MHT CET 2023 14th May Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Which of the following is a structural formula of DDT? 2. Which among the following is haloalkyne? 3. What type of peptide is the glycylalanine? 4. What is Henry's law constant of a gas if solubility of gas in water at $$25^{\circ} \mathrm{C}$$ is $$0.028 \mathrm{~mol 5. Calculate the rate constant of the first order reaction if $$80 \%$$ of the reactant decomposes in 60 minutes. 6. Which from following polymers is classified fibres depending on inter molecular forces? 7. Calculate the frequency if wavelength is $$750 \mathrm{~nm}$$. 8. Calculate the edge length of bcc unit cell if radius of metal atom is $$227 \mathrm{~pm}$$. 9. Identify the compound '$$\mathrm{A}$$' in the following sequence of reactions. $$\text { A } \xrightarrow[\text { Dryeth 10. A solution of nonvolatile solute is obtained by dissolving $$15 \mathrm{~g}$$ in $$200 \mathrm{~mL}$$ water has depressi 11. For a reaction $$\mathrm{A}+\mathrm{B} \rightarrow$$ products $$\Delta \mathrm{H}$$ is $$-84.2 \mathrm{~kJ}$$ and $$\Del 12. The solubility product of $$\mathrm{PbCl}_2$$ at $$298 \mathrm{~K}$$ is $$3.2 \times 10^{-5}$$. What is its solubility i 13. Which among the following elements does NOT exhibit ferromagnetic properties? 14. Which of the following is a secondary allylic alcohol? 15. Which from following elements is in liquid state at room temperature? 16. Identify major product formed in the following reaction. 3-Bromo-2-methylpentane $$\xrightarrow[\Delta]{\text { Alc.KOH 17. What is molecular formula of cyclohexylamine? 18. Identify base$$_2$$ for following equation according to Bronsted-Lowry theory. $$\mathrm{HCl}_{(\mathrm{aq})}+\mathrm{H} 19. Which of the following is Clemmensen reduction? 20. Which of the following gases is readily adsorbed by solid adsorbent? 21. Which from following is an example of two dimensional nanostructures? 22. A conductivity cell containing $$0.001 \mathrm{~M} \mathrm{~AgNO}_3$$ solution develops resistance $$6530 \mathrm{ohm}$$ 23. What is the number of $$\mathrm{sp}^3$$ hybrid carbon atoms in $$\mathrm{HO}\left(\mathrm{CH}_2\right)_3 \mathrm{CH}\lef 24. Which from following thermodynamic properties is a path function? 25. Which among the following species is reduced by tin easily? 26. Which from following combinations is an example for construction of n-type semiconductor? 27. Calculate the density of metal having molar mass $$210 \mathrm{~g} \mathrm{~mol}^{-1}$$ that forms simple cubic unit cel 28. Which element from following rapidly loses its luster in air and tarnishes? 29. A neon-dioxygen mixture contains $$64 \mathrm{~g} \mathrm{~O}_2$$ and $$160 \mathrm{~g} \mathrm{~Ne}$$. If the total pre 30. Identify anionic sphere complex from following. 31. What is the number of moles of ethane obtained from $$2 n$$ moles of bromomethane using $$2 n$$ moles of sodium atoms in 32. Calculate $$\mathrm{E}_{\text {cell }}^0$$ for $$\mathrm{Cd}_{(\mathrm{s})}\left|\mathrm{Cd}_{(\mathrm{1M})}^{++}\right| 33. Find the number of unpaired electrons for copper in ground state configuration. 34. Identify the element having highest ionization enthalpy. 35. What is the oxidation number of $$\mathrm{Pt}$$ in $$\mathrm{PtCl}_6^{2-}$$ ? 36. What is the value of rate constant for first order reaction if slope for the graph of rate versus concentration is $$2.5 37. An organic monobasic acid has dissociation constant $$2.25 \times 10^{-6}$$. What is percent dissociation in its $$0.01 38. Which of the following pair of compounds demonstrates the law of multiple proportions? 39. Which of the following amines on heating with chloroform generate foul smelling product? 40. The rate law for the reaction $$\mathrm{A}+\mathrm{B} \rightarrow$$ product is rate $$=\mathrm{k}[\mathrm{A}][\mathrm{B} 41. What is IUPAC name of following compound? 42. Identify substrate 'A' in the following reaction. 2nA $$\mathrm{\buildrel {Dimethyl\,cadmium} \over \longrightarrow}$$ 43. Which of the following is NOT a basic amino acid? 44. Calculate the PV type of work for the following reaction at 1 bar pressure. $$\mathrm{\mathop {{C_3}{H_{6(g)}}}\limits_{ 45. Which among the following is NOT dicarboxylic acid? 46. Identify the element having positive electron gain enthalpy. 47. Identify the use of HDP from following. 48. Which coordination complex from following contains neutral ligand? 49. What type of following solutions is the gasoline? 50. What is formal charge on carbon in the following Lewis structure?

