MHT CET 2023 13th May Evening Shift
Paper was held on Sat, May 13, 2023 9:30 AM
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Chemistry

What is the $$\mathrm{pH}$$ of solution containing $$4.62 \times 10^{-4} \mathrm{M} \mathrm{H}^{+}$$ ions?
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Which of the following is vinylic alcohol?
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Which among the following is benzylic halide?
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Which among the following is a simple ketone?
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Identify glycosidic linkage present in maltose.
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Which statement from following about nano-material is NOT correct?
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Which from following species is NOT a monodentate ligand?
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Two moles of an ideal gas expand freely and isothermally from $$5 \mathrm{~dm}^3$$ to $$50 \mathrm{~dm}^3$$. What is the
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What is IUPAC name of following compound?
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What is the molecular formula of an alkane if it exhibits three structural isomers?
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What is the bond order in N$$_2^+$$?
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Identify alkaline earth metal from following.
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What is the molality of solution of a non-volatile solute having boiling point elevation $$7.15 \mathrm{~K}$$ and molal
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Which from following statements about rate constant is NOT true?
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Identify '$$B$$' in the following conversions $$\mathrm{CH}_3 \mathrm{Br} \xrightarrow{\mathrm{KCN}} A \xrightarrow{\mat
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Find the radius of metal atom in bcc unit cell having edge length $$450 \mathrm{~pm}$$.
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Which from following statements is true for the molecule
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Which among the following salt solution in water is acidic in nature?
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Which among the following is intensive and extensive properties respectively?
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Which of the following compounds has lowest boiling point?
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Which of the following statements is NOT true about polymorphism?
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Which from the following expression represents molar conductivity of an electrolyte $$\mathrm{A}_2 B_3$$ type?
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Which of the following electromagnetic radiations possesses lowest energy?
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Which among the following is an example of branched chain polymer?
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For the reaction, $$\mathrm{CH}_3 \mathrm{Br}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{CH}_3 \mathrm{OH}(a q)+
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For the reaction, $$2 A+2 B \longrightarrow 2 C+D$$, the rate law is expressed as rate $$=k[A]^2[B]$$. Calculate the rat
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What is the molar conductivity of $$0.005 \mathrm{~M} \mathrm{~NaI}$$ solution if it's conductivity is $$6.065 \times 1
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Which of the following is not a disaccharide?
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Which from following is a correct decreasing order of ionisation enthalpy for different elements?
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Which among the following salts exhibits inverse relation between it's solubility and temperature?
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Which from following series of elements is correctly arranged according to their decreasing order of ionisation enthalpy
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Identify the product formed by the action of $$\mathrm{H}_2(\mathrm{~g})$$ with $$\mathrm{CO}(\mathrm{g})$$ in presence
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Calculate $$E^{\circ}$$ cell for following. $$\mathrm{Zn}(s)\left|\mathrm{Zn}^{++}(1 \mathrm{M}) \| \mathrm{Pb}^{++}(1 \
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Which from following elements exhibits usual tendency to undergo reduction?
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According to reaction, $$\mathrm{Mg}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{MgCl}_2(a q)+\mathrm{H}_2(g) \uparro
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A closed container contains mixture of non-reacting gases $$A$$ and $$B$$. Partial pressure of $$A$$ and $$B$$ are 4.5 b
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Which from following compounds is obtained when toluene is treated with $$\mathrm{CrO}_2 \mathrm{Cl}_2$$ in presence of
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Which of the following is NOT prepared by the action of Grignard's reagent on methanal?
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What is the number of elements present in each series of transition element?
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Which of the following is Wolf-Kishner reduction?
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Calculate the wave number of photon emitted during transition from the orbit of $$n=3$$ to $$n=2$$ in hydrogen atom $$\l
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What is the molar concentration of acetic acid if value of it's, dissociation constant is $$1.8 \times 10^{-5}$$ and deg
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An ideal gas absorbs $$210 \mathrm{~J}$$ of heat and undergoes expansion from $$3 \mathrm{~L}$$ to $$6 \mathrm{~L}$$ aga
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What is the molecular formula of $$p$$-toluidine?
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If $$0.01 \mathrm{~m}$$ aqueous solution of an electrolyte freezes at $$-0.056 \mathrm{~K}$$. Calculate van't Hoff facto
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Which element from following does NOT belong to chalcogen family?
