MHT CET 2024 9th May Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Identify fibrous protein from following. 2. For the reaction, $$\mathrm{C}_3 \mathrm{H}_{8(\mathrm{~g})}+5 \mathrm{O}_{2(\mathrm{~g})} \longrightarrow 3 \mathrm{CO} 3. Which from following reactions is not possible for benzene due to reversible nature? 4. Calculate the volume of unit cell when metal having density $1 \mathrm{~g} \mathrm{~cm}^{-3}$ and molar mass $23 \mathrm 5. Which polymer is obtained from monomers using 6. Which from following elements belongs to the actinoids? 7. Which of the following rules states that it is impossible to determine simultaneously the exact position and exact momen 8. Calculate the cryoscopic constant of solvent when 2.5 gram solute is dissolved in 35 gram solvent lowers its freezing po 9. Which of the following solvents reduces the environmental pollution? 10. What is the number of electrons present in d-subshell if its atomic number is 27 and oxidation state is +2 ? 11. What is the volume occupied by 1 molecule of water, if its density is $1 \mathrm{~g} \mathrm{~cm}^{-3}$ ? 12. Identify the reason for the solubility of polar solute in polar solvent from the following. 13. Identify biodegradable polymer from following. 14. What is the pOH of millimolar solution of $\mathrm{Ca}(\mathrm{OH})_2$ ? 15. Which from following pairs is an example of isotones? 16. What is change in internal energy of the system when work done by the system is 150 J and system release 300 J of heat? 17. Which from following coordinate complexes is a heteroleptic complex? 18. Identify glycosidic linkage present in maltose. 19. What is the number of moles of Cl atoms and N atoms respectively present in n moles of tear gas? 20. What is bond angle $\mathrm{F}-\mathrm{B}-\mathrm{F}$ in $\mathrm{BF}_3$ ? 21. Which from the following statements about $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$ complex is NOT cor 22. What is the relation between edge length and total volume occupied by atoms in bec unit cell? 23. What is the value of $x$ and $y$ in order to balance following redox reaction? $$\mathrm{xCuO}+\mathrm{yNH}_3 \longright 24. Molar conductivity of 0.02 M weak acid is $7.92 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ and its molar conductivit 25. Which from following compounds is most covalent? 26. What is the total number of atoms present in fcc unit cell? 27. For which electrolyte the molar conductivity at infinite dilution can not be obtained graphically? 28. The major product formed in carbylamine reaction is 29. Which among the following elements has highest electronegativity? 30. Consider the reaction $3 \mathrm{I}^{-}+\mathrm{S}_2 \mathrm{O}_8^{2-} \longrightarrow \mathrm{I}_3^{-}+2 \mathrm{SO}_4^ 31. For the reaction, $\mathrm{NO}_{2(\mathrm{~g})}+\mathrm{CO}_{(\mathrm{g})} \longrightarrow \mathrm{NO}_{(\mathrm{g})}+\m 32. Which among the following compounds does not correctly match with its formula? 33. Which among the following forces of attraction is developed between polar and non polar molecules? 34. Which among the following is correct conjugate acid base pair for the equation stated below? $$\mathrm{HCl}+\mathrm{NH}_ 35. Which among the following compounds is NOT a tertiary amine? 36. Which among the following reactions is used for the preparation of alkyl fluorides? 37. What type of colloid is milk? 38. What is the osmotic pressure of solution prepared by dissolving 3 gram solute in $2 \mathrm{dm}^3$ water at 300 K . (Mol 39. Which among the following is the method for the preparation of ethers? 40. Identify the bond line formula for propan-1-ol 41. IUPAC name of the compound 42. Dissociation constant and degree of dissociation of weak acid are $1.8 \times 10^{-5}$ and 0.03 respectively. What will 43. The decreasing order of reactivity of following alcohols with halo acid is (I) $\mathrm{CH}_3 \mathrm{OH}$ (II) $\mathrm 44. What is the product obtained in the reaction? $\mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_2-\mathrm{CHO} \xrighta 45. Two moles of an ideal gas is expanded isothermally from a volume of $300 \mathrm{~cm}^3$ to 2.5 $\mathrm{dm}^3$ at 298 K 46. Identify name of from following. 47. Which of the following compounds is used to convert acetaldehyde into acetaldehyde cynanohydrin? 48. What volume of chlorine gas (molar mass 71) is evolved at STP during electrolysis of fused NaCl by passage of 1 amp curr 49. Identify the test from following so that aldehyde when boiled with ammoniacal silver nitrate solution deposts silver. 50. Find the percentage of unreacted reactant for zero order reaction in 90 second having rate constant $1 \mathrm{~mol} \ma

