MHT CET 2024 15th May Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Which from following is semisynthetic polymer? 2. Identify reactant 'A' in following reaction. 3. An aqueous solution of strong monoacidic base is of $1 \times 10^{-4} \mathrm{M}$. What is the value of pH at $25^{\circ 4. The correct stability order of alkyl substituted alkenes is 5. What is the volume occupied by 2.5 mol of ammonia gas at STP? 6. Which group element from following achieves noble gas configuration after gaining two electrons? 7. The reaction given below $2 \mathrm{NH}_{3(\mathrm{g})} \xrightarrow{\mathrm{Pt}} \mathrm{N}_{2(\mathrm{g})}+3 \mathrm{H 8. Identify the correct statement about glucose from following. 9. In a solid, $\mathrm{B}^{-}$ions occupy corners of a cube forming ccp structure. If $\mathrm{A}^{+}$ion occupy half the 10. Calculate the radius of first orbit of He$^+$. 11. Identify reagent 'A' used in the following reaction? 12. Acidic buffer solution is prepared by mixing proportionate quantity of 13. Which among the following is NOT a feature of $\mathrm{S}_{\mathrm{N}} 2$ mechanism? 14. 3.4 moles of an ideal gas occupies volume of 68 mL at 300 K . What would be the pressure of gas? $\left(\mathrm{R}=8.314 15. Which of the following alloys is used in construction of outer fuselage of ultra-high speed air craft? 16. Calculate the percentage dissociation of 0.05 M solution of weak electrolyte if its molar conductivity and molar conduct 17. Identify the polymer used to obtain disposable cups and plates. 18. Beryllium shows diagonal relationship with 19. Which of the following is a simple ketone? 20. Calculate molar mass of a solute at 300 K if 400 mg of it is dissolved in 300 mL of water exerts osmotic pressure of 0.2 21. According to carbinol system tert-butyl alcohol is named as 22. A system performs mechanical work equal to 15 kJ and looses 2 kJ of heat to surrounding. What is the change in internal 23. What is the designation of an orbital with quantum numbers $\mathrm{n}=4$ and $l=3$? 24. Which among the following properties is NOT exhibited by transition elements? 25. For reaction $\mathrm{A}+\mathrm{B} \rightarrow$ product, rate of reaction is $3.6 \times 10^{-2} \mathrm{sec}^{-1}$. Wh 26. Which of following polymer does not contain 27. Unit cell of an element has edge length of 5$$\mathop A\limits^o $$ with density $4 \mathrm{~g} \mathrm{~cm}^{-3}$, if i 28. Which among the following gases is difficult to liquify? 29. Phenol on heating with zinc dust forms 30. The degree of dissociation of 0.01 M solution of $\mathrm{NH}_4 \mathrm{OH}$ is $4.2 \times 10^{-2}$. What is the percen 31. Which among the following is an example of odd electron molecule? 32. Which among the following is a cationic complex? 33. The conductivity of 0.02 M solution of $\mathrm{AgNO}_3$ is $0.00216 \Omega^{-1} \mathrm{~cm}^{-1}$ at 298 K . What is i 34. Which among following is a strongest base? 35. What is the vapour pressure of a solution containing 0.1 mol of non volatile solute dissolved in 16.2 g water? $\left(\m 36. Which of the following compounds does not undergo Williamson's synthesis? 37. Find the constant external pressure required to expand a gas from 2.5 L to 4.5 L if amount of work done is 500 J at 298 38. What is change in oxidation number of nitrogen when $\mathrm{NO}_3^{-}$is converted to $\mathrm{NH}_4^{+}$ion? 39. What type of hybridization is present in $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$ complex? 40. For a reaction $\mathrm{r}=\mathrm{k}[\mathrm{A}][\mathrm{B}]^2$, if concentration of $A$ is doubled the rate of reactio 41. The correct zwitter ion structure of glycine is 42. What is the volume of one particle in BCC structure if ' $a$ ' is edge length? 43. Identify product ' B ' in following reaction. $$\mathrm{CH}_3-\mathrm{I}+\mathrm{KCN} \longrightarrow \mathrm{~A} \xrigh 44. Which of the following alkenes does NOT exhibit cis-trans isomerism? 45. Carbonated water is an example of a solution of 46. Which of the following is vinylic halide? 47. In a particular reaction ' x ' kJ of heat is released by the system and ' y ' kJ of work done is done on the system. Wha 48. Which of the following compounds contains S atom in its ring? 49. Which element from following combines with hydrogen to form a compound with lowest thermal stability? 50. What is the decreasing order of deposition of metal on electrode if standard reduction potentials are given as - $\mathr

