MHT CET 2024 4th May Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Identify the orbital having lowest energy from following. 2. What is the IUPAC name of following compound? 3. Which of the following is a molecular formula of cyclohexylamine? 4. Calculate heat required to convert 9 g of liquid water to water vapours from following equations. $$\begin{aligned} & \m 5. Which from following compounds is NOT in solid state at $25^{\circ} \mathrm{C}$ ? 6. Calculate the molar mass of solute when 4 g of it dissolved in $1 \mathrm{dm}^3$ solvent has osmotic pressure 2 atm at 3 7. Identify thermoplastic polymer from following. 8. Calculate radius of fourth orbit of $\mathrm{B}^{4+}$ ion. 9. Identify ' B ' in the following conversion. $$\mathrm{CH}_3-\mathrm{I} \xrightarrow{\mathrm{KCN}} \mathrm{~A} \xrightarr 10. What is the number of lone pair of electrons on central halogen atom in BrF$_3$? 11. One mole of a gas occupying 3 L volume is expanded against a constant external pressure of 1 bar to a volume of 15 L . C 12. Calculate $\Delta \mathrm{T}_{\mathrm{f}}$ of aqueous 0.01 m formic acid if van't Hoff factor is 1.1 $$\left[\mathrm{K}_ 13. Which among the following is NOT allylic halide? 14. Calculate the void volume of simple cubic unit cell if the volume of unit cell is $5.5 \times 10^{-22} \mathrm{~cm}^3$. 15. Calculate number of moles present in $9.10 \times 10^{-2} \mathrm{~kg}$ of water. 16. Identify the product 'B' in the following reaction. Toluene $\xrightarrow[\mathrm{CS}_2]{\text { Chromylchloride }} \mat 17. Which from following properties of lanthanoids is NOT true? 18. Which from the following defines enthalpy of a system? 19. Which from following salts is NOT derived from weak acid and weak base? 20. Which of the following is IUPAC name of hydroquinone? 21. Calculate the number of atoms in 0.3 gram metal if it forms bec structure $\left[\rho \times \mathrm{a}^3=3 \times 10^{- 22. Identify the product ' $Z$ ' in the following series of reactions. Ethanol $\xrightarrow[\Delta]{\mathrm{SOCl}_2} \mathr 23. Which of the following formula is used to calculate compressibility factor? 24. Which among the following is a pair of monocarboxylic acids? 25. What is the half life of a first order reaction if time required to decrease concentration of reactant from 0.8 M to 0.2 26. Which element from following has half filled If orbital at observed ground state? 27. What is the number of moles of nitrogen atoms present in one mole cytosine? 28. Which from following anions has lowest coagulating power for precipitation of positive sol? 29. Which of the following elements belongs to first group and fifth period of periodic table? 30. If $\mathrm{E}^{\circ}$ cell for $\mathrm{Cd}_{(\mathrm{s})}\left|\mathrm{Cd}_{(\mathrm{IM})}^{2+} \square \mathrm{Ag}_{ 31. Identify a zero dimensional nano structure from following 32. Identify the product ' $B$ ' in the following series of reactions. Isopropylcyanide $\xrightarrow[H \mathrm{Cl}]{\mathrm 33. For the reaction $2 \mathrm{~N}_2 \mathrm{O}_{5(\mathrm{~g})} \longrightarrow 4 \mathrm{NO}_{2(\mathrm{~g})}+\mathrm{O}_ 34. Which from following ligands is able to form linkage isomers? 35. Identify the bond order and magnetic nature of $\mathrm{Li}_2$ molecule respectively. 36. What is the conductivity of $0.02 \mathrm{~M} \mathrm{~AgNO}_3$ solution having cell constant $1.1 \mathrm{~cm}^{-1}$ an 37. What is the oxidation state of S in $\mathrm{SO}_4^{2-}$ ? 38. What is the general molecular formula of aldehydes? 39. Which among the following is NOT a pair of isomers? 40. Identify the total number of complexes having bidentate ligands in them from following list of complexes. a) Tetracyanon 41. What is the relation between the vapour pressure of solution, vapour pressure of solvent and its mole fraction in the so 42. Which of the following is obtained on oxidation of prop-1-ene with acidic $\mathrm{KMnO}_4$ ? 43. Calculate the solubility product of sparingly soluble salt BA at $25^{\circ} \mathrm{C}$ if its solubility is $7.2 \time 44. Which of the following expressions for conductivity of solution of an electrolyte is NOT correct? 45. What is the order of following reaction $$2 \mathrm{H}_2 \mathrm{O}_{2(\mathrm{~g})} \longrightarrow 2 \mathrm{H}_2 \mat 46. Crotonyl alcohol is an example of 47. Identify basic amino acid from following. 48. Which from following is a copolymer? 49. What is the total number of different types of unit cells present in triclinic crystal system? 50. Calculate the $[\mathrm{OH}]$ if pOH of solution is 4.94