Mathematics

1. If $A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & a & 3 \\ 3 & 2 & 2\end{array}\right]$ and $B=\left[\begin{array}{ccc}-2 & 2. If $\int \mathrm{f}(x) \mathrm{d} x=\psi(x)$, then $\int x^5 \mathrm{f}\left(x^3\right) \mathrm{d} x$ is equal to 3. The population of a town increases at a rate proportional to the population at that time. If the population increases fr 4. If X is a random variable with distribution given below .tg {border-collapse:collapse;border-spacing:0;} .tg td{border 5. An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random with 6. The area (in sq. units) bounded by the curves $y=(x+1)^2, y=(x-1)^2$ and the line $y=\frac{1}{4}$ is 7. If $\int \frac{d x}{\sqrt[3]{\sin ^{11} x \cos x}}=-\left(\frac{3}{8} f(x)+\frac{3}{2} g(x)\right)+c$ then 8. A random variable X takes values $-1,0,1,2$ with probabilities $\frac{1+3 \mathrm{p}}{4}, \frac{1-\mathrm{p}}{4}, \frac{ 9. Let C be a curve given by $y(x)=1+\sqrt{4 x-3}$, $x>\frac{3}{4}$. If P is a point on C , such that the tangent at P has 10. The equation of the circle, the end points of whose diameter are the centres of the circles $x^2+y^2+6 x-14 y+5=0$ and $ 11. The equation of the plane, passing through the point $(1,1,1)$ and perpendicular to the planes $2 x+y-2 z=5$ and $3 x-6 12. If for $x \in\left(0, \frac{1}{4}\right)$, the derivative of $\tan ^{-1}\left(\frac{6 x \sqrt{x}}{1-9 x^3}\right)$ is $\ 13. If the vectors $a \hat{i}+\hat{j}+\hat{k}, \hat{i}+b \hat{j}+\hat{k}, \hat{i}+\hat{j}+c \hat{k}$ $(a \neq b, c \neq 1)$ 14. The sides of a triangle are $\sin \theta, \cos \theta$ and $\sqrt{1+\sin \theta \cos \theta}$ for some $0 15. If $\lim\limits_{x \rightarrow \infty}\left(\frac{x^2+x+1}{x+1}-a x-b\right)=4$ then 16. If $y=y(x)$ is the solution of the differential equation $x \frac{\mathrm{dy}}{\mathrm{d} x}+2 y=x^2$ satisfying $y(1)=1 17. The value of $\cos ^{-1}\left\{\frac{1}{\sqrt{2}}\left(\cos \frac{9 \pi}{10}-\sin \frac{9 \pi}{10}\right)\right\}$ is 18. Consider the statements given by following : (A) If $3+3=7$, then $4+3=8$. (B) If $5+3=8$, then earth is flat. (C) I 19. If $\alpha+\beta=\frac{\pi}{2}$ and $\beta+\gamma=\alpha$, then $\tan \alpha$ equals 20. If $\mathrm{f}(x)=\frac{\log x}{x}(x>0)$, then it is increasing in 21. If $\overline{\mathrm{a}}, \overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ are three non-coplanar vectors, then $(\ba 22. In a class of 300 students, every student reads 5 news papers and every news paper is read by 60 students. Then the numb 23. The maximum value of $\frac{\log x}{x}$ is 24. Derivative of $\mathrm{e}^x$ w.r.t. $\sqrt{x}$ is 25. The curve satisfying the differential equation $y \mathrm{~d} x-\left(x+3 y^2\right) \mathrm{dy}=0$ and passing