MHT CET 2023 14th May Morning Shift
Paper was held on Sun, May 14, 2023 3:30 AM
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Chemistry

Which from following molecules does NOT contain nitrogen in it?
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Calculate the volume of unit cell if an element having molar mass $$56 \mathrm{~g} \mathrm{~mol}^{-1}$$ that forms bcc u
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Find the number of orbitals and maximum electrons respectively present in $$\mathrm{M}$$-shell?
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Which from following expressions is used to find the cell potential of $$\mathrm{Cd}_{(\mathrm{s})}\left|\mathrm{Cd}_{(\
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Which of the following is formed when propene is heated with bromine at high temperature?
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Identify the product '$$B$$' in the following sequence of reactions. $$\mathrm{CH}_3 \mathrm{Br} \xrightarrow{\mathrm{KC
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Identify '$$\mathrm{A}$$' in the following reaction. A+ Acetic anhydride $$\xrightarrow{\mathrm{H}^{+}}$$ Aspirin + Acet
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What is the value of $$\angle \mathrm{S}-\mathrm{S}-\mathrm{S}$$ in puckered $$\mathrm{S}_8$$ rhombic sulfur?
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Identify the reagent used in the following reaction. Benzoic acid $$\xrightarrow[\Delta]{\text { Reagent }}$$ Benzoyl ch
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Which activity from following is exhibited by Lewis base according to definition?
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Which of the following ion has greater coagulating power for negatively charged sol?
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If enthalpy change for following reaction at $$300 \mathrm{~K}$$ is $$+7 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ find the entr
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Identify the polymer obtained from
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What is IUPAC name of the following compound?
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Calculate the $$\mathrm{pH}$$ of $$0.01 \mathrm{~M}$$ strong dibasic acid.
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Which among the following cations produces colourless aqueous solution in their respective oxidation state?
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What is the number of moles of electrons gained by one mole oxidizing agent in following redox reaction? $$\mathrm{Zn_{(
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Find the temperature in degree Celsius if volume and pressure of 2 mole ideal gas is $$20 \mathrm{~dm}^3$$ and $$4.926 \
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What is the geometry of $$\mathrm{PCl}_5$$ molecule as per VSEPR?
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What is coordination number of central metal ion in $$\left[\mathrm{Fe}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{
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Which among the following is NOT a true statement for enantiomers?
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Which from following formulae is of sodium hexanitrocobaltate(III)?
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Which isomer among the following has the highest boiling point?
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Which element from following exhibits the highest number of allotropes?
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Which of the following is a pair of dihydric phenols?
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Calculate $$\Delta \mathrm{H}$$ for following reaction, at $$25{ }^{\circ} \mathrm{C}$$. $$\mathrm{NH}_2 \mathrm{CN}_{(\
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What is number of atoms present in $$2.24 \mathrm{~dm}^3 \mathrm{~NH}_{3(\mathrm{~g})}$$ at STP?
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What is the number of moles of tertiary carbon atoms in a molecule of isobutane?
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According to carbinol system, name of isopropyl alcohol is
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Calculate the relative lowering of vapour pressure if the vapour pressure of benzene and vapour pressure of solution of
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Which from following is NOT true about voltaic cell?
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Calculate the percent atom economy when a product of formula weight $$175 \mathrm{u}$$ is obtained in a chemical reactio
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Identify false statement regarding isothermal process from following.
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Calculate dissociation constant of $$0.001 \mathrm{M}$$ weak monoacidic base undergoing $$2 \%$$ dissociation.
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Find the rate law for the reaction, $$\mathrm{CHCl}_{3(\mathrm{~g})}+\mathrm{Cl}_{2(\mathrm{~g})} \rightarrow \mathrm{CC
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The rate for reaction $$2 \mathrm{~A}+\mathrm{B} \rightarrow$$ product is $$6 \times 10^{-4} \mathrm{~mol} \mathrm{~dm}^
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Calculate molar conductivity of $$\mathrm{NH}_4 \mathrm{OH}$$ at infinite dilution if molar conductivities of $$\mathrm{
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Calculate radius of third orbit of $$\mathrm{He}^{+}$$.
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Calculate the depression in freezing point of solution when $$4 \mathrm{~g}$$ nonvolatile solute of molar mass $$126 \ma
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In an ionic crystalline solid, atoms of element Y forms hep structure. The atoms of element X occupy one third of tetrah
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What is total number of crystal systems associated with 14 Bravais lattices?
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Which from following catalyst is used in decomposition of $$\mathrm{KCl}_3$$ ?
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Which from following polymers is used to obtain plastic dinner ware?
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Identify non reducing sugar from following.