Mathematics

1. The Solution set of the equation $\sin ^2 \theta-\cos \theta=\frac{1}{4}$ in the interval $[0,2 \pi]$ is 2. If the points $(1,-1, \lambda)$ and $(-3,0,1)$ are equidistant from the plane $3 x-4 y-12 z+13=0$, then the sum of all p 3. If $\bar{a}=\hat{i}-2 \hat{j}+3 \hat{k}$ and $\bar{b}=2 \hat{i}+3 \hat{j}-\hat{k}$, then the angle between the vectors $ 4. The maximum value of the objective function $\mathrm{z}=4 x+6 y$ subject to $3 x+2 y \leq 12, x+y \geq 4, x$, $y \geq 0$ 5. $$\frac{\mathrm{d}}{\mathrm{~d} x}\left(\cos ^{-1}\left(\frac{x-\frac{1}{x}}{x+\frac{1}{x}}\right)\right)=$$ 6. If $\bar{a}, \bar{b}, \bar{c}$ are non-coplanar vectors and $\overline{\mathrm{p}}=\frac{\overline{\mathrm{b}} \times \o 7. The approximate value of $\tan ^{-1}(0.999)$ is (use $\pi=3.1415$ ) 8. Let P be a plane passing through the points $(2,1,0),(4,1,1)$ and $(5,0,1)$ and $R$ be the point $(2,1,6)$. Then image o 9. If $\mathrm{O}(0,0), \mathrm{A}(1,2)$ and $\mathrm{B}(3,4)$ are the vertices of triangle OAB , then the joint equation o 10. The equation of the plane, passing through the point $(-1,2,-3)$ and parallel to the lines $\frac{x-1}{3}=\frac{y-2}{2}= 11. The incenter of the triangle ABC , whose vertices are $\mathrm{A}(0,2,1), \mathrm{B}(-2,0,0)$ and $\mathrm{C}(-2,0,2)$ i 12. The combined equation of two lines through the origin and making an angle of $45^{\circ}$ with the line $3 x+y=0$, is 13. The general solution of the differential equation $\frac{1}{x} \frac{\mathrm{~d} y}{\mathrm{~d} x}=\tan ^{-1}$ is 14. The area (in square units) in the first quadrant bounded by the curve $y=x^2+2$ and the lines $y=x+1, x=0$ and $x=3$, is 15. The co-ordinates of the point where the line through $\mathrm{A}(3,4,1)$ and $\mathrm{B}(5,1,6)$ crosses the $x y$-plane 16. The value of $\frac{\tan ^{-1}(\sqrt{3})-\sec ^{-1}(-2)}{\operatorname{cosec}^{-1}(-\sqrt{2})+\cos ^{-1}\left(\frac{-1}{ 17. The value of $\int \frac{\mathrm{d} x}{x^2\left(x^4+1\right)^{\frac{3}{4}}}$ is 18. If $(a+b) \cos C+(b+c) \cos A+(c+a) \cos B=72$ and if $a=18, b=24$, then area of the triangle $A B C$ is 19. If $\cot ^{-1}(7)+\cot ^{-1}(8)+\cot ^{-1}(18)=\cot ^{-1} x$, then the value of $x$ is 20. If $\mathrm{P}(\mathrm{X}=2)=0.3, \mathrm{P}(\mathrm{X}=3)=0.4, \mathrm{P}(\mathrm{X}=4)=0.3$, then the variance of rand 21. The Cartesian equation of a line is $2 x-2=3 y+1=6 z-2$, then the vector equation of the line is 22. Let $\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$ and $\overline{\mathrm{b}}=\hat{\math 23. If $\int\left(\frac{4 e^x-25}{2 e^x-5}\right) d x=A x+B \log \left(2 e^x-5\right)+c \quad$ (where c is a constant of int 24. The converse of $[p \wedge(\sim q)] \rightarrow r$ is 25. The differential equation obtained by eliminating arbitrary constant from the equation $y^2=(x+c)^3$ is 