MHT CET 2021 20th September Morning Shift

Paper was held on
Mon, Sep 20, 2021 3:30 AM

## Chemistry

Which of the following solutions does not flow in either direction, when separated by semipermeable membrane? (Molar mas

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For the reaction, $$3 \mathrm{I}_{(\mathrm{aq})}^{-}+\mathrm{S}_2 \mathrm{O}_{8(\mathrm{aq})}^{2-} \longrightarrow \math

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When alcoholic solution of an organic compound is treated with few drops of Schiff's reagent, pink colour appears. This

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What is O$$-$$O bond length in resonance hybrid of ozone?

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What is the number of unit cells present in 3.9 g of potassium if it crystallizes in BCC structure?

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When 2-Methylbut-2-ene is treated with hydrogen chloride, the major product obtained is

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Which among the following elements has completely filled 4d-orbital?

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Which of the following compounds on reaction with Grignard reagent followed by hydrolysis forms secondary alcohol?

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How many water molecules are present in formula of crystalline chloride of lithium?

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The solubility of AgCl in it's solution is 1.25 $$\times$$ 10$$^{-5}$$ mol dm$$^{-3}$$. What is solubility product of Ag

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The reagent used in Gatterman-Koch formylation of arene is

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Which among the following statements is true for Pt[(NH$$_3$$)$$_2$$Cl$$_2$$] ?

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What type of crystal structure from following has 52.36% packing efficiency?

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The molar conductivity of 0.1 M BaCl$$_2$$ solution is 106 $$\Omega^{-1}$$ cm$$^2$$ mol$$^{-1}$$ at 25$$^\circ$$C. What

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Identify the compound obtained in following reaction?

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A gas occupies 11.2 dm$$^3$$ at 105 kPa. What is it's volume if pressure is increased to 210 kPa?

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Identify the use of Buna-N from following.

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Which from following compounds accepts proton from water molecule according to Bronsted-Lowry theory?

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What amount of oxygen is used at S.T.P. to obtain 9 g water from sufficient amount of hydrogen gas?

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A solution of 6 g of solute in 100 g of water boils at 100.52$$^\circ$$C. The molal elevation constant of water is 0.52

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Which among the following compounds has highest melting point?

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Instantaneous rate of a reaction is $$ - {1 \over 2}{{d[x]} \over {dt}} = - {{d[y]} \over {dt}} = {1 \over 2}{{d[z]} \o

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Which of the following reactions shows work of compression?

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Identify total number carbon atoms present in undecane.

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What is value of percent atom economy if formula weight of product is 46 u and sum of formula weight of all reactants is

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Half life for a first order reaction is 6.93 hour. What is the time required for 80% completion of the reaction?

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What is the number of moles of H atoms required to prepare one mole ethylamine from one mole acetamide?

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If vapour pressure of pure solvent and solution are 240 and 216 mm Hg respectively then mole fraction of solvent in solu

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Identify an orbital with the quantum numbers n = 4, $$l$$ = 3, m = 0.

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The pH of 0.1 M solution of monobasic acid is 2.34. Calculate the degree of dissociation of the acid.

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Calculate change in enthalpy when 39 g acetylene is completely burnt with oxygen and enthalpy of combustion of acetylene

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Which from following is NOT correct regarding electrolysis?

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A conductivity cell shows resistance of 600 ohm. If conductivity of 0.01 M KCl is 0.0015 $$\Omega^{-1}$$ cm$$^{-1}$$, wh

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An element (molar mass 180 ) has BCC crystal structure with density $$18 \mathrm{~g} \mathrm{~cm}^{-3}$$. What is the ed

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What is the number of allotropes of selenium?

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Which among the following is a multi-molecular colloid?

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Which among following statements is NOT true about Gabriel phthalimide synthesis?

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Identify the reagent R used in following reaction?

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Identify highest field strength ligand from following.

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Which among the following compounds is NOT a carbocyclic compound?

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Identify the glycosidic linkage present in lactose.

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Which from following elements of halogen family is in liquid state at room temperature?

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Which of the following compounds on reaction with ammonical silver nitrate solution forms precipitate of silver?

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Which of the following polymers is used in electrophoresis in the form of gel?

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An ideal gas on isothermal reversible compression from 10L to 5L performs 1730J of work at 300 K. Calculate number of mo

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Identify the correct statement about properties of interstitial compounds.

