MHT CET 2021 21th September Morning Shift

Paper was held on
Tue, Sep 21, 2021 3:30 AM

## Chemistry

Find the value of $$-197^\circ$$C temperature in Kelvin.

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Identify the hydrolysis product of starch.

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Which carbon atom of ribose sugar is joined to nitrogen base to form nucleoside?

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Identify secondary allylic alcohol from following.

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What is the rate of appearance of $$\mathrm{Z}$$ in following reaction? $$3 \mathrm{x} \rightarrow 2 \mathrm{y}+\mathrm{

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Slope of the graph between rate ( $$\mathrm{Y}$$-axis) and $$[\mathrm{A}](\mathrm{X}$$-axis) for the first order reactio

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Identify the product 'P' of following reaction.
Ethanoyl chloride $$\buildrel {{H_2}O} \over
\longrightarrow $$ P

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Identify the reagent used in following conversion.

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Which of following statements is correct for physisorption?

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Which among the following is NOT an extensive property?

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Which among the following statements is true for conductivity?

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Which among the following salts turns blue litmus red in it's aqueous solution?

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Which from following statements is true for tetrahydrofuran?

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Identify metal halide from following having highest ionic character? (M = metal atom)

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What is spin only magnetic moment of an element having one unpaired electron?

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What is the formal charge on carbon atom in CO$$_3^{2-}$$ ion ?

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What is the pH of 0.02 M NaOH solution?

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Which of the following compounds has lower boiling point?

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A gas is allowed to expand in an insulated container against a constant external pressure of 2.5 atm from $$2.5 \mathrm{

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Which of the following solutions shows positive deviation from Raoult's law?

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Which of the following conjugate bases is stabilized to greater extent due to solvation of ammonia and amines?

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What is vapour pressure of a solution containing 0.1 mol of non-volatile solute dissolved in 16.2 g of water ? (P$$_1^0=

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What is the percentage efficiency of packing in BCC structure?

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Identify amphoteric oxide from following.

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Identify homopolymer from following.

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The molar conductivity of $$0.4 \mathrm{~M} \mathrm{~KCl}$$ solution is $$2.5 \times 10^5 \Omega^{-1} \mathrm{~cm}^2 \ma

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Sunscreen lotions contains nanoparticles of

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Which from following reactions converts carbonyl group of aldehydes and ketones to methylene group on treatment with zin

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Which of the following reactions is used for the conversion of alkyl chloride to alkyl iodide?

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Which of the following amines acts as strongest base?

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Which among the following is NOT a neutral ligand?

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What is the volume (in dm$$^3$$) occupied by 75 g ethane at S.T.P. ?

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Identify the reactant, reagent and condition of Kolbe's reaction from following.

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The wavelength of a spectral line of caesium is $$460 \mathrm{~nm}$$. What is the frequency of spectral line?

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Select the catalyst used in hydrogenation of ethene.

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What is the number of $$-$$CH$$_2$$ - groups present in dodecane?

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Which among the following statements is NOT true?

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An element with simple cubic close structure has edge length of unit cell $$3.86 ~\mathop A\limits^o$$. What is the radi

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In a first order reaction, concentration of reactant is reduced to (1/8)th of concentration in 23.03 minutes. What is ha

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What is boiling point of a decimolal aqueous solution of glucose if molal elevation constant for water is 0.52$$^\circ$$

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What is the work done when a gas is compressed from 2.5 $$\times$$ 10$$^{-2}$$ m$$^3$$ to 1.3 $$\times$$ 10$$^{-2}$$ m$$

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Identify homoleptic complex from following :

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Dissociation constant of propionic acid is $$1.32 \times 10^{-5}$$. Calculate the degree of dissociation of acid in $$0.

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Identify the product obtained when phenol reacts with concentrated sulphuric acid at $$293 \mathrm{~K}$$ ?

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The reaction of propane with bromine in presence of UV light predominantly forms

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Oxidation state of Cr in potassium dichromate is

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What is the volume of unit cell of a metal (at. mass $$25 \mathrm{~g} \mathrm{~mol}^{-1}$$ ) having $$\mathrm{BCC}$$ str

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Which among following monomers is used to prepare PVC?

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What is the number of electrons passed through an electrolyte solution when 1 ampere current is passed for 16.1 minutes?