26. If the statements $p, q$ and $r$ have the truth values $\mathrm{F}, \mathrm{T}, \mathrm{F}$ respectively, then the truth 27. The decay rate of radium is proportional to the amount present at any time $t$. If initially 60 gms was present and half 28. If $\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi$, then the value of $x^2+y^2+z^2-2 x y z$ is 29. Let $\mathrm{A}=\left[\begin{array}{cc}1 & 2 \\ -5 & 1\end{array}\right]$ and $\mathrm{A}^{-1}=x \mathrm{~A}+y \mathrm{I 30. If $\mathrm{f}(x)=\frac{x+x^2+x^3+\ldots \ldots \ldots \ldots+x^{\mathrm{n}}-\mathrm{n}}{x-1}$, for $x \neq 1$ is contin 31. The particular solution of differential equation $\left(1+y^2\right)(1+\log x) \mathrm{d} x+x \mathrm{~d} y=0$ at $x=1, 32. If $\lim _\limits{x \rightarrow 1} \frac{x^2-a x+b}{x-1}=7$, then $a+b$ is equal to 33. A ladder 5 m long rests against a vertical wall. If its top slides downwards at the rate of $10 \mathrm{~cm} / \mathrm{s 34. If $\mathrm{f}(x)=\frac{x}{2-x}, \mathrm{~g}(x)=\frac{x+1}{x+2}$, then (gogof) $(x)=$ 35. If $\mathrm{f}(x)=\cos ^{-1} x, \mathrm{~g}(x)=\mathrm{e}^x$ and $\mathrm{h}(x)=\mathrm{g}(\mathrm{f}(x))$, then $\frac{ 36. Five persons $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ and E are seated in a circular arangement, if each of them 37. The value of $\int_{\frac{\pi}{6}}^{\frac{\pi}{4}} \frac{1}{\sin 2 x\left(\tan ^5 x+\cot ^5 x\right)} d x$ is 38. If $\left|\frac{\mathrm{z}}{1+\mathrm{i}}\right|=2$, where $\mathrm{z}=x+\mathrm{i} y, \mathrm{i}=\sqrt{-1}$ represents 39. If $y=A \cos \mathrm{n} x+\mathrm{B} \sin \mathrm{nx}$, then $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}=$ 40. A man and his wife appear for an interview for two posts. The probability of the husband's selection is $\frac{1}{7}$ an 41. The expected value of the sum of the two numbers obtained on the uppermost faces, when two fair dice are rolled, is 42. $$\int \tan ^{-1}\left(\frac{1-\sin x}{1+\sin x}\right) d x=$$ 43. The mean and variance of seven observations are 8 and 16 respectively. If 5 of the observations are $2,4,10,12,14$, then 44. The equation of the tangent to the curve $y=1-\mathrm{e}^{\frac{x}{3}}$ at the point of intersection with Y -axis is 45. $$\int \frac{\left(x^2+1\right)}{(x+1)^2} \mathrm{~d} x=$$ 46. The equation of the circle which passes through the centre of the circle $x^2+y^2+8 x+10 y-7=0$ and concentric which the 47. The acute angle between the lines $x \cos 30^{\circ}+y \sin 30^{\circ}=3$ and $x \cos 60^{\circ}+y \sin 60^{\circ}=5$ is 48. If $f(x)=\left(\sin ^4 x+\cos ^4 x\right), 0 49. For an entry to a certain course, a candidate is given twenty problems to solve. If the probability that the candidate c 50. If $\mathrm{A}>\mathrm{B}$ and $\tan \mathrm{A}-\tan \mathrm{B}=x$ and $\cot \mathrm{B}-\cot \mathrm{A}=y$, then $\cot (

