MHT CET 2021 20th September Evening Shift
Paper was held on Mon, Sep 20, 2021 8:30 AM
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Chemistry

What are the formulae of the compounds formed when lanthanoids (Ln) react with nitrogen and halogen respectively?
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Identify '$$\mathrm{A}$$' in the following reaction. $$A \stackrel{\text { Na/dry ether }}{\longrightarrow}$$ 3,4-diethy
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For the reaction $$2 \mathrm{NO}+\mathrm{Cl}_2 \rightarrow 2 \mathrm{NOCl}$$ What is the relation between $$\frac{\mathr
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What type of hybridization is exhibited by [CoF$$_6$$]$$^{3-}$$ ?
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Which among the following is NOT the use of SO$$_2$$ gas?
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Glucose and gluconic acid on oxidation with dilute nitric acid forms saccharic acid. This reaction confirms that glucose
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Identify $$-$$I effect causing group from following.
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Which from following instruments is used to determine the crystal structure?
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Solubility of $$\mathrm{AgCl}$$ is $$7.2 \times 10^{-7} \mathrm{~mol} ~\mathrm{dm}^{-3}$$. What is it's solubility produ
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Identify compound $$\mathrm{A}$$ used in following reaction. Benzoic acid $$\underset{\Delta}{\stackrel{A}{\longrightarr
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In a first order reaction concentration of reactant decreases from 20 m mol to 10 m mol in 1.151 min. What is rate const
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Which among following compounds is a primary amine?
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Which among following properties of lanthanoids is NOT true?
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How many total voids are present in 1 mole of compound that forms hcp structure?
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Identify neutral complex from following.
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How many molecules of methyl iodide are required to obtain tetramethyl ammonium iodide from dimethyl amine?
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Which of the following processes does NOT involve use of dihydrogen?
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Which of the following compounds does NOT exhibit optical isomerism?
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What is the value of '$$\mathrm{x}$$' in order to balance the following redox reaction by ion electron method? $$\quad \
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Which among the following carbohydrates is a trisaccharide?
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"Mass can neither be created nor destroyed" is the statement of
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What is bond angle O-S-O in SO$$_2$$ molecule?
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Which of the following bonds has highest bond enthalpy?
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Which of the following compounds is optically inactive?
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Which type of reaction order is followed by radioactive processes?
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What is the total number of Bravais lattices present in seven types of crystal system?
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Which among the following aqueous salt solution is used in conductivity cell to determine cell constant?
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Calculate heat of formation of $$\mathrm{HCl}$$ gas from following reaction. $$\mathrm{H}_{2(\mathrm{~g})}+\mathrm{Cl}_{
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What is the value of frequency of radiation when transition occurs between two stationary states that differ in energy b
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What is molar concentration of weak monobasic acid if dissociation constant is 5 $$\times$$ 10$$^{-8}$$ and undergoes 0.
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A substance containing hydrogen and releasing H$$^+$$ in aqueous medium is acid. Identify theory suggesting this concept
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What is the molar conductivity of $$0.05 \mathrm{M}$$ solution of sodium hydroxide, if it's conductivity is $$0.0118 \ma
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Which among the following compounds has highest boiling point?
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What is IUPAC name of the following compound?
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What is molar mass of metal with BCC structure having density 10 g cm$$^{-3}$$ and edge length 200 pm?
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Calculate difference between $$\Delta \mathrm{H}$$ and $$\Delta \mathrm{U}$$ for following reaction at $$25^{\circ} \mat
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What is cryoscopic constant of water if $$5 \mathrm{~g}$$ of glucose in $$100 \mathrm{~g}$$ of water has depression in f
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Which of the following pairs of alkenes is an example of position isomers?
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Which of the following polymers is used in the preparation of cinema films?
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In carbinol system isobutyl alcohol is named as
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Which among the following is strongest acid?
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Identify the isomerism exhibited by methoxyethane and propan-1-ol.
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Which of the following statements is correct for boiling point of a liquid?
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Henry's law constant for $$\mathrm{CH}_3 \mathrm{Br}$$ is $$0.16 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{bar}^{-1}$$ at $
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Identify negatively charged sol from following.
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Which of the following monomer is used for preparation of Nylon-6?