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Identify reactant (A) used in the following conversion.
Chlorobenzene $$+\mathrm{A} \underset{\mathrm{AlCl}_3}{\stackrel

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## Mathematics

$$2 \sin \left(\theta+\frac{\pi}{3}\right)=\cos \left(\theta-\frac{\pi}{6}\right)$$, then $$\tan \theta=$$

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$$\int[1+2 \tan x(\tan x+\sec x)]^{\frac{1}{2}} d x=
$$

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The general solution of the differential equation $$\left(3 x y+y^2\right) d x+\left(x^2+x y\right) d y=0$$ is

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In a meeting $$60 \%$$ of the members favour and $$40 \%$$ oppose a certain proposal. A member is selected at random and

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The distance between parallel lines
$$\begin{aligned}
& \bar{r}=(2 \hat{i}-\hat{j}+\hat{k})+\lambda(2 \hat{i}+\hat{j}-2

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If $$e^{-y} \cdot y=x$$, then $$\frac{d y}{d x}$$ is

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If the two lines given by $$a x^2+2 h x y+b y^2=0$$ make inclinations $$\propto$$ and $$\beta$$, then $$\tan (\alpha+\be

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The vertices of triangle $$\mathrm{ABC}$$ are $$\mathrm{A} \equiv(3,0,0) ; \mathrm{B} \equiv(0,0,4) ; \mathrm{C} \equiv(

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If the lines $\frac{1-x}{3}=\frac{7 y-14}{2 \lambda}=\frac{z-3}{2}$ and $\frac{7-7 x}{3 \lambda}=\frac{y-5}{1}=\frac{6-z

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A lot of 100 bulbs contains 10 defective bulbs. Five bulbs selected at random from the lot and sent to retain store, the

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The differential equation of family of circles whose centres lie on $$\mathrm{X}$$-axis is

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If $$\frac{\cos (A+B)}{\cos (A-B)}=\frac{\sin (C+D)}{\sin (C-D)}$$, then $$\tan A \tan B \tan C=$$

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The area of the region bounded by the curve y$$^2$$ = 4x and the line y = x is

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The general solution of the differential equation $$y(1+\log x)\left(\frac{d x}{d y}\right)-x \log x=0$$ is

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Negation of the statement $$\forall x \in R, x^2+1=0$$ is

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The Cartesian equation of the plane passing through the point A(7, 8, 6) and parallel to the XY plane is

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If $$F(\propto)=\left[\begin{array}{ccc}\cos \propto & -\sin \propto & 0 \\ \sin \propto & \cos \propto & 0 \\ 0 & 0 & 1

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In a quadrilateral PQRS, M and N are mid-points of the sides PQ and RS respectively. If $$\overline {PS} + \overline {Q

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A coin is tossed and a die is thrown. The probability that the outcome will be head or a number greater than 4 or both,

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If vectors $$\bar{a}=2 \hat{i}+2 \hat{j}+3 \hat{k}, \bar{b}=-\hat{i}+2 \hat{j}+\hat{k}$$ and $$\bar{c}=3 \hat{i}+\hat{j}

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The equation of the plane passing through $$(-2,2,2)$$ and $$(2,-2,-2)$$ and perpendicular to the plane $$9 x-13 y-3 z=0

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The complex number with argument $$\frac{5 \pi^{\mathrm{c}}}{6}$$ at a distance of 2 units from the origin is

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If $$\bar{a}=3 \hat{i}-5 \hat{j}, \bar{b}=6 \hat{i}+3 \hat{j}$$ are two vectors and $$\bar{c}$$ is a vector such that $$

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If the polar co-ordinates of a point are $$\left(\sqrt{2}, \frac{\pi}{4}\right)$$, then its Cartesian co-ordinates are

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The equation of the circle whose centre lies on the line $$x-4 y=1$$ and which passes through the points $$(3,7)$$ and $

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$$\int_\limits0^{\frac{\pi}{2}} \frac{\sin x-\cos x}{1-\sin x \cos x} d x=$$

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If $$A=\left[\begin{array}{ccc}1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1\end{array}\right], \operatorname{adj} A=\left[\begi

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The shaded figure given below is the solution set for the linear inequations. Choose the correct option.