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What is IUPAC name of following compound?
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Identify the monomers used to prepare novolac.
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Calculate the volume of unit cell if an element having molar mass $$180 \mathrm{~g} \mathrm{~mol}^{-1}$$ forms fcc unit
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Identify homoleptic complex from following.
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Mathematics

If $$x d y=y(d x+y d y), y(1)=1, y(x)>0$$, then $$y(-3)$$ is
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Slope of the tangent to the curve $$y=2 e^x \sin \left(\frac{\pi}{4}-\frac{x}{2}\right) \cos \left(\frac{\pi}{4}-\frac{x
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If the vectors $$p \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+q \hat{\mathbf{j}}+\hat{\mathbf{
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A tetrahedron has vertices at $$P(2,1,3), Q(-1,1,2), R(1,2,1)$$ and $$O(0,0,0)$$, then angle between the faces $$O P Q$$
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Two dice are rolled. If both dice have six faces numbered $$1,2,3,5,7,11$$, then the probability that the sum of the num
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The domain of the definition of the function $$y(x)$$ is given by the equation $$2^x+2^y=2$$ is
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If $$\mathbf{a}=\frac{1}{\sqrt{10}}(3 \hat{\mathbf{i}}+\hat{\mathbf{k}}), \mathbf{b}=\frac{1}{7}(2 \hat{\mathbf{i}}+3 \h
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$$y=\frac{\sqrt[3]{1+3 x} \sqrt[4]{1+4 x} \sqrt[5]{1+5 x}}{\sqrt[7]{1+7 x} \sqrt[8]{1+8 x}} \text {. Then, } \frac{d y}{
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Five students are selected from $$n$$ students such that the ratio of number of ways in which 2 particular students are
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If $$\int \frac{\log \left(t+\sqrt{1+t^2}\right)}{\sqrt{1+t^2}} d t=\frac{1}{2}[g(t)]^2+c$$, (where $$c$$ is a constant
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If $$A=\left[\begin{array}{cc}1 & \tan x \\ -\tan x & 1\end{array}\right]$$, then $$A^T \cdot A^{-1}=$$
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$$\mathbf{a}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\h
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Let $$P Q R$$ be a right angled isosceles triangle, right angled at $$Q(2,1)$$. If the equation of the line $$P R$$ is $
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If a curve $$y=a \sqrt{x}+b x$$ passes through the point $$(1,2)$$ and the area bounded by the curve, line $$x=4$$ and $
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A plane is parallel to two lines whose direction ratios are $$2,0,-2$$ and $$-2,2,0$$ and it contains the point $$(2,2,2
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If $$q$$ is false and $$p \wedge q \leftrightarrow r$$ is true, then ............ is a tautology.
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Negation of contrapositive of statement pattern $$(p \vee \sim q) \rightarrow(p \wedge \sim q)$$ is
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The value of $$\tan \left(\sin ^{-1}\left(\frac{3}{5}\right)+\tan ^{-1}\left(\frac{2}{3}\right)\right)$$ is
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Variance of first $$2 n$$ natural numbers is
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$$\int \frac{x-3}{(x-1)^3} e^x d x=$$
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If $$\mathbf{a}, \mathbf{b}, \mathbf{c}$$ are non-coplanar unit vectors such that $$\mathbf{a} \times(\mathbf{b} \times
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$$\int \frac{2+\cos \frac{x}{2}}{x+\sin \frac{x}{2}} d x=$$
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In $$\triangle A B C$$, with usual notations, if $$\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$$, then the value of $$\
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If slope of the tangent to the curve $$x y+a x+b y=0$$ at the point $$(1,1)$$ on it is 2, then the value of $$3 a+b$$ is
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If $$(3 x+2)-(5 y-3) i$$ and $$(6 x+3)+(2 y-4) i$$ are conjugates of each other, then the value of $$\frac{x-y}{x+y}$$ i
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If $$\left(\tan ^{-1} x\right)^2+\left(\cot ^{-1} x\right)^2=\frac{5 \pi^2}{8}$$, then the value of $$x$$ is
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The solution of $$(1+x y) y d x+(1-x y) x d y=0$$ is
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The integral $$\int_\limits{\pi / 6}^{\pi / 3} \sec ^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x d x$$ is equal
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$$\lim _\limits{x \rightarrow 0} \frac{\sqrt{1+x \sin x}-\sqrt{\cos x}}{\tan ^2 \frac{x}{2}}=$$
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$$A(1,-3), B(4,3)$$ are two points on the curve $$y=x-\frac{4}{x}$$. The points on the curve, the tangents at which are
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Let $$f: R \rightarrow R$$ be a function such that $$f(x)=x^3+x^2 f^{\prime}(1)+x f^{\prime \prime}(2)+f^{\prime \prime
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A radioactive substance, with initial mass $$m_0$$, has a half-life of $$h$$ days. Then, its initial decay rate is given