Mathematics

1. 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 2. 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 $$\bar 3. If both mean and variance of 50 observations $$x_1, x_2, \ldots, x_{50}$$ are equal to 16 and 256 respectively, then mea 4. If the statement $$\mathrm{p} \leftrightarrow(\mathrm{q} \rightarrow \mathrm{p})$$ is false, then true statement/stateme 5. If $$|\bar{a}|=2,|\bar{b}|=3,|\bar{c}|=5$$ and each of the angles between the vectors $$\bar{a}$$ and $$\bar{b}, \bar{b} 6. The shaded region in the following figure represents the solution set for a certain linear programming problem. Then lin 7. The function $\mathrm{f}$ defined on $$\left(-\frac{1}{3}, \frac{1}{3}\right)$$ by $$\mathrm{f}(x)=\left\{\begin{array}{ 8. The mirror image of $$\mathrm{P}(2,4,-1)$$ in the plane $$x-y+2 z-2=0$$ is $$(\mathrm{a}, \mathrm{b}, \mathrm{c})$$, the 9. If the slope of the tangent of the curve at any point is equal to $$-y+\mathrm{e}^{-x}$$, then the equation of the curve 10. If $$A=\left[\begin{array}{ll}1 & -1 \\ 2 & -1\end{array}\right], B=\left[\begin{array}{cc}1 & 1 \\ 4 & -1\end{array}\ri 11. The function $$\mathrm{f}(x)=x^3-6 x^2+9 x+2$$ has maximum value when $$x$$ is 12. If $$I_n=\int_\limits0^{\frac{\pi}{4}} \tan ^n \theta d \theta$$, then $$I_{12}+I_{10}=$$ 13. 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 14. A fair die with numbers 1 to 6 on their faces is thrown. Let $$\mathrm{X}$$ denote the number of factors of the number, 15. Let $$\overline{\mathrm{u}}, \overline{\mathrm{v}}$$ and $$\overline{\mathrm{w}}$$ be the vectors such that $$|\overline 16. If $$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}$$ 17. If $$x=\sqrt{\mathrm{e}^{\sin ^{-1} t}}$$ and $$y=\sqrt{\mathrm{e}^{\cos ^{-1} t}}$$, then $$\frac{\mathrm{d}^2 y}{\math 18. If $$\sum_\limits{r=1}^{50} \tan ^{-1} \frac{1}{2 r^2}=p$$ then $$\tan p$$ is 19. The value of $$\int \mathrm{e}^x\left(\frac{x^2+4 x+4}{(x+4)^2}\right) \mathrm{d} x$$ is : 20. The diagonal of a square is changing at the rate of $$0.5 \mathrm{~cm} / \mathrm{sec}$$. Then the rate of change of area 21. 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 22. 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 23. If in a regular polygon, the number of diagonals are 54, then the number of sides of the polygon are 24. Let $$x_0$$ be the point of local minima of $$\mathrm{f}(x)=\overline{\mathrm{a}} \cdot(\overline{\mathrm{b}} \times \ov 25. If a body cools from $$80^{\circ} \mathrm{C}$$ to $$50^{\circ} \mathrm{C}$$ in the room temperature of $$25^{\circ} \mat 26. If $$f(a)=2, f^{\prime}(a)=1, g(a)=-1, g^{\prime}(a)=2$$, then as $$x$$ approaches a, $$\frac{\mathrm{g}(x) \mathrm{f}(\ 27. The differential equation representing the family of curves $$y^2=2 \mathrm{c}(x+\sqrt{\mathrm{c}})$$, where $$\mathrm{c 28. 