MHT CET 2024 10th May Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Calculate dissociation constant of a weak monobasic acid if it is $0.05 \%$ dissociated in 0.02 M solution. 2. Select the correct increasing order of boiling points of alcohols, amines and carboxylic acids of comparable molar mass 3. Which of the following orbitals is represented by $\mathrm{n}=3$ and $l=2$ ? 4. Which of the following is not a property of hydrogen peroxide? 5. The molar conductivity of 0.01 M acetic acid at $25^{\circ} \mathrm{C}$ is $16.5 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol 6. Which from following reactions exhibits good atom economy according to the principles of green chemistry? 7. Which from following statements is NOT true about absorption? 8. Identify the source of linen from following: 9. Identify acidic amino acid from following (represented by using three letter symbols). 10. What is the number of moles of ionisable $\mathrm{Cl^-}$ ions in a coordinate complex if it forms two moles of $\mathrm{ 11. Identify the number of moles of H atoms present in n moles of organic compound represented as 12. What is the number of chiral carbon atoms in threose? 13. Identify a complex having monodentate ligand from following : 14. Which element from following does NOT exhibit magnetic moment in +2 state? 15. Which from following statements is NOT correct about thermoplastic polymers? 16. Which from following elements is NOT a member of group 16 from periodic table? 17. Identify false statement about transition elements. 18. Which among the following is not haloalkyne? 19. Which isomer of $\mathrm{C}_4 \mathrm{H}_9 \mathrm{OH}$ has highest boiling point? 20. A buffer solution contains equal concentrations of weak acid and its salt with strong base. Calculate pH of buffer solut 21. If four different elements A, B, C and D having electronic configuration as $\mathrm{A}=[\mathrm{Ne}] 3 \mathrm{~s}^2 3 22. What is IUPAC name of the following compound? 23. For the reaction $\mathrm{A}+\mathrm{B} \longrightarrow$ product, rate law equation is, rate $=k[A]^2[B]$. If rate of re 24. Which of the following is NOT obtained when a mixture of methyl bromide and ethyl bromide is treated with sodium metal i 25. Calculate the volume of simple cubic unit cell if the radius of particle in it is 400 pm. 26. Calculate the solubility of a gas having partial pressure 0.15 bar at $25^{\circ} \mathrm{C}$. $\left[\mathrm{K}_{\mathr 27. What is the frequency of violet light having wavelength 400 nm ? 28. Identify the product ' B ' in the following series of reactions. $$\text { Propan -1-ol } \xrightarrow[623 \mathrm{~K}]{ 29. Identify an aldehyde used in margarine and in food for its buttery odour. 30. Identify the major product formed in the bromination of 2-Methylpropane. 31. For an ideal gas, the heat of reaction at constant pressure and heat of reaction at constant volume are related by equat 32. What is IUPAC name of the following compound? 33. Which of the following is a tertiary allylic alcohol? 34. Which of the following is Mendius reduction? 35. For the reaction $\mathrm{CH}_{4(\mathrm{~g})}+\mathrm{H}_{2(\mathrm{~g})} \longrightarrow \mathrm{C}_2 \mathrm{H}_{6(\m 36. Rate of a first order reaction is $1.5 \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1}$ minute ${ }^{-1}$ at 0.5 M concent 37. Calculate the density of a metal molar mass $197 \mathrm{~g} \mathrm{~mol}^{-1}$ if it forms fcc structure. $\left[\math 38. A gas expands isothermally against a constant external pressure of 1 bar from 10 dm$^3$ to 20 dm$^3$ by absorbing 800 J 39. Which from following decides the rate of multistep reaction? 40. What is minimum number of spheres required of develop a tetrahedral void? 41. Which from following ionic solids exhibits decrease in its solubility in water with increase of temperature? 42. Which from the following equations represents the relation between solubility ( $\mathrm{mol} \mathrm{~L}^{-1}$ ) and so 43. Which of the following is released at cathode during electrolysis of aqueous sodium chloride? 44. Identify structural formula of DDT. 45. What is the change in oxidation number of S in following reaction? $$\mathrm{H}_2 \mathrm{~S}+\mathrm{NO}_3^{-} \longrig 46. Which law is illustrated by compounds $\mathrm{H}_2 \mathrm{O}$ and $\mathrm{H}_2 \mathrm{O}_2$ formed from two differen 47. Calculate the $\mathrm{E}_{\text {cell }}^{\circ}$ of $\mathrm{Al}\left|\mathrm{Al}_2\left(\mathrm{SO}_4\right)_{3(\math 48. What is the volume of a gas at $1.032 \times 10^5 \mathrm{~Nm}^{-2}$ if it occupies $1 \mathrm{~dm}^3$ of volume at norm 49. Calculate molar mass of nonvolatile solute if a solution containing 0.35 g solute in 100 g water has boiling point eleva 50. What is the number of Lewis structures for $\mathrm{NO}_2^{-}$?