Physics

1. Two surfaces A and B are enclosing the charges as shown below. The total normal electric induction (T.N.E.I) through the 2. An alternating current is given by $\mathrm{I}=100 \sin (50 \pi \mathrm{t})$. How many times will the current become zer 3. Two bodies ' X ' and ' Y ' at temperatures ' $\mathrm{T}_1$ ' K and ' $T_2$ ' K respectively have the same dimensions. I 4. The planar concentric rings of metal wire having radii $r_1$ and $r_2$ (with $r_1>r_2$ ) are placed in air. The current 5. A spherical rubber balloon carries a charge, uniformly distributed over the surface. As the balloon is blown up and incr 6. In a Wheatstone's bridge, the resistances in four arms are as shown in the figure. The balancing condition of the bridge 7. Two solid spheres ( A and B ) are made of metals having densities $\rho_A$ and $\rho_B$ respectively. If there masses ar 8. A stationery wave is represented by $y=12 \cos \left(\frac{\pi}{6} x\right) \sin (8 \pi t)$, where $x \& y$ are in cm an 9. A hemispherical portion of radius ' $R$ ' is removed from the bottom of a cylinder of radius ' R '. The volume of the re 10. A parallel beam of light of intensity $I_0$ is incident on a glass plate, $25 \%$ of light is reflected by upper surface 11. A convex lens of refractive index $\frac{3}{2}$ has a power 2.5. If it is placed in a liquid of refractive index 2, the 12. The truth table for the given logic circuit is 13. A single slit of width $d$ is illuminated by violet light of wavelength 400 nm and the width of the diffraction pattern 14. A thin uniform circular disc of mass ' $M$ ' and radius ' $R$ ' is rotating with angular velocity ' $\omega$ ' in a hori 15. A particle carrying a charge equal to 100 times the charge on an electron is rotating one rotation per second in a circu 16. A carpet of mass ' $M$ ' made of a material is rolled along its length in the form of a cylinder of radius ' $R$ ' and k 17. A water film is formed between two parallel wires of 10 cm length. The distance of 0.5 cm between the wires is increased 18. A coil of self inductance L is connected in series with a bulb B and an a.c. source. Brightness of the bulb decreases wh 19. A transverse wave travelling along a stretched string has a speed of $30 \mathrm{~m} / \mathrm{s}$ and a frequency of 25 20. A lead bullet moving with velocity ' $v$ ' strikes a wall and stops. If $50 \%$ of its energy is converted into heat, th 21. A pendulum is oscillating with frequency ' $n$ ' on the surface of earth. If it is taken to a depth $\frac{R}{4}$ below 22. The ratio of minimum wavelengths of Lyman and Balmer series will be 23. If a $10 \mu \mathrm{C}$ charge exists at the centre of a square, the work done in moving a $2 \mu \mathrm{C}$ point cha 24. If $C_p$ and $C_v$ are molar specific heats of an ideal gas at constant pressure and volume respectively and ' $\gamma$ 25. A magnetic field of $2 \times 10^{-2} \mathrm{~T}$ acts at right angles to a coil of area $100 \mathrm{~cm}^2$ with 50 t 26. A body moves along a circular path of radius 15 cm . It starts from a point on the circular path and reaches the end of 27. The kinetic energy of an electron is increased by 2 times, then the de-Broglie wavelength associated with it changes by 28. The change in the internal energy of the mass of gas, when the volume changes from ' $V$ ' to ' 2 V ' at constant pressu 29. In the circuit diagram shown in figure, the current through the zener diode is 30. If the electric flux entering and leaving an enclosed surface are $\phi_1$ and $\phi_2$ respectively, the electric charg 31. Some water is filled in a container of height 30 cm . If is is to appear half filled to the observer when viewed from th 32. A solid cylinder of mass ' $M$ ' and radius ' $R$ ' rolls down an inclined plane of height ' $h$ '. When it reaches the 33. The maximum velocity and maximum acceleration of a particle performing a linear S.H.M. is ' $\alpha$ ' and ' $\beta$ ' r 34. When a galvanometer is shunted by a resistance ' $s$ ', its current capacity increases ' $n$ ' times. If the same galvan 35. A pergect gas of volume 5 litre is compressed isothermally to volume of 1 litre. The r.m.s. speed of the molecules will 36. An electron of mass ' $m$ ' and charge ' $q$ ' is accelerated from rest in a uniform electric field of intensity ' $E$ ' 37. In a biprism experiment, monochromatic light of wavelength ' $\gamma$ ' is used. The distance between the two coherent s 38. The ratio of weight of a man in a stationery lift and weight when the lift is moving downward with a uniform acceleratio 39. In series LCR resonant circuit, the capacitance is changed from C to 3 C . To obtain the same resonant frequency, the in 40. A mass ' $m$ ' attached to a spring oscillates with a period of 3 second. If the mass is increased by 0.6 kg , the perio 41. The depletion layer in p-n junction region is caused by 42. Half-lives of two radioactive elements A and B are 30 minute and 60 minute respectively. Initially the samples have equa 43. A train sounding a whistle of frequency 510 Hz approaches a station at $72 \mathrm{~km} / \mathrm{hr}$. The frequency of 44. A set of 28 turning forks is arranged in an increasing order of frequencies. Each fork produces ' $x$ ' beats per second 45. A current of 0.5 A is passed through winding of a long solenoid having 400 turns. The magnetic flux linked with each tur 46. Identify the correct figure which shows the relation between the height of water column in a capillary tube and the capi 47. The escape velocity from earth surface is $11 \mathrm{~km} / \mathrm{s}$. The escape velocity from a planet having twice 48. A magnetic intensity of $500 \mathrm{~A} / \mathrm{m}$, produces a magnetic flux of $2.4 \times 10^{-5} \mathrm{~Wb}$ in 49. A photosensitive metallic surface has work function $\phi$. If photon of energy $3 \phi$ falls on the surface, the elect 50. A real gas behaves as an ideal gas at