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In which of the following carbohydrate, molecular mass increases by $$84 \mathrm{u}$$ after complete acetylation?
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Which element from following exhibits common oxidation state +2 ?
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Calculate half life of first order reaction if rate constant of reaction is $$2.772 \times 10^{-3} \mathrm{~s}^{-1}$$
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Which among the following is NOT colligative property?
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Identify the reaction in which carbonyl group of aldehydes and ketones is reduced to methylene group on treatment with h
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Identify the product '$$\mathrm{B}$$' in the following reaction. Toluene $$\xrightarrow[\mathrm{CS}_2]{\text { Chromylch
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Mathematics

The negation of the statement "The number is an odd number if and only if it is divisible by 3."
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Two cards are drawn successively with replacement from well shuffled pack of 52 cards, then the probability distribution
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For an initial screening of an entrance exam, a candidate is given fifty problems to solve. If the probability that the
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General solution of the differential equation $$\cos x(1+\cos y) \mathrm{d} x-\sin y(1+\sin x) \mathrm{d} y=0$$ is
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The variance of 20 observations is 5. If each observation is multiplied by 2, then variance of resulting observations is
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The statement $$[(p \rightarrow q) \wedge \sim q] \rightarrow r$$ is tautology, when $$r$$ is equivalent to
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The solution set of the inequalities $$4 x+3 y \leq 60, y \geq 2 x, x \geq 3, x, y \geq 0$$ is represented by region
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If the line $$x-2 y=\mathrm{m}(\mathrm{m} \in \mathrm{Z})$$ intersects the circle $$x^2+y^2=2 x+4 y$$ at two distinct po
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If $$\bar{a}, \bar{b}, \bar{c}$$ are three vectors such that $$|\bar{a}+\bar{b}+\bar{c}|=1, \overline{\mathrm{c}}=\lambd
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The equation $$x^3+x-1=0$$ has
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Let $$\bar{a}, \bar{b}, \bar{c}$$ be three vectors such that $$|\bar{a}|=\sqrt{3}, |\bar{b}|=5, \bar{b} \cdot \bar{c}=10
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Let $$A=\left[\begin{array}{cc}2 & -1 \\ 0 & 2\end{array}\right].$$ If $$B=I-{ }^3 C_1(\operatorname{adj} A)+{ }^3 C_2(\
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If $$\triangle \mathrm{ABC}$$ is right angled at $$\mathrm{A}$$, where $$A \equiv(4,2, x), \mathrm{B} \equiv(3,1,8)$$ an
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The angle between the lines, whose direction cosines $$l, \mathrm{~m}, \mathrm{n}$$ satisfy the equations $$l+\mathrm{m}
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Let $$f: R \rightarrow R$$ be a function such that $$\mathrm{f}(x)=x^3+x^2 \mathrm{f}^{\prime}(1)+x \mathrm{f}^{\prime \
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If $$\sin (\theta-\alpha), \sin \theta$$ and $$\sin (\theta+\alpha)$$ are in H.P., then the value of $$\cos 2 \theta$$ i
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$$\text { If } y=\left(\sin ^{-1} x\right)^2+\left(\cos ^{-1} x\right)^2, \text { then }\left(1-x^2\right) y_2-x y_1=$$
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If $$a>0$$ and $$z=\frac{(1+i)^2}{a-i}, i=\sqrt{-1}$$, has magnitude $$\frac{2}{\sqrt{5}}$$, then $$\bar{z}$$ is
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In $$\triangle \mathrm{ABC}$$, with usual notations, $$2 \mathrm{ac} \sin \left(\frac{1}{2}(\mathrm{~A}-\mathrm{B}+\math
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$$\int \frac{\sin 2 x\left(1-\frac{3}{2} \cos x\right)}{e^{\sin ^2 x+\cos ^3 x}} d x=$$
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If $$\mathrm{f}^{\prime}(x)=\tan ^{-1}(\sec x+\tan x),-\frac{\pi}{2}
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If $$\int \frac{\cos \theta}{5+7 \sin \theta-2 \cos ^2 \theta} d \theta=A \log _e|f(\theta)|+c$$ (where $$c$$ is a const
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If $$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$$ are unit vectors and $$\theta$$ is angle betw
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The integral $$\int_\limits{\frac{\pi}{6}}^{\frac{\pi}{3}} \sec ^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x d
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The principal solutions of the equation $$\sec x+\tan x=2 \cos x$$ are
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If $$\bar{a}, \bar{b}, \bar{c}$$ are three vectors with magnitudes $$\sqrt{3}$$, 1, 2 respectively, such that $$\bar{a}
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Let the curve be represented by $$x=2(\cos t+t \sin t), y=2(\sin t-t \cos t)$$. Then normal at any point '$$t$$' of the
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Equation of the plane passing through $$(1,-1,2)$$ and perpendicular to the planes $$x+2 y-2 z=4$$ and $$3 x+2 y+z=6$$ i
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If $$\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi$$, then the value of $$x^{2025}+x^{2026}+x^{2027}$$ is
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$$\mathrm{p}$$ is the length of perpendicular from the origin to the line whose intercepts on the axes are a and $$\math