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Which of the following sugar is found in milk?

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How many chiral carbon atoms are present in 2 - Bromo - 3, 4, 5 - trimethylhexane?

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Which among the following is NOT correct statement about $$\mathrm{S_N1}$$ reaction?

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Identify reductant in following reaction.
$$\mathrm{{C_2}O_4^{2 - } + MnO_4^ - + {H^ + } \longrightarrow M{n^{2 + }} +

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## Mathematics

$$\int \tan ^{-1}(\sec x+\tan x) d x=$$

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$$A(\propto)=\left[\begin{array}{cc}\cos \propto & \sin \propto \\ -\sin \propto & \cos \propto\end{array}\right]$$, the

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Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number, is

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If the acute angle between the lines given by $$\mathrm{a x^2+2 h x y+b y^2=0}$$ is $$\frac{\pi}{4}$$, then $$\mathrm{4

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A wire of length 20 units is divided into two parts such that the product of one part and cube of the other part is maxi

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The shaded part of the given figure indicates the feasible region. Then the constraints are

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If the volume of a tetrahedron whose conterminous edges are $$\vec{\mathrm{a}}+\vec{\mathrm{b}}, \vec{\mathrm{b}}+\vec{\

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The joint equation of the pair of lines through the origin and making an equilateral triangle with the line $$x=3$$ is

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If 1 is added to first 10 natural numbers, then variance of the numbers so obtained is

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A random variable X has the following probability distribution
.tg {border-collapse:collapse;border-spacing:0;}
.tg td

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A differential equation for the temperature 'T' of a hot body as a function of time, when it is placed in a bath which i

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$$\int_\limits0^{\pi / 4} \log (1+\tan x) d x=$$

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A particle is moving on a straight line. The distance $$\mathrm{S}$$ travelled in time $$\mathrm{t}$$ is given by $$\mat

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The negation of a statement 'x $$\in$$ A $$\cap$$ B $$\to$$ (x $$\in$$ A and x $$\in$$ B)' is

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The Cartesian equation of the plane passing through the point $$(0,7,-7)$$ and containing the line $$\frac{x+1}{-3}=\fra

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If $$\overline{\mathrm{e}}_1, \overline{\mathrm{e}}_2$$ and $$\overline{\mathrm{e}}_1+\overline{\mathrm{e}}_2$$ are unit

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If $$y=\log \tan \left(\frac{x}{2}\right)+\sin ^{-1}(\cos x)$$, then $$\frac{d y}{d x}=$$

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If $$\overline{\mathrm{a}}, \overline{\mathrm{b}} , \overline{\mathrm{c}}$$ are three vectors which are perpendicular to

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If the lines $$\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$$ and $$\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$$ intersect, th

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If inverse of $$\left[\begin{array}{ccc}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{array}\right]$$ does not exist, then $

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The general solution of the differential equation $$\frac{d y}{d x}=\frac{x+y+1}{x+y-1}$$ is given by

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The logical expression $$\mathrm{p} \wedge(\sim \mathrm{p} \vee \sim \mathrm{q}) \equiv$$

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The parametric equations of a line passing through the points $$\mathrm{A}(3,4,-7)$$ and $$\mathrm{B}(1,-1,6)$$ are

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The value of (1 + i)$$^5$$ (1 $$-$$ i)$$^7$$ is

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Rajesh has just bought a VCR from Maharashtra Electronics and the shop offers after sales service contract for Rs. 1000

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The area of the region bounded by the parabola x$$^2$$ = y and the line y = x is

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If $$A = \left[ {\matrix{
3 & 2 & 4 \cr
1 & 2 & 1 \cr
3 & 2 & 6 \cr
} } \right]$$ and A$$_{ij}$$ are co

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The general solution of the differential equation $$x+y \frac{d y}{d x}=\sec \left(x^2+y^2\right)$$ is

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$$\mathop {\lim }\limits_{x \to \infty } \left( {\sqrt {{x^2} + 5x - 7} - x} \right) = $$

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The differential equation of all circles which pass through the origin and whose centre lie on Y-axis is

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With usual notations if the angles of a triangle are in the ratio 1 : 2 : 3, then their corresponding sides are in the r

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$$(2 \hat{\mathrm{i}}+6 \hat{\mathrm{i}}+27 \hat{\mathrm{k}}) \times(\hat{\mathrm{i}}+\lambda \hat{\mathrm{j}}+\mu \hat{

