right)m$

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A current through 1 $$\Omega$$ resistance in the following circuit is

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Three bodies P, Q and R have masses 'm' kg, '2m' kg and '3m' kg respectively. If all the bodies have equal kinetic energ

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Equal volumes of two gases are kept in different containers having densities in the ratio 1 : 16. They exert equal press

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In Young's experiment, fringes are obtained on a screen placed at a distance $$75 \mathrm{~cm}$$ from the slits. When th

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Combination of NAND gates is shown in the figure. It is equivalent to

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A molecule of mass 'm' moving with velocity 'v' makes 5 elastic collisions with a wall of container per second. The chan

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In thermodynamics, for an isochoric process, which one of the following statement is INCORRECT?

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The ratio of energy required to raise a satellite of mass '$$m$$' to height '$$h$$' above the earth's surface to that re

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When a piece of polythene is rubbed with wool, a negative charge of $$4 \times 10^{-7} \mathrm{C}$$ is developed on the

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Ratio centripetal acceleration for an electron revolving in 3rd and 5th Bohr orbit of hydrogen atom is

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In an ideal junction diode, the current flowing through PQ is

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LED is manufactured using zinc selenide then it emits.

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If '$$\mathrm{E}$$' is the kinetic energy per mole of an ideal gas and '$$\mathrm{T}$$' is the absolute temperature, the

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A child is sitting on a swing which performs S.H.M. It has minimum and maximum heights from ground $$0.75 \mathrm{~cm}$$

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The north pole of a long horizontal bar magnet is being brought towards closed circuit consisting of a coil. The directi

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The wave number of the last line of the Balmer series in the hydrogen spectrum will be $$\left(\right.$$ Rydberg's cons

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The refractive index of glass is 1.5 and that of water is 1.33 . The critical angle for a ray of light going from glass

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A, B and C are three parallel conductors of equal lengths carrying currents $$\mathrm{I}, \mathrm{I}$$ and $$2 \mathrm{I

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Three pure inductors each of inductance 6H are connected as shown in the figure. Their equivalent inductance between the

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A body at rest falls through a height 'h' with velocity 'V'. If it has to fall down further for its velocity to become t

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A convex lens is dipped in a liquid whose refractive index is equal to refractive index of lens material. Then its focal

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Photoemission from metal surface takes place for frequencies '$$v_1$$' and '$$v_2$$' of incident rays $$\left(v_1>v_2\ri

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The angle of banking '$$\theta$$' for a meter gauge railway line is given by $$\theta=\tan ^{-1}\left(\frac{1}{20}\right

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Three rings each of mass 'M' and radius 'R' are arranged as shown in the figure. The moment of inertia of system about

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The instantaneous value of an alternating current is given by $$\mathrm{i}=50 \sin (100 \pi \mathrm{t})$$. It will achie

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A proton and alpha particle are accelerated through the same potential difference. The ratio of the de-Broglie wavelengt

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Two rods of same length and material are joined end to end. They transfer heat in 8 second. When they are joined in para

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A pendulum clock is running fast. To correct its time, we should

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A pipe closed at one end has length $$0.8 \mathrm{~m}$$. At its open end $$0.5 \mathrm{~m}$$ long uniform string is vibr

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Two coherent sources 'P' and 'Q' produce interference at point 'A' on the screen, where there is a dark band which is fo

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The equation of simple harmonic wave produced in the string under tension $$0.4 \mathrm{~N}$$ is given by $$\mathrm{y=4

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A condenser of capacity '$$\mathrm{C}_1$$' is charged to potential '$$\mathrm{V}_1$$' and then disconnected. Uncharged c

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In a step up transformer, which one of the following statements is correct?

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Magnetic moment of revolving electron of charge (e) and mass (m) in terms of angular momentum (L) of electron is :

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A particle is performing S.H.M. with maximum velocity '$$v$$'. If the amplitude is tripled and periodic time is doubled

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A big water drop is divided into 8 equal droplets. $$\Delta \mathrm{P}_{\mathrm{s}}$$ and $$\Delta \mathrm{P}_{\mathrm{B

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A hollow metal sphere has a radius 'r'. The potential difference between a point on its surface and at a point at a dist

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The magnetic flux near the axis and inside the air core solenoid of length $$60 \mathrm{~cm}$$ carrying current '$$\math

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