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$$\text { If } f(x)= \begin{cases}3\left(1-2 x^2\right) & ; 0
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$$\int \frac{\sin x+\sin ^3 x}{\cos 2 x} d x=A \cos x+B \log \mathrm{f}(x)+c$$ (where $$\mathrm{c}$$ is a constant of in
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If $$y=[(x+1)(2 x+1)(3 x+1) \ldots \ldots(\mathrm{n} x+1)]^n$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x=0$$ i
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Let $$\mathrm{B} \equiv(0,3)$$ and $$\mathrm{C} \equiv(4,0)$$. The point $$\mathrm{A}$$ is moving on the line $$y=2 x$$
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$$\lim _\limits{x \rightarrow \infty} x^3\left\{\sqrt{x^2+\sqrt{1+x^4}}-x \sqrt{2}\right\}=$$
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The money invested in a company is compounded continuously. If ₹ 200 invested today becomes ₹ 400 in 6 years, then at th
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The range of the function $$\mathrm{f}(x)=\frac{x^2}{x^2+1}$$ is
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The differential equation of $$y=\mathrm{e}^x(\mathrm{a} \cos x+\mathrm{b} \sin x)$$ is
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If $$\int \frac{x^3 \mathrm{~d} x}{\sqrt{1+x^2}}=\mathrm{a}\left(1+x^2\right) \sqrt{1+x^2}+\mathrm{b} \sqrt{1+x^2}+\math
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The perpendiculars are drawn to lines $$L_1$$ and $$L_2$$ from the origin making an angle $$\frac{\pi}{4}$$ and $$\frac{
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The function $$\mathrm{f}(x)=[x] \cdot \cos \left(\frac{2 x-1}{2}\right) \pi$$, where $$[\cdot]$$ denotes the greatest i
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A line with positive direction cosines passes through the point $$\mathrm{P}(2,-1,2)$$ and makes equal angles with the c
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If the shortest distance between the lines $$\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{\lambda}$$ and $$\frac{x-2}{1}=\frac
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If the angles $$\mathrm{A}, \mathrm{B}$$, and $$\mathrm{C}$$ of a triangle are in an Arithmetic Progression and if $$\ma
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A linguistic club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this group including the se
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The maximum value of the function $$f(x)=3 x^3-18 x^2+27 x-40$$ on the set $$\mathrm{S}=\left\{x \in \mathrm{R} / x^2+30
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Let $$f(x)=\int \frac{x^2-3 x+2}{x^4+1} \mathrm{~d} x$$, then function decreases in the interval
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Three critics review a book. For the three critics the odds in favour of the book are $$2: 5, 3: 4$$ and $$4: 3$$ respec
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Consider the lines $$\mathrm{L}_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{\mathrm{z}+1}{2}$$ $$\mathrm{L}_2: \frac{x-2}{1}=\f
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The area bounded by the curves $$y=(x-1)^2, y=(x+1)^2$$ and $$y=\frac{1}{4}$$ is
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Physics

A sphere and a cube, both of copper have equal volumes and are black. They are allowed to cool at same temperature and i
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An alternating voltage is applied to a series LCR circuit. If the current leads the voltage by $$45^{\circ}$$, then $$\l
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A horizontal wire of mass '$$m$$', length '$$l$$' and resistance '$$R$$' is sliding on the vertical rails on which unifo
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Frequency of the series limit of Balmer series of hydrogen atom in terms of Rydberg's constant (R) and velocity of light
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A string is stretched between two rigid supports separated by $$75 \mathrm{~cm}$$. There are no resonant frequencies bet
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A straight wire carrying a current (I) is turned into a circular loop. If the magnitude of the magnetic moment associate
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The diffraction fringes obtained by a single slit are of
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A particle moves around a circular path of radius '$$r$$' with uniform speed '$$V$$'. After moving half the circle, the
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On dry road, the maximum speed of a vehicle along a circular path is '$$V$$'. When the road becomes wet, maximum speed b
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A wire of length $$3 \mathrm{~m}$$ connected in the left gap of a meter-bridge balances $$8 \Omega$$ resistance in the r
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By adding soluble impurity in a liquid, angle of contact
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For a common emitter configuration, if '$$\alpha$$' and '$$\beta$$' have their usual meanings, the incorrect relation be
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A simple pendulum of length '$$l$$' and a bob of mass '$$\mathrm{m}$$' is executing S.H.M. of small amplitude '$$A$$'. T
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Which of the following combination of 7 identical capacitors each of $$2 \mu \mathrm{F}$$ gives a capacitance of $$\frac
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The potential energy of a molecule on the surface of a liquid compared to the molecules inside the liquid is