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The abscissae of two points $$A$$ and $$B$$ are the roots of the equation $$x^2+2 a x-b^2=0$$ and their ordinates are ro
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The incentre of the $$\triangle A B C$$, whose vertices are $$A(0,2,1), B(-2,0,0)$$ and $$C(-2,0,2)$$, is
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The acute angle between the line joining the points $$(2,1,-3),(-3,1,7)$$ and a line parallel to $$\frac{x-1}{3}=\frac{y
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A random variable $$X$$ has the probability distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td{borde
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The shaded area in the given figure is a solution set for some system of inequations. The maximum value of the function
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The foot of the perpendicular from the point $$(1,2,3)$$ on the line $$\mathbf{r}=(6 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}
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Water is running in a hemispherical bowl of radius $$180 \mathrm{~cm}$$ at the rate of 108 cubic decimeters per minute.
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The solution of $$\sin x+\sin 5 x=\sin 3 x$$ in $$(0, \pi / 2)$$ are
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If $$(1+\sqrt{1+x}) \tan x=1+\sqrt{1-x}$$, then $$\sin 4 x$$ is
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If the sum of the mean and the variance of a binomial distribution for 5 trials is 1.8 , then the value of $$p$$ is
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If $$I=\int \frac{e^x}{e^{4 x}+e^{2 x}+1} d x$$ and $$J=\int \frac{e^{-x}}{e^{-4 x}+e^{-2 x}+1} d x$$, then for any arbi
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The principal value of $$\sin ^{-1}(\sin (3 \pi / 4))$$ is
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If $$x=\log _e\left(\frac{\cos \frac{y}{2}-\sin \frac{y}{2}}{\cos \frac{y}{2}+\sin \frac{y}{2}}\right), \tan \frac{y}{2}
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The c.d.f. $$F(x)$$ associated with p.d.f. $$f(x)$$ $$f(x)=\left\{\begin{array}{cl}12 x^2(1-x), & \text { if } 0
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If $$f(x)$$ is continuous on its domain $$[-2,2]$$, where $$f(x)=\left\{\begin{array}{cc} \frac{\sin a x}{x}+3 & , \text
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$$P S$$ is the median of the triangle with vertices at $$P(2,2), Q(6,-1)$$ and $$R(7,3)$$, then the intercepts on the co
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If Rolle's theorem holds for the function $$f(x)=x^3+b x^2+a x+5$$ on $$[1,3]$$ with $$c=2+\frac{1}{\sqrt{3}}$$, then th
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The distance of the point $$(1,6,2)$$ from the point of intersection of the line $$\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2
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Physics

A sample of oxygen gas and a sample of hydrogen gas both have the same mass, same volume and the same pressure. The rati
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If two planets have their radii in the ratio $$x: y$$ and densities in the ratio $$m: n$$, then the acceleration due to
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An excited hydrogen atom emits a photon of wavelength $$\lambda$$ in returning to ground state. The quantum number $$n$$
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There is hole of area $$A$$ at the bottom of a cylindrical vessel. Water is filled to a height $$h$$ and water flows out
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The number of turns in the primary and the secondary of a transformer are 1000 and 3000 , respectively. If $$80 \mathrm{
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The ratio of magnetic field at the centre of the current carrying circular loop and magnetic moment is $$X$$. When both
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Light of wavelength $$5000 \mathop A\limits^o$$ is incident normally on a slit. The first minimum of the diffraction pat
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When two tuning forks are sounded together, 5 beats per second are heard. One of the forks is in unison with $$0.97 \mat
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The work done in rotating a dipole placed parallel to the electric field through $$180^{\circ}$$ is W. So, the work done
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When an electron is excited from its 4 th orbit to 5 th stationary orbit, the change in the angular momentum of electron
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The Boolean expression for the following combination is
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Under the influence of force $$F_1$$ the body oscillates with a period $$T_1$$ and due to another force $$F_2$$ body osc
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The internal energy of a monoatomic ideal gas molecule is
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A gas at pressure $$p_0$$ is contained in a vessel. If the masses of all the molecules are halved and their velocities a
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The equation of a progressive wave is $$Y=a \sin 2 \pi\left(n t-\frac{x}{5}\right)$$. The ratio of maximum particle velo
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For an adiabatic process, which one of the following is wrong statement?