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 29. 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 30. The value of $$\tan ^{-1}\left(\frac{1}{8}\right)+\tan ^{-1}\left(\frac{1}{2}\right)+\tan ^{-1}\left(\frac{1}{5}\right)$ 31. The p.m.f. of a random variable $$\mathrm{X}$$ is $$\mathrm{P}(x)=\left\{\begin{array}{cl}\frac{2 x}{\mathrm{n}(\mathrm{ 32. If the lines $$\frac{x-\mathrm{k}}{2}=\frac{y+1}{3}=\frac{\mathrm{z}-1}{4}$$ and $$\frac{x-3}{1}=\frac{y-\frac{9}{2}}{2} 33. If $$|\vec{a}|=\sqrt{3} ;|\vec{b}|=5 ; \bar{b} \cdot \bar{c}=10$$, angle between $$\overline{\mathrm{b}}$$ and $$\overli 34. 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 $$\mathr 35. The centroid of the triangle formed by the lines $$x+3 y=10$$ and $$6 x^2+x y-y^2=0$$ is 36. The statement $$[\mathrm{p} \wedge(\mathrm{q} \vee \mathrm{r})] \vee[\sim \mathrm{r} \wedge \sim \mathrm{q} \wedge \math 37. 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 38. If $$\mathrm{f}^{\prime}(x)=\sin (\log x)$$ and $$y=\mathrm{f}\left(\frac{2 x+3}{3-2 x}\right)$$, then $$\frac{\mathrm{d 39. The area bounded by the curve $$y=|x-2|, x=1, x=3$$ and $$X$$-axis is 40. $$\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}$ 41. There are 6 positive and 8 negative numbers. From these four numbers are chosen at random and multiplied. Then the proba 42. If $$\mathrm{a} \cos 2 \theta+\mathrm{b} \sin 2 \theta=\mathrm{c}$$ has $$\alpha$$ and $$\beta$$ as its roots, then the 43. A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to retail st 44. Given $$0 \leq x \leq \frac{1}{2}$$, then the value of $$\tan \left(\sin ^{-1}\left(\frac{x}{\sqrt{2}}+\frac{\sqrt{1-x^2 45. A vector parallel to the line of intersection of the planes $$\bar{r} \cdot(3 \hat{i}-\hat{j}+\hat{k})=1$$ and $$\bar{r} 46. The length of the perpendicular drawn from the point $$(1,2,3)$$ to the line $$\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2 47. If $$I=\int \frac{d x}{\sin (x-a) \sin (x-b)}$$, then I is given by 48. Let $$\mathrm{P}(x)$$ be a polynomial of degree 2, with $$\mathrm{P}(2)=-1, \mathrm{P}^{\prime}(2)=0, \mathrm{P}^{\prime 49. If $$y=\sqrt{(x-\sin x)+\sqrt{(x-\sin x)+\sqrt{(x-\sin x) \ldots.}}}$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}=$$ 50. 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