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Keeping temperature constant the pressure of 11.2 dm$$^3$$ of a gas was increased from 105 kPa to 420 kPa. What is the n
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The change in internal energy of a system depends upon
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How many faraday of electricity is required to produce 10 g of calcium metal (molar mass = 40 g mol$$^{-1}$$) from calci
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Identify the product formed in the following reaction, $$\mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_2-\mathrm{CHO
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Mathematics

$$\sin ^{-1}\left[\sin \left(-600^{\circ}\right)\right]+\cot ^{-1}(-\sqrt{3})=$$
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If $$\mathrm{m}$$ is order and $$\mathrm{n}$$ is degree of the differential equation $$y=\frac{d p}{d x}+\sqrt{a^2 p^2-b
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The surface area of a spherical balloon is increasing at the rate $$2 \mathrm{~cm}^2 / \mathrm{sec}$$. Then rate of incr
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The p.m.f. of a random variable X is $$\mathrm{P(X = x) = {1 \over {{2^5}}}\left( {_x^5} \right),x = 0,1,2,3,4,5}=0$$ th
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$$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$$ are vectors such that $$|\overline{\mathrm{a}}|=
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If $$\frac{n !}{2 !(n-2) !}$$ and $$\frac{n !}{4 !(n-4) !}$$ are in the ratio $$2: 1$$, then $$n=$$
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p : It rains today q : I am going to school r : I will meet my friend s : I will go to watch a movie. Then symbolic form
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If $$a=\lim _\limits{n \rightarrow \infty} \frac{1+2+3+\ldots+n}{n^2}$$ and $$b=\lim _\limits{n \rightarrow \infty} \fra
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If $$\omega$$ is complex cube root of unity and $$(1+\omega)^7=A+B\omega$$, then values of A and B are, respectively
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If $$[\bar{a} \bar{b} \bar{c}]=4$$, then the volume (in cubic units) of the parallelopiped with $$\bar{a}+2 \bar{b}, \ba
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The variance of the following probability distribution is,
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The general solution of the differential equation $$\cos x \cdot \sin y d x+\sin x \cdot \cos y d y=0$$ is
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$$\overline{\mathrm{a}}, \overline{\mathrm{b}}$$ and $$\overline{\mathrm{c}}$$ are three vectors such that $$\overline{\
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$$\int \sec ^4 x \cdot \tan ^4 x d x=\frac{\tan ^m x}{m}+\frac{\tan ^n x}{n}+c$$ (where c is constant of integration), t
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The x-intercept of a line passing through the points $$\left(\frac{-1}{2}, 1\right)$$ and (1, 2) is :
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The Cartesian equation of the line passing through the points A(2, 2, 1) and B(1, 3, 0) is
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If the variance of the numbers $$2,3,11$$ and $$x$$ is $$\frac{49}{4}$$, then the values of $$x$$ are
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The differential equation of an ellipse whose major axis is twice its minor axis, is
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The solution set for the system of linear inequations $$x+y \geq 1 ; 7 x+9 y \leq 63 ; y \leq 5 ; x \leq 6, x \geq 0$$ a
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$$\cos ^{-1}\left(\frac{4}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)=$$
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The co-factors of the elements of second column of $$\left[\begin{array}{ccc}1 & -1 & 2 \\ 3 & 2 & 1 \\ -1 & 3 & 4\end{a
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The Cartesian equation of the plane $$\overline{\mathrm{r}}=(\hat{\mathrm{i}}-\hat{\mathrm{j}})+\lambda(\hat{\mathrm{i}}
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The principal solutions of $$\sqrt{3} \sec x+2=0$$ are
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$$\int \operatorname{cosec}(x-a) \operatorname{cosec} x d x=$$
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If $$f(x)=2x^3-15x^2-144x-7$$, then $$f(x)$$ is strictly decreasing in
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The equation of the plane that contains the line of intersection of the planes. $$x+2 y+3 z-4=0$$ and $$2 x+y-z+5=0$$ an
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If the sum of mean and variance of a binomial distribution for 5 trials is 1.8, then probability of a success is
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$$y=\sqrt{e^{\sqrt{x}}}$$, then $$\frac{d y}{d x}=$$
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If area of the parallelogram with $$\bar{a}$$ and $$\bar{b}$$ as two adjacent sides is 20 square units, then the area of
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If $$f(x) = {{{4^{x - \pi }} + {4^{x - \pi }} - 2} \over {{{(x - \pi )}^2}}}$$, for $$x \ne \pi $$, is continuous at $$x