Mathematics

1. Let two non-collinear unit vectors $\hat{\mathrm{a}}$ and $\hat{\mathrm{b}}$ form an acute angle. A point P moves, so th 2. The vector equation of the plane passing through the point $\mathrm{A}(1,2,-1)$ and parallel to the vectors $2 \hat{i}+\ 3. In a triangle ABC , with usual notations, if $\mathrm{m} \angle \mathrm{A}=45^{\circ}, \mathrm{m} \angle B=75^{\circ}$, 4. If $y$ is a function of $x$ and $\log (x+y)=2 x y$, then the value of $y^{\prime}(0)$ is 5. If $\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$ are mutually perpendicular vectors having magni 6. The volume of a ball is increasing at the rate of $4 \pi \mathrm{cc} / \mathrm{sec}$. The rate of increase of the radius 7. $$\int_\limits0^{\frac{\pi}{4}} \log \left(\frac{\sin x+\cos x}{\cos x}\right) d x=$$ 8. $A$ and $B$ are independent events with $P(A)=\frac{3}{10}$, $\mathrm{P}(\mathrm{B})=\frac{2}{5}$, then $\mathrm{P}\left 9. Let $\mathrm{f}(x)=(x-1)(x-2)(x-3), x \in[0,4]$. Values of C will be __________ if L.M.V.T. (Lagrange's Mean Value Theor 10. The general solution of the differential equation $\mathrm{e}^{y-x} \frac{\mathrm{~d} y}{\mathrm{~d} x}=y\left(\frac{\si 11. Minimum number of times a fair coin must be tossed, so that the probability of getting at least one head, is more than $ 12. The vector of magnitude 6 units and perpendicular to vectors $2 \hat{i}+\hat{j}-3 \hat{k}$ and $\hat{\mathrm{i}}-2 \hat{ 13. The shortest distance between lines $\bar{r}=(\hat{i}+2 \hat{j}-\hat{k})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})$ and $\bar 14. The graphical solution set of the system of inequations $x+y \geq 1,7 x+9 y \leq 63, y \leq 5, x \leq 6$, $x \geq 0, y \ 15. $\tan \left(\cos ^{-1} \frac{1}{\sqrt{2}}+\tan ^{-1} \frac{1}{2}\right)=$ 16. If $x^2 y^2=\sin ^{-1} x+\cos ^{-1} x$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=1$ and $y=2$ is 17. If $\overline{\mathrm{a}}=\hat{\mathrm{j}}-\hat{\mathrm{k}}$ and $\overline{\mathrm{c}}=\hat{\mathrm{i}}-\hat{\mathrm{j} 18. The expression $((p \wedge q) \vee(p \vee \sim q)) \wedge(\sim p \wedge \sim q)$ is equivalent to 19. If $y=4 x-5$ is a tangent to the curve $y^2=p x^3+q$ at $(2,3)$, then the values of $p$ and $q$ are respectively 20. If $\mathrm{w}=\frac{-1-\mathrm{i} \sqrt{3}}{2}$ where $\mathrm{i}=\sqrt{-1}$, then the value of $\left|\begin{array}{cc 21. $$\int_\limits0^a \frac{x-a}{x+a} d x=$$ 22. Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius $r$. If PS and RQ intersect at a p 23. A random variable X assumes values $1,2,3, \ldots \ldots ., \mathrm{n}$ with equal probabilities. If $\operatorname{var} 24. $\overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{b}}=4 \hat{\mathrm{i}}-2 \h 25. If $y=\sin ^2\left(\cot ^{-1} \sqrt{\frac{1+x}{1-x}}\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ has the value 26. If the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-\mathrm{k}}{2}=\frac{\mathrm{z}}{1}$ 27. Inverse of the matrix $\left[\begin{array}{cc}0.8 & -0.6 \\ 0.6 & 0.8\end{array}\right]$ is 28. $\int \frac{\mathrm{d} x}{\sqrt{\mathrm{e}^x-1}}=2 \tan ^{-1}(\mathrm{f}(x))+\mathrm{c}$ where $x>0$ and c is a constant 29. If $\mathrm{f}(x)=\left(\frac{1+\tan x}{1+\sin x}\right)^{\operatorname{cosec} x}$ is continuous at $x=0$ then $f(0)$ is 30. The value of $\cos \left(2 \cos ^{-1} x+\sin ^{-1} x\right)$ at $x=\frac{1}{5}$ is 31. $\int_\limits{\frac{-\pi}{4}}^{\frac{\pi}{4}}(\sin x)^{-4} \mathrm{~d} x$ has the value 32. The mean and variance of 7 observations are 8 and 16 respectively. If first five observations are $2,4,10,12,14$, then a 33. The projection of $\overline{\mathrm{AB}}$ on $\overline{\mathrm{CD}}$, where $A \equiv(2,-3,0), B \equiv(1,-4,-2), C \e 34. The equation of the plane through the point $(2,-1,-3)$ and parallel to the lines $\frac{x-1}{3}=\frac{y+2}{2}=\frac{z}{ 35. If $x, y, z$ are in Arithmetic Progression and $\tan ^{-1} x, \tan ^{-1} y, \tan ^{-1} z$ are also in Arithmetic progres 36. Derivative of $\tan ^{-1} \sqrt{\frac{1-x}{1+x}}$ w.r.t. $\cos ^{-1}\left(4 x^3-3 x\right)$ is 37. If $\frac{\mathrm{d}}{\mathrm{d} x} \mathrm{f}(x)=4 x^3-\frac{3}{x^4}$ such that $\mathrm{f}(2)=0$, then $\mathrm{f}(x)$ 38. $$\lim _\limits{x \rightarrow 0} \frac{9^x-4^x}{x\left(9^x+4^x\right)}=$$ 39. If the length of the perpendicular to a line from the origin is $2 \sqrt{2}$ units, which makes an angle of $135^{\circ} 40. A spherical rain drop evaporates at a rate proportional to its surface area. If initially its radius is 3 mm and after 1 41. If $\overline{\mathrm{a}}=2 \hat{i}+2 \hat{j}+3 \hat{k}, \bar{b}=-\hat{i}+2 \hat{j}+\hat{k}$ and $\bar{c}=3 \hat{i}+\hat 42. The number of integer values of $m$, for which $x$-coordinate of the point of intersection of the lines $3 x+4 y=9$ and 43. If $\tan ^{-1}(x+2)+\tan ^{-1}(x-2)-\tan ^{-1}\left(\frac{1}{2}\right)=0$, then one value of $x$ is 44. The value of $\int \frac{\mathrm{d} x}{x^2\left(x^4+1\right)^{\frac{3}{4}}}$ is 45. The converse of "If 3 is a prime number, then 3 is odd." is 46. $$\int \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) \mathrm{d} x=$$ 47. Let $\mathrm{f}(x)=\frac{a x}{x+1}, x \neq-1$, then for $\alpha=$ ________, $\mathrm{f}(\mathrm{f}(x))=x$. 48. The area (in sq. units) of the region $\left\{(x, y) / x \geq 0, x+y \leq 3, x^2 \leq 4 y\right.$ and $\left.y \leq 1+\s 49. The order of the differential equation, whose general solution is given by $$y=\left(c_1+c_2\right) \cos \left(x+c_3\rig 50. If $(p \wedge \sim r) \rightarrow(\sim p \vee q)$ has truth value False, then truth values of $p, q, r$ are respectively