Physics

1. The power factor of an R-L circuit is $$\frac{1}{\sqrt{2}}$$. If the frequency of $$\mathrm{AC}$$ is doubled the power f 2. Ratio of longest wavelength corresponding to Lyman and Balmer series in hydrogen spectrum is 3. A uniform circular disc of mass $$12 \mathrm{~kg}$$ is held by two identical springs. When the disc is slightly pressed 4. A charge $$17.7 \times 10^{-4} \mathrm{C}$$ is distributed uniformly over a large sheet of area $$200 \mathrm{~m}^2$$. T 5. Sound waves of frequency $$600 \mathrm{~Hz}$$ fall normally on a perfectly reflecting wall. The shortest distance from t 6. A long solenoid has 1500 turns. When a current of $$3.5 \mathrm{~A}$$ flows through it, the magnetic flux linked with ea 7. A metal rod cools at the rate of $$4{ }^{\circ} \mathrm{C} / \mathrm{min}$$ whon its temperature is $$90^{\circ} \mathrm 8. On replacing a thin film of mica of thickness $$12 \times 10^{-5} \mathrm{~cm}$$ in the path of one of the interfering b 9. In the hysteresis curve the value of magnetization (B) which will be present in a substance when value of magnetizing fo 10. The output of following combination is same as that of 11. A parallel plate capacitor with air medium between the plates has a capacitance of $$10 \mu \mathrm{F}$$. The area of ca 12. Refractive index of a glass convex lens is 1.5. The radius of curvature of each of the two surfaces of the lens is $$20 13. Earth is assumed to be a sphere of radius R. If '$$\mathrm{g}_\phi$$' is value of effective acceleration due to gravity 14. Four identical uniform solid spheres each of same mass '$$M$$' and radius '$$R$$' are placed touching each other as show 15. Two condensers one of capacity $$\frac{\mathrm{C}}{2}$$ and other capacity $$\mathrm{C}$$ are connected to a battery of 16. When two light waves each of amplitude '$$A$$' and having a phase difference of $$\frac{\pi}{2}$$ superimposed then the 17. In an n-p-n transistor, the collector current is $$28 \mathrm{~mA}$$. If $$80 \%$$ of electrons reach the collector, its 18. 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 19. The molecular mass of a gas having r.m.s. speed four times as that of another gas having molecular mass 32 is 20. 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 21. When the conductivity of a semiconductor is only due to the breaking of the covalent bonds, the semiconductor is called 22. A coil having effective area A, is held with its plane normal to magnetic field of induction B. The magnetic induction i 23. At constant temperature, increasing the pressure of a gas by $$5 \%$$ its volume will decrease by 24. Half life of radio-active element is 1600 years. The fraction of sample remains undecayed after 6400 years will be 25. Figure shows two semicircular loops of radii $$R_1$$ and $$R_2$$ carrying current $I$. The magnetic field at the common 26. When radiation of wavelength '$$\lambda$$' is incident on a metallic surface, the stopping potential is 4.8 V. If the su 27. A long wire is bent into a circular coil of one turn and then into a circular coil of smaller radius having $$\mathrm{n} 28. When moving coil galvanometer (MCG) is converted into a voltmeter, the series resistance is '$$n$$' times the resistance 29. The self induction (L) produced by solenoid of length '$$l$$' having '$$\mathrm{N}$$' number of turns and cross sectiona 30. A wire $$P Q$$ has length $$4.8 \mathrm{~m}$$ and mass $$0.06 \mathrm{~kg}$$. Another wire QR has length $$2.56 \mathrm{ 31. When a monochromatic ray of light is passed through an equilateral glass prism, it is found that the refracted ray in gl 32. A solid cylinder and a solid sphere having same mass and same radius roll down on the same inclined plane. The ratio of 33. An alternating voltage $$E=200 \sqrt{2} \sin (100 t)$$ volt is connected to a $$1 \mu \mathrm{f}$$ capacitor through an 34. A sonometer wire $$49 \mathrm{~cm}$$ long is in unison with a tuning fork of frequency '$$n$$'. If the length of the wir 35. Two spherical soap bubbles of radii '$$a$$' and '$$b$$' in vacuum coalesce under isothermal conditions. The resulting bu 36. A mass '$$M$$' is moving with constant velocity parallel to $$\mathrm{X}$$-axis. Its angular momentum with respect to th 37. A block of mass '$$M$$' rests on a piston executing S.H.M. of period one second. The amplitude of oscillations, so that 38. A machine gun fires bullets of mass $$30 \mathrm{~g}$$ with velocity of $$1000 \mathrm{~m} / \mathrm{s}$$. The man holdi 39. The temperature of a gas is measure of 40. A body (mass $$\mathrm{m}$$ ) starts its motion from rest from a point distant $$R_0\left(R_0>R\right)$$ from the centre 41. An ideal refrigerator has freezer at a temperature of $$-13^{\circ} \mathrm{C}$$. The coefficient of performance of the 42. 1000 small water drops of equal size combine to form a big drop. The ratio of final surface energy to the total initial 43. It is easier to spray water to which soap is added because addition of soap to water 44. What will be the phase difference between virtual voltage and virtual current when current in the circuit is wattless? 45. Two wavelengths of sodium light $$590 \mathrm{~nm}$$ and $$596 \mathrm{~nm}$$ are used one after another to study diffra 46. A coil having an inductance of $$\frac{1}{\pi} \mathrm{H}$$ is connected in series with a resistance of $$300 \Omega$$. 47. The pressure and density of a diatomic gas $$\left(\gamma=\frac{7}{5}\right)$$ changes adiabatically from $$(\mathrm{P}, 48. A source of sound is moving towards a stationary observer with $$\left(\frac{1}{10}\right)^{\text {th }}$$ the of the sp 49. If $$\mathrm{E}_{\mathrm{a}}$$ and $$\mathrm{E}_{\mathrm{q}}$$ represent the electric field intensity due to a short dip 50. In potentiometer experiment, the balancing length is $$8 \mathrm{~m}$$ when two cells $$E_1$$ and $$E_2$$ are joined in