through 26. The maximum value of $z=x+y$, subjected to $x+y \leq 10,5 x+3 y \geq 15, x \leq 6, x, y \geq 0$ 27. The distance of the point $(1,3,-7)$ from the plane passing through the point $(1,-1,-1)$ having normal perpendicular to 28. Domain of definition of the real valued function $f(x)=\sqrt{\sin ^{-1}(2 x)+\frac{\pi}{6}}$ is 29. The value of m , such that $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-m}{2}$ lies in the plane $2 x-4 y+z=7$, is 30. Suppose that $\bar{p}, \bar{q}$ and $\overline{\mathrm{r}}$ are three non-coplanar vectors in $\mathbb{R}^3$. Let the co 31. $\int \frac{x^4+x^2+1}{x^2-x+1} d x$ is equal to 32. If the curves $y^2=6 x, 9 x^2+\mathrm{b} y^2=16$ intersect each other at right angles, then the value of $b$ is 33. Let $\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$ and $\overline{\mathrm{b}}=\hat{\math 34. The mean and the standard deviation of 10 observations are 20 and 2 respectively. Each of these 10 observations is multi 35. If Mean value theorem holds for the function $\mathrm{f}(x)=(x-1)(x-2)(x-3), x \in[0,4]$ then the values of $c$ as per t 36. The value of $\mathrm{I}=\mathrm{I}=\int_{\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{x^2 \cos x}{1+\mathrm{e}^{-x}} \mathrm{~d 37. If $\overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{a}} \cdot \overline{\mat 38. If the mean and the variance of Binomial variate $X$ are 2 and 1 respectively, then the probability that X takes a value 39. The value of $I=\int \frac{(x-1) \mathrm{e}^x}{(x+1)^3} \mathrm{dx}$ is 40. If $Z=\frac{-2}{1+\sqrt{3} i}, i=\sqrt{-1}$, then the value of $\arg Z$ is 41. In $(0,2 \pi)$, the number of solutions of $\tan \theta+\sec \theta=2 \cos \theta$ are 42. If the area of the parallelogram with $\bar{a}$ and $\bar{b}$ as two adjacent sides is 15 square units, then the area (i 43. If an equation $h x y+g x+f y+c=0$ represents a pair of lines, then 44. The general solution of $\sin x-3 \sin 2 x+\sin 3 x=\cos x-3 \cos 2 x+\cos 3 x$ is 45. The length of the perpendicular from the point $\mathrm{A}(1,-2,-3)$ on the line $\frac{x-1}{2}=\frac{y+3}{-1}=\frac{z+1 46. The straight line, $2 x-3 y+17=0$ is perpendicular to the line passing through the points $(7,17)$ and $(15, \beta)$, th 47. If $\mathrm{f}(x)=\frac{x^2-x}{x^2+2 x}$ then $\frac{\mathrm{d}}{\mathrm{d} x}\left(\mathrm{f}^{-1}(x)\right)$ at $x=2$ 48. For the triangle ABC , with usual notations, if the angles $A, B, C$ are in A.P. and $\mathrm{m} \angle \mathrm{A}=30^{\ 49. Let $p, q, r$ be three statements such that the truth value of $(p \wedge q) \rightarrow(\sim q \vee r)$ is $F$. Then th 50. Let k be a non-zero real number. If $f(x)=\left\{\begin{array}{cl}\frac{\left(\mathrm{e}^x-1\right)^2}{\sin \left(\frac{

