MHT CET 2023 14th May Evening Shift
Paper was held on Sun, May 14, 2023 9:30 AM
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Chemistry

Which of the following is a structural formula of DDT?
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Which among the following is haloalkyne?
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What type of peptide is the glycylalanine?
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What is Henry's law constant of a gas if solubility of gas in water at $$25^{\circ} \mathrm{C}$$ is $$0.028 \mathrm{~mol
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Calculate the rate constant of the first order reaction if $$80 \%$$ of the reactant decomposes in 60 minutes.
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Which from following polymers is classified fibres depending on inter molecular forces?
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Calculate the frequency if wavelength is $$750 \mathrm{~nm}$$.
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Calculate the edge length of bcc unit cell if radius of metal atom is $$227 \mathrm{~pm}$$.
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Identify the compound '$$\mathrm{A}$$' in the following sequence of reactions. $$\text { A } \xrightarrow[\text { Dryeth
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A solution of nonvolatile solute is obtained by dissolving $$15 \mathrm{~g}$$ in $$200 \mathrm{~mL}$$ water has depressi
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For a reaction $$\mathrm{A}+\mathrm{B} \rightarrow$$ products $$\Delta \mathrm{H}$$ is $$-84.2 \mathrm{~kJ}$$ and $$\Del
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The solubility product of $$\mathrm{PbCl}_2$$ at $$298 \mathrm{~K}$$ is $$3.2 \times 10^{-5}$$. What is its solubility i
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Which among the following elements does NOT exhibit ferromagnetic properties?
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Which of the following is a secondary allylic alcohol?
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Which from following elements is in liquid state at room temperature?
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Identify major product formed in the following reaction. 3-Bromo-2-methylpentane $$\xrightarrow[\Delta]{\text { Alc.KOH
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What is molecular formula of cyclohexylamine?
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Identify base$$_2$$ for following equation according to Bronsted-Lowry theory. $$\mathrm{HCl}_{(\mathrm{aq})}+\mathrm{H}
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Which of the following is Clemmensen reduction?
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Which of the following gases is readily adsorbed by solid adsorbent?
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Which from following is an example of two dimensional nanostructures?
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A conductivity cell containing $$0.001 \mathrm{~M} \mathrm{~AgNO}_3$$ solution develops resistance $$6530 \mathrm{ohm}$$
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What is the number of $$\mathrm{sp}^3$$ hybrid carbon atoms in $$\mathrm{HO}\left(\mathrm{CH}_2\right)_3 \mathrm{CH}\lef
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Which from following thermodynamic properties is a path function?
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Which among the following species is reduced by tin easily?
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Which from following combinations is an example for construction of n-type semiconductor?
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Calculate the density of metal having molar mass $$210 \mathrm{~g} \mathrm{~mol}^{-1}$$ that forms simple cubic unit cel
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Which element from following rapidly loses its luster in air and tarnishes?
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A neon-dioxygen mixture contains $$64 \mathrm{~g} \mathrm{~O}_2$$ and $$160 \mathrm{~g} \mathrm{~Ne}$$. If the total pre
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Identify anionic sphere complex from following.
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What is the number of moles of ethane obtained from $$2 n$$ moles of bromomethane using $$2 n$$ moles of sodium atoms in
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Calculate $$\mathrm{E}_{\text {cell }}^0$$ for $$\mathrm{Cd}_{(\mathrm{s})}\left|\mathrm{Cd}_{(\mathrm{1M})}^{++}\right|
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Find the number of unpaired electrons for copper in ground state configuration.
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Identify the element having highest ionization enthalpy.
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What is the oxidation number of $$\mathrm{Pt}$$ in $$\mathrm{PtCl}_6^{2-}$$ ?
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What is the value of rate constant for first order reaction if slope for the graph of rate versus concentration is $$2.5
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An organic monobasic acid has dissociation constant $$2.25 \times 10^{-6}$$. What is percent dissociation in its $$0.01
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Which of the following pair of compounds demonstrates the law of multiple proportions?