Mathematics

1. If $x=\sin \theta, y=\sin ^3 \theta$, then $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}$ at $\theta=\frac{\pi}{2}$ is 2. Let $P, Q, R$ and $S$ be the points on the plane with position vectors $-2 \hat{i}-\hat{j}, 4 \hat{i}, 3 \hat{i}+3 \hat{ 3. If $y=\frac{x^{\frac{2}{3}}-x^{\frac{-1}{3}}}{x^{\frac{2}{3}}+x^{\frac{-1}{3}}}, x \neq 0$, then $(x+1)^2 y_1=$ 4. The Number of values of C that satisfy the conclusion of Rolle's theorem in case of following function $\mathrm{f}(x)=\s 5. An open tank with a square bottom, to contain 4000 cubic cm . of liquid, is to be constructed. The dimensions of the tan 6. $$\int \operatorname{cosec}(x-a) \cdot \operatorname{cosec} x d x=$$ 7. The contrapositive of the inverse of $\mathrm{p} \rightarrow(\mathrm{p} \rightarrow \mathrm{q})$ is 8. The area enclosed between the parabola $y^2=4 x$ and the line $y=2 x-4$ is 9. There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 q 10. The order of the differential equation, whose solution is $y=\left(C_1+C_2\right) \mathrm{e}^x+C_3 \mathrm{e}^{x+C_4}$, 11. If the sides of a rectangle are given by the equations $x=-2, x=6, y=-2, y=5$, then the equation of the circle, drawn on 12. The solution set of the equation $\tan x+\sec x=2 \cos x$, in the interval $[0,2 \pi]$ is 13. If one of the lines represented by $a x^2+2 h x y+b y^2=0$ is perpendicular to $\mathrm{m} x+\mathrm{n} y=18$, then 14. If $\sin ^{-1}\left(\frac{x}{13}\right)+\operatorname{cosec}^{-1}\left(\frac{13}{12}\right)=\frac{\pi}{2}$, then the val 15. The graphical solution set of the system of inequations $2 x+3 y \leq 6, x+4 y \geq 4, x \geq 0, y \geq 0$ is given by 16. The derivative of $\sin ^{-1}\left(2 x \sqrt{1-x^2}\right)$ w.r.t. $\sin ^{-1}\left(3 x-4 x^3\right)$ is 17. If $A=\left[\begin{array}{cc}5 a & -b \\ 3 & 2\end{array}\right]$ and $A \cdot \operatorname{adj} A=A A^T$, then $5 a+b$ 18. The function $\mathrm{f}(x)=2 x^3-9 x^2+12 x+2$ is decreasing in 19. $\int\left(1+x-\frac{1}{x}\right) \mathrm{e}^{x+\frac{1}{x}} \mathrm{~d} x$ is equal to 20. If the function $f(x)= \begin{cases}-2 \sin x & \text {, if } x \leq \frac{-\pi}{2} \\ A \sin x+B & , \text { if } \frac 21. $$\int\limits_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{\sqrt{1+\cos x}}{(1-\cos x)^{\frac{5}{2}}} d x=$$ 22. If the complex number $z=x+i y$, where $i=\sqrt{-1}$, satisfies the condition $|z+1|=1$, then $z$ lies on 23. The general solution of the differential equation $\frac{d y}{d x}=\frac{3 e^{2 x}+3 e^{4 x}}{e^x+e^{-x}}$ is 24. If $\cos ^{-1} x=\alpha(0 25. If the points $\mathrm{P}, \mathrm{Q}$ and R are with the position vectors $\hat{i}-2 \hat{j}+3 \hat{k},-2 \hat{i}+3 \ha 26. A line makes $45^{\circ}$ angle with positive X -axis and makes equal angles with positive Y -axis ad Z-axis respectivel 27. If the lines $\frac{x-1}{2}=\frac{y+2}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-\mathrm{k}}{2}=\frac{\mathrm{z}}{1}$ 28. The vector equation of the plane through the line of intersection of the planes $x+y+z=1$ and $2 x+3 y+4 z=5$, which is 29. The equation of motion of a particle is $s=a t^2+b t+c$. If the displacement after 1 second is 20 m , velocity after 2 s 30. One side and one diagonal of a parallelogram are represented by $3 \hat{i}+\hat{j}-\hat{k}$ and $2 \hat{i}+\hat{j}-2 \ha 31. If $\int \mathrm{e}^{x^2} \cdot x^3 \mathrm{dx}=\mathrm{e}^{x^2} \mathrm{f}(x)+\mathrm{c}$ and $\mathrm{f}(1)=0$ (where 32. If $\cot ^{-1}(\sqrt{\cos \alpha})-\tan ^{-1}(\sqrt{\cos \alpha})=x$, then the value of $\sin x$ is 33. If $[x]^2-5[x]+6=0$, where $[\cdot]$ denotes the greatest integer function, then 34. The value of the integral $\int_0^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}} \mathrm{dx}$ is 35. Variance of first n natural numbers is ________. 36. Suppose three coins are tossed simultaneously. If $X$ denotes the number of heads, then probability distribution of x i 37. Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three o 38. If $0 39. If the vector $\overline{\mathrm{c}}$ lies in the plane of $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$, where $\ 40. The equation of a line passing through the point $(2,-1,1)$ and parallel to the line joining the points $\hat{i}+2 \hat{ 41. The foot of the perpendicular drawn from origin to a plane is $\mathrm{M}(2,1,-2)$, then vector equation of the plane is 42. If $f(1)=1, f^{\prime}(1)=3$, then the derivative of $\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f}(x))^2$ at $x=1$ 43. In a triangle ABC , with usual notations, $\frac{\cos \mathrm{B}+\cos \mathrm{C}}{\mathrm{b}+\mathrm{c}}+\frac{\cos \mat 44. If $\mathrm{f}(x)=\frac{x}{x+1}, x \neq-1$ and (fof) $(x)=\mathrm{F}(x)$, then $\int \mathrm{F}(x) \mathrm{d} x$ is 45. If p : The total prime numbers between 2 to 100 are 26. q : Zero is a complex number. $r$ : Least common multiple (L.C.M 46. $$\lim _\limits{x \rightarrow 2} \frac{3^x+3^{3-x}-12}{3^{3-x}-3^{\frac{x}{2}}}=$$ 47. $$\int_0^{\frac{\pi}{4}} \frac{\sec ^2 x}{(1+\tan x)(2+\tan x)} d x=$$ 48. If two fair dice are rolled, then the probability that the sum of the numbers on the upper faces is at least 9, is 49. After $t$ seconds, the acceleration of a particle, which starts from rest and moves in a straight line is $\left(8-\frac 50. If $\mathrm{A}+\mathrm{B}=225^{\circ}$, then $\frac{\cot \mathrm{A}}{1+\cot \mathrm{A}} \cdot \frac{\cot \mathrm{B}}{1+\