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A mine is located at depth $$R / 3$$ below earth's surface. The acceleration due to gravity at that depth in mine is ($$
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A $$10 \mathrm{~m}$$ long wire of resistance $$20 \Omega$$ is connected in series with a battery of emf $$3 \mathrm{~V}$
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A group of lamps having total power rating of $$1000 \mathrm{~W}$$ is supplied by an AC voltage of $$E=200 \sin \left(31
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At a particular angular frequency, the reactance of capacitor and that of inductor is same. If the angular frequency is
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A metal disc of radius $$R$$ rotates with an angular velocity $$\omega$$ about an axis perpendicular to its plane passin
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A mass $$M$$ is suspended from a light spring. An additional mass $$M_1$$ added extends the spring further by a distance
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The path difference between two identical light waves at a point $$Q$$ on the screen is $$3 \mu \mathrm{m}$$. If wavelen
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If the maximum efficiency of a full wave rectifier is $$x \%$$ and that of half-wave rectifier is $$y \%$$, then the rel
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Two bodies $$A$$ and $$B$$ start from the same point at the same instant and move along a straight line. body $$A$$ move
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A small steel ball is dropped from a height of $$1.5 \mathrm{~m}$$ into a glycerine jar. The ball reaches the bottom of
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In a parallel plate capacitor with air between the plates, the distance $$d$$ between the plates is changed and the spac
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A ray of light passes through an equilateral prism such that the angle of incidence $$(i)$$ is equal to angle of emergen
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The radii of curvature of both the surfaces of a convex lens of focal length $$f$$ and power $$P$$ are equal. One of the
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A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring balance reads $$
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In a $$L$$-$$R$$ circuit the inductive reactance is equal to the resistance $R$ in the circuit. An emf $$E=E_0 \cos \ome
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Four identical uniform solid spheres each of same mass $$M$$ and radius $$R$$ are placed touching each other as shown in
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A transverse wave strike against a wall,
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A circular current carrying coil has radius $$R$$. The magnetic induction at the centre of the coil is $$B_C$$. The magn
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In the electric field due to a charge $$Q$$, a charge $$q$$ moves from point $$A$$ to $$B$$. The work done is ( $$\varep
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Of the two slits producing interference in Young's experiment, one is covered with glass so that light intensity passing
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Magnetic shielding is done by surrounding the instrument to be protected from magnetic field by
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In the given figure, the equivalent capacitance between points A and B is
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If work done in blowing a soap bubble of volume $$V$$ is $$W$$, then the work done in blowing the bubble of volume $$2 \
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Which one of the following is based on convection?
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A simple spring has length $$l$$ and force constant $$K$$. It is cut in to two springs of length $$l_1$$ and $$l_2$$ suc
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A closed pipe and an open pipe have their first overtone equal in frequency. Then, the lengths of these pipe are in the
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A conductor $$10 \mathrm{~cm}$$ long is moves with a speed $$1 \mathrm{~m} / \mathrm{s}$$ perpendicular to a field of st
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Dual nature of light is exhibited by
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A carnot engine operates with source at $$227^{\circ} \mathrm{C}$$ and sink at $$27^{\circ} \mathrm{C}$$. If the source
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Doping of a semiconductor (with small impurity atoms) generally changes the resistivity as follows.
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A stone is projected at angle $$\theta$$ with velocity $$u$$. If it executes nearly a circular motion at its maximum poi
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When radiations of wavelength $$\lambda$$ is incident on a metallic surface the stopping potential required is $$4.8 \ma
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A thin uniform $$\operatorname{rod} A B$$ of mass $$m$$ and length $$l$$ is hinged at one end $$A$$ to the ground level.
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Only $$4 \%$$ of the total current in the circuit passes through a galvanometer. If the resistance of the galvanometer i
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