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The equation of tangent to the circle $$x^2+y^2=64$$ at the point $$\mathrm{P\left(\frac{2\pi}{3}\right)}$$ is
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If $$2 f(x)-3 f\left(\frac{1}{x}\right)=x$$, then $$\int_\limits1^e f(x) d x=$$
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Water is being poured at the rate of 36 m$$^3$$/min. into a cylindrical vessel, whose circular base is of radius 3 m. T
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If the equation $$3x^2-kxy-3y^2=0$$ represents the bisectors of angles between the lines $$x^2-3xy-4y^2=0$$, then value
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The general solution of $$\left(x \frac{d y}{d x}-y\right) \sin \frac{y}{x}=x^3 e^x$$ is
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The area bounded by the parabola $$y=x^2$$ and the line $$y=x$$ is
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If $$y=\sin ^{-1}\left[\cos \sqrt{\frac{1+x}{2}}\right]+x^x$$, then $$\frac{d y}{d x}$$ at $$x=1$$ is
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Negation of $$(p \wedge q) \rightarrow(\sim p \vee r)$$ is
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If $$A^{-1}=\left[\begin{array}{lll}3 & 2 & 6 \\ 1 & 1 & 2 \\ 2 & 5 & 5\end{array}\right]$$, then $$A=$$
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The joint equation of pair of lines through the origin and making an equilateral triangle with the line $$y=3$$ is
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If $$\bar{r}=-4 \hat{i}-6 \hat{j}-2 \hat{k}$$ is a linear combination of the vectors $$\bar{a}=-\hat{i}+4 \hat{j}+3 \hat
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If $$A^{-1}=\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$$ and $$B^{-1}=\left[\begin{array}{cc}1 & 0 \\ -3
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Two unbiased dice are thrown. Then the probability that neither a doublet nor a total of 10 will appear is
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The population of a city increases at a rate proportional to the population at that time. If the population of the city
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Let $$A=[a, b, c, d], B=[1,2,3]$$. Relation $$R_1, R_2, R_3, R_4$$ are as follows : $$\begin{aligned} & R_1=[(\mathrm{a}
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If $$\cos x=\frac{25}{24}$$ and $$x$$ lięs in first quadrant, then $$\sin \frac{x}{2}+\cos \frac{x}{2}=$$
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If $$\int_\limits2^e\left[\frac{1}{\log x}-\frac{1}{(\log x)^2}\right] d x=a+\frac{b}{\log 2}$$, then
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The vector equation of the line whose Cartesian equations are y = 2 and 4x $$-$$ 3z + 5 = 0 is
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$$\int \frac{2 x^2-1}{x^4-x^2-20} d x=$$
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If $$x=a(t+\sin t), y=a(1-\cos t)$$, then $$\frac{d y}{d x}=$$
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Physics

A perfect gas of volume 10 litre n compressed isothermally to a volume of 1 litre. The rms speed of the molecules will
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In the arrangement of the capacitors as shown in figure, each capacitor is of 6 $$\mu$$F, then equivalent capacity betwe
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The relation obeyed by a perfect gas during an adiabatic process is $$\mathrm{PV}^{3 / 2}$$. The initial temperature of
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What is the additional energy that should be supplied to a moving electron to reduce its de Broglie wavelength from $$1
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A convex lens of focal length $$\mathrm{T}$$ is used to form an image whose size is one fourth that of size of the objec
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A particle at rest starts moving with a constant angular acceleration of $$4 \mathrm{~rad} / \mathrm{s}^2$$ in a circula
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A metal conductor of length $$1 \mathrm{~m}$$ rotates vertically about one of its ends at an angular velocity of $$5 \ma
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A black rectangular surface of area '$$\mathrm{A}$$' emits energy '$$\mathrm{E}$$' per second at $$27^{\circ} \mathrm{C}
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A disc of radius 0.4 metre and mass 1 kg rotates about an axis passing through its centre and perpendicular to its plane
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The output of an 'OR' gate is 'one'
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A monoatomic gas is suddenly compressed to (1/8)th of its initial volume adiabatically. The ratio of the final pressure
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In the case of insulators, a band gap and conduction band is respectively
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In a single slit diffraction pattern, the distance between the first minimum on the left and the first minimum on the ri
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A conducting rod of length $$1 \mathrm{~m}$$ has area of cross-section $$10^{-3} \mathrm{~m}^2$$. One end is immersed in
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Which one of the following statements is true?