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Which of the following amines on heating with chloroform generate foul smelling product?
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The rate law for the reaction $$\mathrm{A}+\mathrm{B} \rightarrow$$ product is rate $$=\mathrm{k}[\mathrm{A}][\mathrm{B}
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What is IUPAC name of following compound?
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Identify substrate 'A' in the following reaction. 2nA $$\mathrm{\buildrel {Dimethyl\,cadmium} \over \longrightarrow}$$
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Which of the following is NOT a basic amino acid?
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Calculate the PV type of work for the following reaction at 1 bar pressure. $$\mathrm{\mathop {{C_3}{H_{6(g)}}}\limits_{
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Which among the following is NOT dicarboxylic acid?
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Identify the element having positive electron gain enthalpy.
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Identify the use of HDP from following.
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Which coordination complex from following contains neutral ligand?
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What type of following solutions is the gasoline?
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What is formal charge on carbon in the following Lewis structure? Image
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Mathematics

Let $$z \in C$$ with $$\operatorname{Im}(z)=10$$ and it satisfies $$\frac{2 z-n}{2 z+n}=2 i-1, i=\sqrt{-1}$$ for some na
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Let $$\bar{a}=2 \hat{i}+\hat{j}-2 \hat{k}$$ and $$\bar{b}=\hat{i}+\hat{j}$$. If $$\bar{c}$$ is a vector such that $$\bar
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If both mean and variance of 50 observations $$x_1, x_2, \ldots, x_{50}$$ are equal to 16 and 256 respectively, then mea
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If the statement $$\mathrm{p} \leftrightarrow(\mathrm{q} \rightarrow \mathrm{p})$$ is false, then true statement/stateme
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If $$|\bar{a}|=2,|\bar{b}|=3,|\bar{c}|=5$$ and each of the angles between the vectors $$\bar{a}$$ and $$\bar{b}, \bar{b}
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The shaded region in the following figure represents the solution set for a certain linear programming problem. Then lin
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The function $\mathrm{f}$ defined on $$\left(-\frac{1}{3}, \frac{1}{3}\right)$$ by $$\mathrm{f}(x)=\left\{\begin{array}{
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The mirror image of $$\mathrm{P}(2,4,-1)$$ in the plane $$x-y+2 z-2=0$$ is $$(\mathrm{a}, \mathrm{b}, \mathrm{c})$$, the
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If the slope of the tangent of the curve at any point is equal to $$-y+\mathrm{e}^{-x}$$, then the equation of the curve
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If $$A=\left[\begin{array}{ll}1 & -1 \\ 2 & -1\end{array}\right], B=\left[\begin{array}{cc}1 & 1 \\ 4 & -1\end{array}\ri
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The function $$\mathrm{f}(x)=x^3-6 x^2+9 x+2$$ has maximum value when $$x$$ is
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If $$I_n=\int_\limits0^{\frac{\pi}{4}} \tan ^n \theta d \theta$$, then $$I_{12}+I_{10}=$$
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The centre of the circle whose radius is 3 units and touching internally the circle $$x^2+y^2-4 x-6 y-12=0$$ at the poin
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A fair die with numbers 1 to 6 on their faces is thrown. Let $$\mathrm{X}$$ denote the number of factors of the number,
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Let $$\overline{\mathrm{u}}, \overline{\mathrm{v}}$$ and $$\overline{\mathrm{w}}$$ be the vectors such that $$|\overline
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If $$y=4 x-5$$ is a tangent to the curve $$y^2=\mathrm{p} x^3+\mathrm{q}$$ at $$(2,3)$$, then $$\mathrm{p}-\mathrm{q}$$
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If $$x=\sqrt{\mathrm{e}^{\sin ^{-1} t}}$$ and $$y=\sqrt{\mathrm{e}^{\cos ^{-1} t}}$$, then $$\frac{\mathrm{d}^2 y}{\math
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If $$\sum_\limits{r=1}^{50} \tan ^{-1} \frac{1}{2 r^2}=p$$ then $$\tan p$$ is