Physics

1. In semiconductors at room temperature, 2. In the given circuit, Zener breakdown voltage is 8 V . If power of Zener diode is 1.6 W . The value of $R$ is 3. An a.c. voltage source $\mathrm{V}=\mathrm{V}_0 \sin \omega \mathrm{t}$ is connected across resistance ' $R$ ' and capac 4. The black discs $\mathrm{x}, \mathrm{y}$ and z have radii $1 \mathrm{~m}, 2 \mathrm{~m}$ and 3 m respectively. The wavel 5. The height ' h ' from the surface of the earth at which the value of ' $g$ ' will be reduced by $64 \%$ than the value a 6. The length of a sonometer wire 'AB' is 110 cm . Where should the two bridges be placed from end ' $A$ ' to divide the wi 7. If a unit charge is taken from one point to another point over an equipotential surface, then 8. Two soap bubbles having radii ' $r_1$ ' and ' $r_2$ ' has inside pressure ' $P_1$ ' and ' $\mathrm{P}_2$ ' respectively. 9. A transformer has 120 turns in the primary coil and carries 5 A current. Input power is one kilowatt. To have 560 V outp 10. A vehicle runs on a straight road of length 'L'. It travels half the distance with speed V and the remaining distance wi 11. A particle of mass ' $m$ ' performs uniform circular motion of radius ' $r$ ' with linear speed ' $v$ ' under the applic 12. In Young's double slit experiment, the distance between the two coherent sources is ' d ' and the distance between the s 13. A particle starts oscillating simple harmonically from its equilibrium position with time period ' T '. What is the rati 14. A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm. The power of combination is 15. A particle performs linear S.H.M. When the displacement of the particle from mean position is 3 cm and 4 cm , correspond 16. A photoelectric surface is illuminated successively by monochromatic light of wavelength ' $\lambda$ ' and $\left(\frac{ 17. The magnitude of magnetic field at point 'O' in the following figure will be 18. Radius of first orbit in H -atom is ' $a_0$ ' Then, de-Broglie wavelength of electron in the third orbit is 19. For a gas, $\frac{\mathrm{R}}{\mathrm{C}_{\mathrm{v}}}=0.4$ where R is the universal gas constant and ' $\mathrm{C}_{\ma 20. Which one of the following is 'NOT' a contact force? 21. In a thermodynamic system ' $\Delta \mathrm{U}$ ' represents the increase in internal energy and ' $W$ ' the work done b 22. If current of 4 A produces magnetic flux of $3 \times 10^{-3} \mathrm{~Wb}$ through a coil of 400 turns, the energy stor 23. Two bodies A and B have their moments of inertia $I_1$ and $I_2$ respectively about their axis of rotation. If their kin 24. A body starts from rest from a distance $\mathrm{R}_0$ from the centre of the earth. The velocity acquired by the body w 25. Two metal spheres are falling through a liquid of density $2.5 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$ with the same un 26. In series LCR circuit, 'R' represents resistance of electric bulb. If the frequency of a.c. supply is doubled, the value 27. Two point charges $\mathrm{q}_1=6 \mu \mathrm{C}$ and $\mathrm{q}_2=4 \mu \mathrm{C}$ are kept at points $A$ and $B$ in 28. Two light rays having the same wavelength ' $\lambda$ ' in vacuum are in phase initially. Then, the first ray travels a 29. Prong of a vibrating tuning fork is in contact with water surface. It produces concentric circular waves on the surface 30. Rate of radiation by a black body is ' R ' at temperature 'T'. Another body has same area but emissivity is 0.2 and temp 31. The end correction for the vibrations of air column in a tube of circular cross-section will be more if the tube is 32. The potential difference $\left(V_A-V_B\right)$ between the points ' $A$ ' and ' $B$ ' in the given part of the circuit 33. The logic gate represented by following logic circuit is 34. A coil of ' $n$ ' turns and radius ' $R$ ' carries a current 'I'. It is unwound and rewound to make a new coil of radius 35. A particle rotates in a horizontal circle of radius 'R' in a conical funnel with constant speed 'V'. The inner surface o 36. Two point charges $(A$ and $B)+4 q$ and $-4 q$ are placed along a line separated by a distance I '. Force acting between 37. In Young's double slit experiment, the slits are separated by 0.6 mm and screen is placed at a distance of 1.2 m from sl 38. A charged particle is moving in a uniform magnetic field in a circular path of radius ' $R$ '. When the kinetic energy o 39. In the Bohr model of hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and 40. A Carnot's cycle operating between $T_H=600 \mathrm{~K}$ and $T_c=300 \mathrm{~K}$ produces 1.5 kJ of mechanical work pe 41. Two concentric circular coils having radii ' $r_1{ }^{\prime}$ and ' $r_2$ ' $\left(r_2 \ll r_1\right)$ are placed co-ax 42. An ordinary body cools from ' $4 \theta^{\prime}$ ' to ' $3 \theta^{\prime}$ ' in ' t ' minutes. The temperature of that 43. Stationary wave is produced along the stretched string of length 80 cm . The resonant frequencies of string are $90 \mat 44. For the series $L C R$ circuit, $R=\frac{X_L}{2}=2 \mathrm{X}_{\mathrm{c}}$. The impedance of the circuit and the phase 45. In compound microscope, the focal length and the aperture of the objective used is respectively 46. A glass capillary of radius 0.35 mm is inclined at $60^{\circ}$ with the vertical in water. The height of the water colu 47. When a photosensitive surface is irradiated by lights of wavelengths ' $\lambda_1$ ' and ' $\lambda_2$ ', kinetic energi 48. In an ammeter, $0.25 \%$ of main current passes through the galvanometer. If the resistance of the galvanometer is ' G ' 49. A simple pendulum of length ' $l$ ' has a brass bob attached at its lower end. It's period is ' T '. A steel bob of the 50. The electric potential at a point on the axis of an electric dipole is proportional to [r = distance between centre of t