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A particle executes S.H.M. of period $$\frac{2 \pi}{\sqrt{3}}$$ second along a straight line $$4 \mathrm{~cm}$$ long. Th
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Two consecutive harmonics of an air column in a pipe closed at one end are of frequencies 150 Hz and 250 Hz. The fundame
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Two masses '$$m_{\mathrm{a}}$$' and '$$\mathrm{m}_{\mathrm{b}}$$' moving with velocities '$$v_{\mathrm{a}}$$' and '$$v_{
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A sample of radioactive element contains $$8 \times 10^{16}$$ active nuclei. The halt-life of the element is 15 days. Th
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In Young's double slit experiment, with a source of light having wavelength $$6300 \mathop A\limits^o$$, the first maxim
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What should be the radius of water drop so that excess pressure inside it is 72 Nm$$^{-2}$$ ? (The surface tension of w
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A body of density $$V$$ is dropped from (at rest) height '$$h$$' into a lake of density '$$\delta$$' $$(\delta > \rho)$$
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A parallel plate air capacitor is charged upto 100 V. A plate 2 mm thick is inserted between the plates. Then to maintai
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A uniformly charged semicircular arc of radius '$$r$$' has linear charge density $$(\lambda)$$, is the electric field at
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The P.E. 'U' of a moving particle of mass 'm' varies with 'x'-axis as shown in figure. The deBroglie wavelength or the p
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An inductive coil has a resistance of $$100 ~\Omega$$. When an a.c. signal of frequency $$1000 \mathrm{~Hz}$$ is applied
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The ratio of radii of gyration of a circular ring and circular disc of the same mass and radius, about an axis passing t
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Two wires carrying currents $$5 \mathrm{~A}$$ and $$2 \mathrm{~A}$$ are enclosed in a circular loop as shown in the figu
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A particle is suspended from a vertical spring which is executing S.H.M. of frequency $$5 \mathrm{~Hz}$$. The spring is
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Photoelectrons are emitted when photons of energy $$4.2 ~\mathrm{eV}$$ are incident on a photosensitive metallic sphere
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A cricket player hit a ball like a projectile but the fielder caught the ball after 2 second. The maximum height reached
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In an ideal step down transformer, out of the following quantities, which quantity increases in the secondary coil?
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An air column in a pipe, which is closed at one end will be in resonance with a vibrating tuning fork of frequency 264 H
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The surface energy of a liquid drop is 'U'. It splits up into 512 equal droplets. The surface energy becomes
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A rectifier is used to
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Two stars 'P' and 'Q' emit yellow and blue light respectively. The relation between their temperatures $$\left(\mathrm{T
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Inside a vessel filled with liquid a converging lens is placed as shown in figure. The lens has focal length $$15 \mathr
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A metal wire of length $$2500 \mathrm{~m}$$ is kept in east-west direction, at a height of $$10 \mathrm{~m}$$ from the g
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A body is projected from earth's surface with thrice the escape velocity from the surface of the earth. What will be its
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The depth at which acceleration due to gravity becomes $$\frac{\mathrm{g}}{\mathrm{n}}$$ is [ $$\mathrm{R}$$ = radius of
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A series LCR circuit with resistance (R) $$500 ~\mathrm{ohm}$$ is connected to an a.c. source of $$250 \mathrm{~V}$$. Wh
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The gyromagnetic ratio of an electron in an hydrogen atom, according to Bohr model is
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A body performs S.H.M. under the action of force '$$\mathrm{F}_1$$' with period '$$\mathrm{T}_1$$' second. If the force
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Beats are produced by waves $$\mathrm{y_1=a\sin2000\pi t}$$ and $$\mathrm{y_2=a\sin2008\pi t}$$. The number of beats hea
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In Young's double slit experiment, the intensity at a point where the path difference is $$\frac{\lambda}{4}$$ [ $$\lamb
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The magnetic field at the centre of a current carrying circular coil of area 'A' is 'B'. The magnetic moment of the coil
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A galvanometer has resistance '$$\mathrm{G}$$' $$\Omega$$ and '$$\mathrm{I}_{\mathrm{g}}$$' is current flowing through i
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In potentiometer experiment, null point is obtained at a particular point for a cell on potentiometer wire '$$\mathrm{x}
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A hollow charged metal sphere has radius 'R'. If the potential difference between its surface and a point at a distance
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The relation between magnetic moment 'M' of revolving electron and principle quantum number 'n' is
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