MHT CET 2024 4th May Evening Shift

MCQ (Single Correct Answer)

-0

The particular solution of differential equation $\left(1+y^2\right)(1+\log x) \mathrm{d} x+x \mathrm{~d} y=0$ at $x=1, y=1$ is

$\log x-\frac{1}{2}(\log x)^2-\tan ^{-1} y=-\frac{\pi}{4}$

$\log x+\frac{1}{2}(\log x)^2+\tan ^{-1} y=\frac{\pi}{4}$

$\log x-\frac{1}{2}(\log x)^2+\tan ^{-1} y=\frac{\pi}{4}$

$\log x+\frac{1}{2}(\log x)^2-\tan ^{-1} y=\frac{\pi}{4}$

MHT CET 2024 4th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\lim _\limits{x \rightarrow 1} \frac{x^2-a x+b}{x-1}=7$, then $a+b$ is equal to

$-$1

$-$11

MHT CET 2024 4th May Evening Shift

MCQ (Single Correct Answer)

-0

A ladder 5 m long rests against a vertical wall. If its top slides downwards at the rate of $10 \mathrm{~cm} / \mathrm{sec}$., then the foot of the ladder is sliding at the rate of _________ $\mathrm{m} / \mathrm{sec}$., when it is 4 m away from the wall.

0.75

7.5

0.0075

0.075

MHT CET 2024 4th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\mathrm{f}(x)=\frac{x}{2-x}, \mathrm{~g}(x)=\frac{x+1}{x+2}$, then (gogof) $(x)=$

$\frac{6+x}{10-2 x}$

$\frac{6-x}{10+2 x}$

$\frac{6+x}{10+2 x}$

$\frac{6-x}{10-2 x}$