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The value of $$\int \mathrm{e}^x\left(\frac{x^2+4 x+4}{(x+4)^2}\right) \mathrm{d} x$$ is :
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The diagonal of a square is changing at the rate of $$0.5 \mathrm{~cm} / \mathrm{sec}$$. Then the rate of change of area
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Let $$\bar{a}=\hat{i}+2 \hat{j}-\hat{k}$$ and $$\bar{b}=\hat{i}+\hat{j}-\hat{k}$$ be two vectors. If $$\bar{c}$$ is a ve
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Let $$P \equiv(-3,0), Q \equiv(0,0)$$ and $$R \equiv(3,3 \sqrt{3})$$ be three points. Then the equation of the bisector
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If in a regular polygon, the number of diagonals are 54, then the number of sides of the polygon are
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Let $$x_0$$ be the point of local minima of $$\mathrm{f}(x)=\overline{\mathrm{a}} \cdot(\overline{\mathrm{b}} \times \ov
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If a body cools from $$80^{\circ} \mathrm{C}$$ to $$50^{\circ} \mathrm{C}$$ in the room temperature of $$25^{\circ} \mat
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If $$f(a)=2, f^{\prime}(a)=1, g(a)=-1, g^{\prime}(a)=2$$, then as $$x$$ approaches a, $$\frac{\mathrm{g}(x) \mathrm{f}(\
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The differential equation representing the family of curves $$y^2=2 \mathrm{c}(x+\sqrt{\mathrm{c}})$$, where $$\mathrm{c
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If $$\cos ^{-1} x-\cos ^{-1} \frac{y}{3}=\alpha$$, where $$-1 \leq x \leq 1$, $-3 \leq y \leq 3, x \leq \frac{y}{3}$$, t
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In a triangle $$\mathrm{A B C, m \angle A, m \angle B, m \angle C}$$ are in A.P. and lengths of two larger sides are 10
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The value of $$\tan ^{-1}\left(\frac{1}{8}\right)+\tan ^{-1}\left(\frac{1}{2}\right)+\tan ^{-1}\left(\frac{1}{5}\right)$
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The p.m.f. of a random variable $$\mathrm{X}$$ is $$\mathrm{P}(x)=\left\{\begin{array}{cl}\frac{2 x}{\mathrm{n}(\mathrm{
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If the lines $$\frac{x-\mathrm{k}}{2}=\frac{y+1}{3}=\frac{\mathrm{z}-1}{4}$$ and $$\frac{x-3}{1}=\frac{y-\frac{9}{2}}{2}
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If $$|\vec{a}|=3 ;|\vec{b}|=5 ; \bar{b} \cdot \bar{c}=10$$, angle between $$\overline{\mathrm{b}}$$ and $$\overline{\mat
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If $$\int \frac{x^2}{\sqrt{1-x}} \mathrm{~d} x=\mathrm{p} \sqrt{1-x}\left(3 x^2+4 x+8\right)+\mathrm{c}$$ where $$\mathr
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The centroid of the triangle formed by the lines $$x+3 y=10$$ and $$6 x^2+x y-y^2=0$$ is
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The statement $$[\mathrm{p} \wedge(\mathrm{q} \vee \mathrm{r})] \vee[\sim \mathrm{r} \wedge \sim \mathrm{q} \wedge \math
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If $$\mathrm{f}(x)=\frac{2 x-3}{3 x-4}, x \neq \frac{4}{3}$$, then the value of $$\mathrm{f}^{-1}(x)$$ is
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If $$\mathrm{f}^{\prime}(x)=\sin (\log x)$$ and $$y=\mathrm{f}\left(\frac{2 x+3}{3-2 x}\right)$$, then $$\frac{\mathrm{d
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The area bounded by the curve $$y=|x-2|, x=1, x=3$$ and $$X$$-axis is
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$$\int \frac{\mathrm{d} x}{\cot ^2 x-1}=\frac{1}{\mathrm{~A}} \log |\sec 2 x+\tan 2 x|-\frac{x}{\mathrm{~B}}+\mathrm{c}$
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There are 6 positive and 8 negative numbers. From these four numbers are chosen at random and multiplied. Then the proba
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If $$\mathrm{a} \cos 2 \theta+\mathrm{b} \sin 2 \theta=\mathrm{c}$$ has $$\alpha$$ and $$\beta$$ as its roots, then the
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A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to retail st
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Given $$0 \leq x \leq \frac{1}{2}$$, then the value of $$\tan \left(\sin ^{-1}\left(\frac{x}{\sqrt{2}}+\frac{\sqrt{1-x^2
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A vector parallel to the line of intersection of the planes $$\bar{r} \cdot(3 \hat{i}-\hat{j}+\hat{k})=1$$ and $$\bar{r}
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The length of the perpendicular drawn from the point $$(1,2,3)$$ to the line $$\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2