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A progressive wave is given by, $$\mathrm{Y}=12 \sin (5 \mathrm{t}-4 \mathrm{x})$$. On this wave, how far away are the t
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The de-Broglie wavelength $$(\lambda)$$ of a particle is related to its kinetic energy (E) as
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For a purely inductive or a purely capacitive circuit, the power factor is
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The electric field intensity on the surface of a solid charged sphere of radius '$$r$$' and volume charge density '$$\rh
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A body is said to be opaque to the radiation if (a, r and t are coefficient of absorption, reflection and transmission r
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In a thermodynamic system, $$\Delta U$$ represents the increases in its internal energy and dW is the work done by the s
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A combination of two thin lenses in contact have power $$+10 \mathrm{D}$$. The power reduces to $$+6 \mathrm{D}$$ when t
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The reciprocal of the total effective resistance of LCR a.c. circuit is called
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If the radius of the first Bohr orbit is '$$r$$' then the de-Broglie wavelength of the electron in the $$4^{\text {th }}
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A string of length '$$L$$' fixed at one end carries a body of mass '$$\mathrm{m}$$' at the other end. The mass is revolv
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The temperature of a gas is $$-68^{\circ} \mathrm{C}$$. To what temperature should it be heated, so that the r.m.s. velo
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The displacement of a particle executing S.H.M. is $$x=\mathrm{a} \sin (\omega t-\phi)$$. Velocity of the particle at ti
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A uniformly charged semicircular arc of radius '$$r$$' has linear charge density '$$\lambda$$'. The electric field at it
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A sphere, a cube and a thin circular plate all made of same material and having the same mass are heated to same tempera
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For emission of light, a light emitting diode (LED) is
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A solenoid of length $$0.4 \mathrm{~m}$$ and having 500 turns of wire carries a current $$3 \mathrm{~A}$$. A thin coil h
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In semiconductors at room temperature,
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Considering earth to be a sphere of radius '$$R$$' having uniform density '$$\rho$$', then value of acceleration due to
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The equation of the wave is $$\mathrm{Y}=10 \sin \left(\frac{2 \pi \mathrm{t}}{30}+\alpha\right)$$ If the displacement i
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The bob of simple pendulum of length '$$L$$' is released from a position of small angular displacement $$\theta$$. Its l
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The value of acceleration due to gravity at a depth '$$d$$' from the surface of earth and at an altitude '$$h$$' from th
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A magnetic field of $$2 \times 10^{-2} \mathrm{~T}$$ acts at right angles to a coil of area $$100 \mathrm{~cm}^2$$ with
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In Young's double slit experiment, $$8^{\text {th }}$$ maximum with wavelength '$$\lambda_1$$' is at a distance '$$d_1$$
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The alternating e.m.f. induced in the secondary coil of a transformer is mainly due to
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The efficiency of a heat engine is '$$\eta$$' and the coefficient of performance of a refrigerator is '$$\beta$$'. Then
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A conducting sphere of radius $$0.1 \mathrm{~m}$$ has uniform charge density $$1.8 \mu \mathrm{C} / \mathrm{m}^2$$ on it
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If $$\mathrm{I}_0$$ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be
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Two circular coils made from same wire but radius of $$1^{\text {st }}$$ coil is twice that of $$2^{\text {nd }}$$ coil.
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Five current carrying conductors meet at point $$\mathrm{P}$$. What is the magnitude and direction of the current in con
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Water rises in a capillary tube of radius '$$r$$' upto a height '$$h$$'. The mass of water in a capillary is '$$m$$'. Th
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A person with machine gun can fire 50 g bullets with a velocity of $$240 \mathrm{~m} / \mathrm{s}$$. A $$60 \mathrm{~kg}
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If '$$l$$' is the length of the open pipe, '$$r$$' is the internal radius of the pipe and '$V$ ' is the velocity of soun
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The angle of deviation produced by a thin prism when placed in air is '$$\delta_1$$' and that when immersed in water is
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A thin uniform rod of mass '$$m$$' and length '$$P$$' is suspended from one end which can oscillate in a vertical plane
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Magnetic field at the centre of the hydrogen atom due to motion of electron in $$\mathrm{n}^{\text {th }}$$ orbit is pro
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