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If f(x) = |x|, for x $$\in$$ ($$-1,2$$), then f is discontinuous at (where [x] represents floor function)

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The angle between a line with direction ratios 2, 2, 1 and a line joining (3, 1, 4) and (7, 2, 12) is

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The equation of the tangent to the curve $$y = 4x{e^x}$$ at $$\left( { - 1,{{ - 4} \over e}} \right)$$ is

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The slope of the line through the origin which makes an angle of 30$$^\circ$$ with the positive direction of Y-axis meas

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The domain of the function $$f(x)=\frac{1}{\sqrt{x+|x|}}$$ is

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All the letters of the word 'ABRACADABRA' are arranged in different possible ways. Then the number of such arrangements

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If $$\int \frac{1+x^2}{1+x^4} d x=\frac{1}{\sqrt{2}} \tan ^{-1}\left[\frac{f(x)}{\sqrt{2}}\right]+c$$, then $$f(x)=$$

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The value of $$\sin 18^{\circ}$$ is

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If $$4 \sin ^{-1} x+6 \cos ^{-1} x=3 \pi$$, where $$-1 \leq x \leq 1$$, then $$x=$$

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If $$h(x)=\sqrt{4 f(x)+3 g(x)}, f(1)=4, g(1)=3, f^{\prime}(1)=3, g^{\prime}(1)=4$$, then $$h^{\prime}(1)=$$

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If the line $$\frac{x+1}{2}=\frac{y-m}{3}=\frac{z-4}{6}$$ lies in the plane $$3 x-14 y+6 z+49=0$$, then the value of $$m

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If $$x \in\left(0, \frac{\pi}{2}\right)$$ and $$x$$ satisfies the equation $$\sin x \cos x=\frac{1}{4}$$, then the value

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If $$x=a \cos \theta, y=b \sin \theta$$, then $$\left[\frac{d^2 y}{d x^2}\right]_{\theta=\frac{\pi}{4}}=$$

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$$\int \frac{x+\sin x}{1+\cos x} d x=$$

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An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half the quantity of ice melts

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If $$\int_\limits0^{\frac{\pi}{2}} \frac{d x}{5+4 \sin x}=A \tan ^{-1} B$$, then A + B =

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If $$X \sim B(4, p)$$ and $$P(X=0)=\frac{16}{81}$$, then $$P(X=4)=$$

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If the lines $$3x - 4y + 4 = 0$$ and $$6x - 8y - 7 = 0$$ are tangents to a circle, then the radius of the circle is

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## Physics

A mass '$$\mathrm{m}_1$$' is suspended from a spring of negligible mass. A spring is pulled slightly in downward directi

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If the charge to ratio of an electron is 'A' C/kg, then the gyromagnetic ratio of an orbital electron in C/kg is

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A parallel plate capacitor filled with oil of a dielectric constant 3 between the plates has capacitance 'C'. If the oil

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In Young's double slit experiment, the '$$\mathrm{n^{th}}$$' maximum of wavelength '$$\lambda_1$$' is at a distance '$$\

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A perfectly black body emits a radiation at temperature 'T$$_1$$' K. If it is to radiate at 16 times this power, its tem

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Two conducting wire loops are concentric and lie in the same plane. The current in the outer loop is clockwise and incre

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Two particles $$\mathrm{P}$$ and $$\mathrm{Q}$$ performs S.H.M. of same amplitude and frequency along the same straight

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An electric dipole having dipole moment $$\mathrm{P}=\mathrm{q} \times 2 \ell$$ is placed in a uniform electric field '$

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The frequencies of three tuning forks $$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$ are related as $$\mathrm{n}_{\mathrm

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The magnetic field intensity 'H' at the centre of a long solenoid having 'n' turns per unit length and carrying a curren

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One mole of an ideal gas expands adiabatically at constant pressure such that its temperature $$T \propto {1 \over {\sqr

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On an imaginary linear scale of temperature (called 'W' scale) the freezing and boiling points of water are 39$$^\circ$$

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When a d.c. voltage of $$200 \mathrm{~V}$$ is applied to a coil of self-inductance $$\left(\frac{2 \sqrt{3}}{\pi}\right)

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When light of wavelength '$$\lambda$$' is incident on a photosensitive surface, photons of power 'P' are emitted. The nu