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$$\begin{aligned}
& \text { If the function } \mathrm{f}(\mathrm{x})=1+\sin \frac{\pi}{2}, \quad-\infty
is continuous in

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If $$\int \frac{x^3}{\sqrt{1+x^2}} d x=a\left(1+x^2\right)^{\frac{3}{2}}+b \sqrt{1+x^2}+c$$, then $$a+b=$$, (where $$c$$

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$$\mathrm{A}^{-1}=\frac{-1}{2}\left[\begin{array}{cc}1 & -4 \\ -1 & 2\end{array}\right]$$, then $$2 A+I_2=\quad$$
where

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If $$y=\operatorname{cosec}^{-1}\left[\frac{\sqrt{x}+1}{\sqrt{x}-1}\right]+\cos ^{-1}\left[\frac{\sqrt{x}-1}{\sqrt{x}+1}

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If $$f(x)=|x-1|+|x-2|+|x-3|, \forall x \in[1,4]$$, then $$\int_\limits1^4 f(x) d x=$$

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The general solution of the differential equation $$\frac{d y}{d x}=\frac{x+2 y-1}{x+2 y+1}$$ is

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If $$\mathrm{X}$$ is a random variable with p.m.f. as follows.
$$\begin{aligned}
\mathrm{P}(\mathrm{X}=\mathrm{x}) & =\f

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A body at an unknown temperature is placed in a room which is held at a constant temperature of $$30^{\circ} \mathrm{F}$

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The equation of a line passing through $$(\mathrm{p} \cos \propto, \mathrm{p} \sin \propto)$$ ) and making an angle $$(9

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If $$|\bar{a}|=3,|\bar{b}|=4,|\bar{a}-\bar{b}|=5$$, then $$|\bar{a}+\bar{b}|=$$

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$$\tan ^{-1}\left(\frac{x-1}{x-2}\right)+\tan ^{-1}\left(\frac{x+1}{x+2}\right)=\frac{\pi}{4}$$, then the values of $$x$

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If f(x) = 3[x] + 5{x + 1}, where [x] is greatest integer function of x and {x} is fractional part function of x, then f(

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A stone is thrown into a quite lake and the waves formed move in circles. If the radius of a circular wave increases at

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The function $$f(x)=\cot ^{-1} x+x$$ is increasing in the interval.

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$$\lim _\limits{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^2+x-3}=$$

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The derivative of $$(\log x)^x$$ with respect to $$\log x$$ is

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$$\int e^{\tan x}\left(\sec ^2 x+\sec ^3 x \sin x\right) d x=$$

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The product of the perpendicular distances from $$(2,-1)$$ to the pair of lines $$2 x^2-5 x y+2 y^2=0$$ is

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For two data sets each of size 5 , the variance are given to be 4 and 5 and the corresponding means are given to be 2 an

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The number of ways in which 8 different pearls can be arranged to form a necklace is

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If $$p, q$$ are true statements and $$r$$ is false statement, then which of the following is correct.

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The curves $$\frac{x^2}{a^2}+\frac{y^2}{4}=1$$ and $$y^3=16 x$$ intersect each other orthogonally, then $$a^2=$$

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## Physics

The magnetic potential energy stored in a certain inductor is $$25 \mathrm{~mJ}$$, when the current in the inductor is $

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A pendulum is oscillating with frequency '$$n$$' on the surface of the earth. It is taken to a depth $$\frac{R}{2}$$ bel

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

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In a pure silicon, number of electrons and holes per unit volume are $$1.6 \times 10^{16} \mathrm{~m}^{-3}$$. If silicon

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A charge moves with velocity '$$V$$' through electric field $$(E)$$ as well as magnetic field (B). then the force acting

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Light of frequency two times the threshold frequency is incident on photosensitive material. If the incident frequency i

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For a transitor, $$\frac{1}{\alpha_{\mathrm{DC}}}-\frac{1}{\beta_{\mathrm{DC}}}$$ is equal to [ $$\alpha_{\mathrm{DC}}$$

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In diffraction experiment, from a single slit, the angular width of central maximum does NOT depend upon

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The resultant capacity between points A and B in the given circuit is

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When an electron in hydrogen atom jumps from third excited state to the ground state, the de-Broglie wavelength associat

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A long solenoid carrying a current produces a magnetic field B along its axis. If the number of turns per $$\mathrm{cm}$

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A ray of light is incident at an angle 'I' on one face of thin prism. The ray emerges normally from the other face. Refr

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The temperature difference bewtween two sides of metal plate, $$3 \mathrm{~cm}$$ thick is $$15^{\circ} \mathrm{C}$$. Hea

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The current in the following circuit is

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A particle of mass '$$m$$' collides with another stationary particle of mass '$$M$$'. A particle of mass '$$\mathrm{m}$$

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An air filled parallel plate capacitor has a capacity $$2 \mathrm{~pF}$$. The sepeartion of the plates is doubled and th