MHT CET 2023 14th May Evening Shift

MCQ (Single Correct Answer)

-0

If $$I=\int \frac{d x}{\sin (x-a) \sin (x-b)}$$, then I is given by

$$\frac{1}{\sin (b-a)} \log |\sin (x-a) \sin (x-b)|+c$$, where $$c$$ is a constant of integration.

$$\log \left|\frac{\sin (x-a)}{\sin (x-b)}\right|+c$$, where $$c$$ is a constant of integration.

$$\frac{1}{\sin (b-a)} \log \left|\frac{\sin (x-a)}{\sin (x-b)}\right|+c$$, where $$c$$ is a constant of integration.

$$\frac{1}{\sin (b-a)} \log \left|\frac{\sin (x-b)}{\sin (x-a)}\right|+c$$, where $$c$$ is a constant of integration.

MHT CET 2023 14th May Evening Shift

MCQ (Single Correct Answer)

-0

Let $$\mathrm{P}(x)$$ be a polynomial of degree 2, with $$\mathrm{P}(2)=-1, \mathrm{P}^{\prime}(2)=0, \mathrm{P}^{\prime \prime}(2)=2$$, then $$\mathrm{P}(1.001)$$ is

0.002

$$-$$0.002

0.004

$$-$$0.004

MHT CET 2023 14th May Evening Shift

MCQ (Single Correct Answer)

-0

If $$y=\sqrt{(x-\sin x)+\sqrt{(x-\sin x)+\sqrt{(x-\sin x) \ldots.}}}$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}=$$

$$\frac{1-\cos x}{2 y-1}$$

$$\frac{1+\cos x}{2 y-1}$$

$$\frac{1-\cos x}{2 y+1}$$

$$\frac{1-\sin x}{2 y-1}$$

MHT CET 2023 14th May Evening Shift

MCQ (Single Correct Answer)

-0

Let $$\mathrm{f}(x)=5-|x-2|$$ and $$\mathrm{g}(x)=|x+1|, x \in \mathrm{R}$$ If $$\mathrm{f}(x)$$ attains maximum value at $$\alpha$$ and $$\mathrm{g}(x)$$ attains minimum value at $$\beta$$, then $$\lim _\limits{x \rightarrow-\alpha \beta} \frac{(x-1)\left(x^2-5 x+6\right)}{x^2-6 x+8}$$ is equal to

$$\frac{1}{2}$$

$$\frac{-3}{2}$$

$$\frac{-1}{2}$$

$$\frac{3}{2}$$

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