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Air is pushed in a soap bubble to increase its radius from 'R' to '2R'. In this case, the pressure inside the bubble

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The equation of wave is given by $$\mathrm{y}=10 \sin \left(\frac{2 \pi \mathrm{t}}{30}+\alpha\right)$$. If the displace

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A uniformly charged half ring of a radius ' $R$ ' has linear charge density '$$\sigma$$'. The electric potential at the

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A sonometer wire resonates with 4 antinodes between two bridges for a given tuning fork, when 1 kg mass is suspended fro

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Let '$$\mathrm{R_1}$$' and '$$\mathrm{R_2}$$' are radii of two mercury drops. A big mercury drop is formed from them und

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A galvanometer of resistance $$50 \Omega$$ is converted to an ammeter. After shunting, the effective resistance of ammet

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The electron in hydrogen atom is initially in the third excited state. When it finally moves to ground state, the maximu

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Two different logic gates moving output '0' for the inputs (0, 1) and then for (1, 0) are

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A straight conductor of length 0.6 M is moved with a speed of 10 ms$$^{-1}$$ perpendicular to magnetic field of inductio

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If the electron in a hydrogen atom moves from ground state orbit to 5th orbit, then the potential energy of the electron

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A particle of mass 5kg is executing S.H.M. with an amplitude 0.3 m and time period $$\frac{\pi}{5}$$s. The maximum value

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The weight of a man in a lift moving upwards with an acceleration 'a' is 620 N. When the lift moves downwards with the s

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Consider the circuit shown in the figure. The value of current 'I' is

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Two bodies '$$\mathrm{A}$$' and '$$\mathrm{B}$$' start from the same point at the same instant and move along a straight

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Light of wavelength '$$\lambda$$' is incident on a single slit of width 'a' and the distance between slit and screen is

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An inductor coil wound uniformly has self inductance
'L' and resistance 'R'. The coil is broken into two identical par

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Two wires of same material of radius 'r' and '2r' respectively are welded together end to end. The combination is then u

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A ray of light travels from a denser medium to a rarer medium. The reflected and the refracted rays are perpendicular to

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Specific heats of an ideal gas at constant pressure and volume are denoted by $$\mathrm{C}_{\mathrm{p}}$$ and $$\mathrm{

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The force required to take away a flat circular plate of radius $$2 \mathrm{~cm}$$ from the surface of water is $$\left[

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The frequency of a given a.c. signal is 'N' Hz. When it is connected to a half wave rectifier, the number of output puls

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A convex lens of focal length 'F' produces a real image 'n' times the size of the object. The image distance is

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A solid sphere of mass $$\mathrm{M}$$, radius $$\mathrm{R}$$ has moment of inertia '$$\mathrm{I}$$' about its diameter.

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The depth 'd' below the surface of the earth where the value of acceleration due to gravity becomes $$\left(\frac{1}{n}\

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Silicon and copper are cooled from 300 K to 100 K, the specific resistance (resistivity)

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Two bodies rotate with kinetic energies 'E$$_1$$' and 'E$$_2$$'. Moments of inertia about their axis of rotation are 'I$

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When a photosensitive surface is irradiated by light of wavelengths '$$\lambda_1$$' and '$$\lambda_2$$', kinetic energie

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An electron (e) moves in circular orbit of radius 'r' with uniform speed 'V'. It produces magnetic field 'B' at the cent

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The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is 'V'. For the satel

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An inductor coil takes current 8A when connected to an 100 V and 50 Hz a.c. source. A pure resistor under the same condi

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A disc of radius 0.4 m and mass one kg rotates about an axis passing through its centre and perpendicular to its plane.

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For a monoatomic gas, work done at constant pressure is W. The heat supplied at constant volume for the same rise in tem

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In Fraunhofer diffraction pattern, slit width is 0.2 mm and screen is at 2m away from the lens. If wavelength of light u

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A spherical conducting shell of inner radius 'r$$_1$$' and outer radius 'r$$_2$$' has a charge 'Q'. A charge $$-$$q is p

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The frequency of a tuning fork is 'n' Hz and velocity of sound in air is 'V' m/s. When the tuning fork completes 'x' vib

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A charge of magnitude '2e' and mass '4m' is moving in an electric field $$\overrightarrow E $$. The acceleration imparte

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