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If $$I=\int \frac{d x}{\sin (x-a) \sin (x-b)}$$, then I is given by
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Let $$\mathrm{P}(x)$$ be a polynomial of degree 2, with $$\mathrm{P}(2)=-1, \mathrm{P}^{\prime}(2)=0, \mathrm{P}^{\prime
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If $$y=\sqrt{(x-\sin x)+\sqrt{(x-\sin x)+\sqrt{(x-\sin x) \ldots.}}}$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}=$$
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Let $$\mathrm{f}(x)=5-|x-2|$$ and $$\mathrm{g}(x)=|x+1|, x \in \mathrm{R}$$ If $$\mathrm{f}(x)$$ attains maximum value a
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Physics

The power factor of an R-L circuit is $$\frac{1}{\sqrt{2}}$$. If the frequency of $$\mathrm{AC}$$ is doubled the power f
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Ratio of longest wavelength corresponding to Lyman and Balmer series in hydrogen spectrum is
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A uniform circular disc of mass $$12 \mathrm{~kg}$$ is held by two identical springs. When the disc is slightly pressed
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A charge $$17.7 \times 10^{-4} \mathrm{C}$$ is distributed uniformly over a large sheet of area $$200 \mathrm{~m}^2$$. T
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Sound waves of frequency $$600 \mathrm{~Hz}$$ fall normally on a perfectly reflecting wall. The shortest distance from t
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A long solenoid has 1500 turns. When a current of $$3.5 \mathrm{~A}$$ flows through it, the magnetic flux linked with ea
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A metal rod cools at the rate of $$4{ }^{\circ} \mathrm{C} / \mathrm{min}$$ whon its temperature is $$90^{\circ} \mathrm
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On replacing a thin film of mica of thickness $$12 \times 10^{-5} \mathrm{~cm}$$ in the path of one of the interfering b
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In the hysteresis curve the value of magnetization (B) which will be present in a substance when value of magnetizing fo
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The output of following combination is same as that of
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A parallel plate capacitor with air medium between the plates has a capacitance of $$10 \mu \mathrm{F}$$. The area of ca
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Refractive index of a glass convex lens is 1.5. The radius of curvature of each of the two surfaces of the lens is $$20
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Earth is assumed to be a sphere of radius R. If '$$\mathrm{g}_\phi$$' is value of effective acceleration due to gravity
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Four identical uniform solid spheres each of same mass '$$M$$' and radius '$$R$$' are placed touching each other as show
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Two condensers one of capacity $$\frac{\mathrm{C}}{2}$$ and other capacity $$\mathrm{C}$$ are connected to a battery of
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When two light waves each of amplitude '$$A$$' and having a phase difference of $$\frac{\pi}{2}$$ superimposed then the
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In an n-p-n transistor, the collector current is $$28 \mathrm{~mA}$$. If $$80 \%$$ of electrons reach the collector, its
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A light spring is suspended with mass $$m_1$$ at its lower end and its upper end fixed to a rigid support. The mass is p
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The molecular mass of a gas having r.m.s. speed four times as that of another gas having molecular mass 32 is
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The position '$$x$$' of a particle varies with a time as $$x=a t^2-b t^3$$ where '$$a$$' and '$$b$$' are constants. The
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When the conductivity of a semiconductor is only due to the breaking of the covalent bonds, the semiconductor is called
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A coil having effective area A, is held with its plane normal to magnetic field of induction B. The magnetic induction i
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At constant temperature, increasing the pressure of a gas by $$5 \%$$ its volume will decrease by