Physics

1. The gyromagnetic ratio and Bohr magneton are given respectively by [Given $\rightarrow \mathrm{e}=$ charge on electron, 2. Two satellites A and B having ratio of masses $3: 1$ are revolving in circular orbits of radii ' $r$ ' and ' 4 r '. The 3. The current amplification factor of a transistor is 50 . The input resistance when used in common emitter mode is $1 \ma 4. Average power associated with an ideal inductor and ideal capacitor over a complete cycle of a.c. is respectively 5. A metal rod of length ' $l$ ' rotates about one of its ends in a plane perpendicular to a magnetic field of induction ' 6. In S.H.M. the displacement of a particle at an instant is $Y=A \cos 30^{\circ}$, where $A=40 \mathrm{~cm}$ and kinetic e 7. Two sound waves having same amplitude ' $A$ ' and angular frequency ' $\omega$ ' but having a phase difference of $\left 8. Out of the following musical instruments, which is 'NOT' a percussion instrument? 9. The function of dielectric in a capacitor is 10. Three identical metal spheres (of same surface area) have red, black and white colors and they are heated up to same tem 11. In an ammeter, $4 \%$ of the main current is passing through the galvanometer, If shunt resistance is $5 \Omega$, then r 12. LC series resonant circuit produces resonant frequency ' $f$ '. If ' $L$ ' is tripled and ' $C$ ' is increased by $3 C$, 13. A wavefront is a surface 14. When the tension in string is increased by $3 \mathrm{~kg} \omega \mathrm{t}$, the frequency of the fundamental mode inc 15. In the system of two particles of masses ' $\mathrm{m}_1$ ' and ' $\mathrm{m}_2$ ', the first particle is moved by a dis 16. The potential energy of a long spring when it is stretched by 3 cm is ' $U$ '. If the spring is stretched by 9 cm , pote 17. A thin uniform rod of length ' $L$ ' and mass ' $M$ ' is swinging freely along a horizontal axis passing through its cen 18. Three immiscible transparent liquids with uniform refractive indices $\frac{3}{2}, \frac{4}{3}$ and $\frac{6}{5}$ are ar 19. When a hydrogen atom is raised from the ground state to the excited state 20. In the logic circuit diagram, when all the four inputs $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ are one, the out 21. Two coils have a mutual inductance $5 \times 10^{-3} \mathrm{H}$. The current changes in the first coil according to the 22. When an air bubble rises from the bottom of lake to the surface, its radius is doubled. The atmospheric pressure is equa 23. The period of a planet around the sun is 8 times that of earth. The ratio of radius of planet's orbit to the radius of t 24. The magnetic induction due to an ideal solenoid is independent of 25. The moment of inertia of thin square plate PQRS of uniform thickness, about an axis passing through centre ' O ' and per 26. In hydrogen atom, ratio of the shortest wavelength in the Balmer series to that in the Paschen series is 27. At certain temperature, $\operatorname{rod} \mathrm{A}$ and $\operatorname{rod} \mathrm{B}$ of different materials have 28. Velocity of light in diamond is $\left(\frac{5}{12}\right)^{\text {th }}$ times that in air. Velocity of light in water 29. When a capacitor is connected in series LR circuit, the alternating current flowing in the circuit 30. The internal energy of a gas will increase when it 31. A sonometer wire is stretched by hanging a metal bob, the fundamental frequency of the wire is ' $n_1$ '. When the bob i 32. The magnetic field intensity inside current carrying solenoid is $\mathrm{H}=2.4 \times 10^3 \mathrm{~A} / \mathrm{m}$. 33. If the electric flux entering and leaving an enclosed surface is $\phi_1$ and $\phi_2$ then charge enclosed in the surfa 34. A gas is contained in closed vessel. The initial temperature of the gas is $100^{\circ} \mathrm{C}$. If the pressure of 35. According to Bohr's theory of hydrogen atom, the ratio of the maximum and minimum wavelength of Lyman series will be 36. In the given circuit diagram, in the steady state the current through the battery and the charge on the capacitor respec 37. Water is flowing in a conical tube as shown in figure. Velocity of water at area ' $\mathrm{A}_2$ ' is $60 \mathrm{~cm} 38. A point object kept at P in front of a glass sphere of radius ' $R$ ' has its image formed at $Q$ such that $\mathrm{PO} 39. The magnetic flux through a coil of resistance ' $R$ ' changes by an amount ' $\Delta \phi$ ' in time ' $\Delta t$ '. Th 40. A circular disc of radius ' $R$ ' and thickness $\frac{R}{8}$ has moment of inertia 'I' about an axis passing through it 41. When the two known resistance ' $R$ ' and ' $S$ ' are connected in the left and right gaps of a meter bridge respectivel 42. For an ideal gas, in an isobaric process, the ratio of heat supplied ' $Q$ ' to the work done ' $w$ ' by the system is ( 43. A particle is performing S.H.M. with an amplitude 4 cm . At the mean position the velocity of the particle is $12 \mathr 44. A velocity - time graph of a body is shown below. The distance covered by the body from 6 second to 9 second is 45. Two identical photocathodes receive light of frequencies ' $\mathrm{n}_1$ ' and ' $\mathrm{n}_2$ '. If the velocities of 46. The temperature of a gas is $-80^{\circ} \mathrm{C}$. To what temperature the gas should be heated so that the r.m.s. sp 47. Two wavelength 590 nm and 596 nm of sodium light are used one after other, to study the diffraction taking place at a si 48. For the diagram shown, the resistance between points A and B when the ideal diode ' $D$ ' is forward biased is ' $R_1$ ' 49. A parallel plate capacitor of capacitance ' $C$ ' is connected to a battery and charged to a potential difference ' $V$ 50. A tuning fork of frequency 340 Hz is vibrated just above a tube of 120 cm height. Water is slowly poured in the tube. Wh