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A black body has maximum wavelength '$$\lambda_{\mathrm{m}}$$' at temperature $$2000 \mathrm{~K}$$. Its corresponding wa

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A monoatomic gas at pressure '$$\mathrm{P}$$' having volume '$$\mathrm{V}$$' expands isothermally to a volume $$2 \mathr

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A particle moves in a circular orbit of radius '$$r$$' under a central attractive force, $$F=-\frac{k}{r}$$, where $$\ma

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A black reactangular surface of area '$$a$$' emits energy '$$\mathrm{E}$$' per second at $$27^{\circ} \mathrm{C}$$. If l

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A closed organ pipe of length '$$\mathrm{L}_c$$' and an open organ pipe of length '$$\mathrm{L}_{\mathrm{o}}$$' contain

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The moment of inertia of a circular disc of radius $$2 \mathrm{~m}$$ and mass $$1 \mathrm{~kg}$$ about an axis XY passin

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A progressive wave of frequency 50 Hz is travelling with velocity 350 m/s through a medium. The change in phase at a giv

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Find the value of $$-$$197$$^\circ$$C temperature in Kelvin.

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The surface tension of most of the liquid decreases with rise in

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Which one of the following equations specifies an isobaric process? $$[Q=$$ heat supplied $$\Delta P, \Delta V$$ and $$\

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A simple harmonic progressive wave is given by $$Y=Y_0 \sin 2 \pi\left(n t-\frac{x}{\lambda}\right)$$. If the wave veloc

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In a meter bridge experiment, the balance point is obtained at length $$\ell_1 \mathrm{~cm}$$ from left end when resista

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In the graphical representation of e.m.f. '$$\mathrm{e}$$' and current '$$\mathrm{i}$$' versus '$$\omega \mathrm{t}$$' f

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The moment of inertia of a body about a given axis is $$1.2 \mathrm{~kg} / \mathrm{m}^3$$. Initially the body is at rest

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An alternating voltge is represented by $$\mathrm{V}=80 \sin (100 \pi \mathrm{t}) \cos (100 \pi \mathrm{t})$$ volt. The

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When the value of acceleration due to gravity '$$g$$' becomes $$\frac{g}{3}$$ above surface of height '$$h$$' then relat

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In biprism experiment, 21 fringes are observed in a given region using light of wavelength 4800 $$\mathop A\limits^o $$.

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A wire of length '$$L$$'; having resistance '$$R$$' falls from a height '$$\ell$$' in earth's horizontal magnetic field

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Two wires '$$\mathrm{A}$$' and '$$\mathrm{B}$$' of equal length are connected in left and right gap respectively of mete

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A glass cube of length $$24 \mathrm{~cm}$$ has a small air bubble trapped inside. When viewed normally from one face it

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What is susceptibility of a medium, if its relative permeability is 0.85?

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In fundamental mode, the time required for the sound wave to reach upto the closed end of pipe filled with air is $$t$$

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A particle of mass '$$m$$' is kept at rest at a height $$3 R$$ from the surface of earth, where '$$R$$' is radius of ear

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'$$\mathrm{F}$$' is the force between the two identical charged particles placed at a distance '$$\mathrm{Y}$$' from eac

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A coil of radius '$$\mathrm{r}$$' is placed on another coil (whose radius is '$$\mathrm{R}$$' and current through it is

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'$$\lambda_1$$' is the wavelength of series limit of Lyman series, '$$\lambda_2$$' is the wavelength of the first line l

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The velocity of a small ball of mass '$$M$$' and density '$$\mathrm{d}_1$$' when dropped in a container filled with glyc

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A sphere of mass 25 gram is placed on a vertical spring. It is compressed by $$0.2 \mathrm{~m}$$ using a force $$5 \math

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A bomb is dropped by an aeroplane flying horizontally with a velocity $$200 \mathrm{~km} / \mathrm{hr}$$ and at a height

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A series combination of resistor 'R' and capacitor 'C' is connected to an a.c. source of angular frequency '$$\omega$$'.

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A double slit experiment is immersed in water of refractive index 1.33. The slit separationis 1 $$\mathrm{mm}$$ and the

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Two small drops of mercury each of radius '$$R$$' coalesce to form a large single drop. The ratio of the total surface e

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On a photosensitive surface, if the intensity of incident radiation is increased, the stopping potential

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A particle executes linear S.H.M.
The mean position of oscillation is at the principal axis of a convex lens of focal le

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