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Half life of radio-active element is 1600 years. The fraction of sample remains undecayed after 6400 years will be
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Figure shows two semicircular loops of radii $$R_1$$ and $$R_2$$ carrying current $I$. The magnetic field at the common
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When radiation of wavelength '$$\lambda$$' is incident on a metallic surface, the stopping potential is 4.8 V. If the su
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A long wire is bent into a circular coil of one turn and then into a circular coil of smaller radius having $$\mathrm{n}
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When moving coil galvanometer (MCG) is converted into a voltmeter, the series resistance is '$$n$$' times the resistance
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The self induction (L) produced by solenoid of length '$$l$$' having '$$\mathrm{N}$$' number of turns and cross sectiona
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A wire $$P Q$$ has length $$4.8 \mathrm{~m}$$ and mass $$0.06 \mathrm{~kg}$$. Another wire QR has length $$2.56 \mathrm{
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When a monochromatic ray of light is passed through an equilateral glass prism, it is found that the refracted ray in gl
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A solid cylinder and a solid sphere having same mass and same radius roll down on the same inclined plane. The ratio of
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An alternating voltage $$E=200 \sqrt{2} \sin (100 t)$$ volt is connected to a $$1 \mu \mathrm{f}$$ capacitor through an
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A sonometer wire $$49 \mathrm{~cm}$$ long is in unison with a tuning fork of frequency '$$n$$'. If the length of the wir
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Two spherical soap bubbles of radii '$$a$$' and '$$b$$' in vacuum coalesce under isothermal conditions. The resulting bu
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A mass '$$M$$' is moving with constant velocity parallel to $$\mathrm{X}$$-axis. Its angular momentum with respect to th
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A block of mass '$$M$$' rests on a piston executing S.H.M. of period one second. The amplitude of oscillations, so that
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A machine gun fires bullets of mass $$30 \mathrm{~g}$$ with velocity of $$1000 \mathrm{~m} / \mathrm{s}$$. The man holdi
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The temperature of a gas is measure of
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A body (mass $$\mathrm{m}$$ ) starts its motion from rest from a point distant $$R_0\left(R_0>R\right)$$ from the centre
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An ideal refrigerator has freezer at a temperature of $$-13^{\circ} \mathrm{C}$$. The coefficient of performance of the
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1000 small water drops of equal size combine to form a big drop. The ratio of final surface energy to the total initial
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It is easier to spray water to which soap is added because addition of soap to water
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What will be the phase difference between virtual voltage and virtual current when current in the circuit is wattless?
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Two wavelengths of sodium light $$590 \mathrm{~nm}$$ and $$596 \mathrm{~nm}$$ are used one after another to study diffra
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A coil having an inductance of $$\frac{1}{\pi} \mathrm{H}$$ is connected in series with a resistance of $$300 \Omega$$.
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The pressure and density of a diatomic gas $$\left(\gamma=\frac{7}{5}\right)$$ changes adiabatically from $$(\mathrm{P},
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A source of sound is moving towards a stationary observer with $$\left(\frac{1}{10}\right)^{\text {th }}$$ the of the sp
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If $$\mathrm{E}_{\mathrm{a}}$$ and $$\mathrm{E}_{\mathrm{q}}$$ represent the electric field intensity due to a short dip
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In potentiometer experiment, the balancing length is $$8 \mathrm{~m}$$ when two cells $$E_1$$ and $$E_2$$ are joined in
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