MHT CET 2024 9th May Morning Shift

MCQ (Single Correct Answer)

-0

The area (in sq. units) bounded by the curves $y=(x+1)^2, y=(x-1)^2$ and the line $y=\frac{1}{4}$ is

$\frac{2}{3}$

$\frac{1}{6}$

$\frac{1}{3}$

$\frac{1}{4}$

MHT CET 2024 9th May Morning Shift

MCQ (Single Correct Answer)

-0

If $\int \frac{d x}{\sqrt[3]{\sin ^{11} x \cos x}}=-\left(\frac{3}{8} f(x)+\frac{3}{2} g(x)\right)+c$ then

$\mathrm{f}(x)=\tan ^{\frac{-8}{3}} x, \mathrm{~g}(x)=\tan ^{\frac{-2}{3}} x$, (where c is a constant of integration)

$\mathrm{f}(x)=\tan ^{\frac{8}{3}} x, \mathrm{~g}(x)=\tan ^{\frac{-2}{3}} x$, (where c is a constant of integration)

$\mathrm{f}(x)=\tan ^{\frac{-8}{3}} x, \mathrm{~g}(x)=\tan ^{\frac{2}{3}} x$, (where c is a constant of integration)

$\mathrm{f}(x)=\tan ^{\frac{8}{3}} x, \mathrm{~g}(x)=\tan ^{\frac{2}{3}} x$, (where c is a constant of integration)

MHT CET 2024 9th May Morning Shift

MCQ (Single Correct Answer)

-0

A random variable X takes values $-1,0,1,2$ with probabilities $\frac{1+3 \mathrm{p}}{4}, \frac{1-\mathrm{p}}{4}, \frac{1+2 \mathrm{p}}{4}, \frac{1-4 \mathrm{p}}{4}$ respectively, where p varies over $\mathbb{R}$. Then the minimum and maximum values of the mean of X are respectively.

$-\frac{7}{4}$ and $\frac{1}{2}$

$-\frac{1}{16}$ and $\frac{5}{16}$

$-\frac{7}{4}$ and $\frac{5}{16}$

$-\frac{1}{16}$ and $\frac{5}{4}$

MHT CET 2024 9th May Morning Shift

MCQ (Single Correct Answer)

-0

Let C be a curve given by $y(x)=1+\sqrt{4 x-3}$, $x>\frac{3}{4}$. If P is a point on C , such that the tangent at P has slope $\frac{2}{3}$, then a point through which the normal at P passes, is

$(1,7)$

$(4,-3)$

$(3,-4)$

$(2,3)$

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