MHT CET 2024 10th May Evening Shift

MCQ (Single Correct Answer)

-0

The value of $\cos \left(2 \cos ^{-1} x+\sin ^{-1} x\right)$ at $x=\frac{1}{5}$ is

$-\frac{\sqrt{6}}{5}$

$\frac{2 \sqrt{6}}{5}$

$-\frac{2 \sqrt{6}}{5}$

$\frac{2 \sqrt{5}}{6}$

MHT CET 2024 10th May Evening Shift

MCQ (Single Correct Answer)

-0

$\int_\limits{\frac{-\pi}{4}}^{\frac{\pi}{4}}(\sin x)^{-4} \mathrm{~d} x$ has the value

$\frac{-3}{2}$

$\frac{3}{2}$

$\frac{-8}{3}$

$\frac{8}{3}$

MHT CET 2024 10th May Evening Shift

MCQ (Single Correct Answer)

-0

The mean and variance of 7 observations are 8 and 16 respectively. If first five observations are $2,4,10,12,14$, then absolute difference of remaining two observations is

MHT CET 2024 10th May Evening Shift

MCQ (Single Correct Answer)

-0

The projection of $\overline{\mathrm{AB}}$ on $\overline{\mathrm{CD}}$, where $A \equiv(2,-3,0), B \equiv(1,-4,-2), C \equiv(4,6,8)$ and $\mathrm{D} \equiv(7,0,10)$ is

$\frac{1}{\sqrt{6}}$

$\frac{1}{7}$

$\frac{4}{\sqrt{6}}$

$\frac{4}{7}$

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