Physics

1. The figure shows currents in a part of electric circuit. Then current I is 2. A metal disc of radius R rotates with an angular velocity $\omega$ about an axis perpendicular to its plane passing thro 3. A body of mass $m$ slides down an incline and reaches the bottom with a velocity V . If the same mass were in the form o 4. For a particle executing S.H.M. having amplitude A, the speed of the article is $\left(\frac{1}{3}\right)^{\text {rd }}$ 5. The minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ in 6. The core used in transformers are laminated to 7. The end correction for the vibrations of air column in a tube of circular cross-section will be more if the tube is 8. If the work done in blowing a soap bubble of volume ' V ' is ' W ', then the work done in blowing a soap bubble of volum 9. A coil has inductance H . The ratio of its reactance when it is connected first to an a.c. source and then to d.c. sourc 10. A particle of mass m collides with another stationary particle of mass $M$. The particle $m$ stops just after collision. 11. In the circuit shown in the following figure, the potential difference cross $3 \mu \mathrm{~F}$ capacitor is 12. Sodium light $\left(\lambda=6 \times 10^{-7} \mathrm{~m}\right)$ is used to produce interference pattern. The observed f 13. The motion of a particle is described by the equation $a=-b x$ where ' $a$ ' is the acceleration, x is the displacement 14. Acceleration of an electron in the first Bohr's orbit is proportional to $\mathrm{m}=$ mass of electron, $\mathrm{r}=$ r 15. A cylindrical rod is having temperatures $\theta_1$ and $\theta_2$ at its ends. The rate of heat flow is $\mathrm{Q} J / 16. A resistor of $50 \Omega$, inductor of self inductance $\left(\frac{3}{\pi^2}\right) \mathrm{H}$ and a capacitor of unkn 17. A monoatomic ideal gas, initially at temperature $T_1$ is enclosed in a cylinder fitted with frictionless piston. The ga 18. Charges of $2 \mu \mathrm{C}$ and $-3 \mu \mathrm{C}$ are placed at two points A and B separated by 1 m . The distance o 19. For detecting light intensity we use 20. A ball is released from the top of a tower of height Hm . It takes T second to reach the ground. The height of the ball 21. 1000 small balls, each weighing 1 gram, strike one square cm of area per second with a velocity $50 \mathrm{~m} / \mathr 22. A wave is given by $Y=3 \sin 2 \pi\left(\frac{t}{0.04}-\frac{x}{0.01}\right)$ where Y is in cm . Frequency of the wave a 23. Two concentric circular coils A and B having radii 20 cm and 10 cm respectively lie in the same plane. The current in co 24. The radius of gyration of a circular disc of radius R and mass m rotating about diameter as axis is 25. What is the current in the following junction diode circuit? 26. When a certain metallic surface is illuminated with monochromatic light wavelength $\lambda$, the stopping potential for 27. A plate of refractive index 1.6 is introduced in the path of light from one of the slits in Young's double slit experime 28. The viscous force between two liquid layers is 29. In the given reaction $${ }_z \mathrm{X}^A \rightarrow{ }_{z+1} \mathrm{Y}^A \rightarrow{ }_{z-1} \mathrm{~K}^{A-4} \rig 30. Two point charges $+q_1$ and $q_2$ repel each other with a force of $100 \mathrm{~N} . q_1$ is increased by $10 \%$ and 31. In an ideal gas at temperature $T$, the average force that a molecule applies on the walls of a closed container depends 32. Which one of the following graph represent correctly the variation of impedance $(\mathrm{Z})$ of a series LCR circuit w 33. A galvanometer may be converted into ammeter or a voltmeter. In which of the following cases the resistance of the devic 34. A glass prism ' A ' deviates the red and blue rays through $10^{\circ}$ and $12^{\circ}$ respectively. A second prism ' 35. In an electric field due to charge $Q$, a charge $q$ moves from point A to B as shown in the figure. The work done is ( 36. An air cored coil has a self inductance 0.1 H . A soft iron core of relative permeability 1000 is introduced and the num 37. Heat engine operating between temperature $T_1$ and $T_2$ has efficiency $\frac{1}{6}$. When $T_2$ is lowered by 62 K , 38. The angle of minimum deviation produced by a thin prism in air is $\delta_1$. If it is immersed in water the angle of mi 39. An electron is revolving in a circular orbit of radius $r$ in a hydrogen atom. The angular momentum of the electron is L 40. A p-n junction diode as a rectifier converts 41. A ball rises to surface at a constant velocity in liquid whose density is 3 times greater than that of the material of t 42. Three infinite straight wires $\mathrm{A}, \mathrm{B}$ and C carry currents as shown in figure. The resultant force on w 43. Velocity of sound waves in air is $330 \mathrm{~m} / \mathrm{s}$. For a particular sound wave in air, path difference of 44. In Young's double slit experiment, the intensity of light at a point on the screen where the path difference is $\lambda 45. The stopping potential as a function of frequency of incident radiation is plotted for two different photoelectric surfa 46. The absolute temperature of a gas is determined by 47. The density of a new planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equa 48. A particle is moving in a circle with uniform speed. It has constant 49. A string has mass per unit length of $10^{-6} \mathrm{~kg} / \mathrm{cm}$ The equation of simple harmonic wave produced 50. A spring has length L and force constant K . It is cut into two springs of length $L_1$ and $L_2$ such that $\mathrm{L}_

MHT CET 2024 15th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\int \mathrm{e}^{x^2} \cdot x^3 \mathrm{dx}=\mathrm{e}^{x^2} \mathrm{f}(x)+\mathrm{c}$ and $\mathrm{f}(1)=0$ (where c is a constant of integration), then the value of $f(x)$ is

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

$\frac{x^2+1}{2}$

$\frac{x+1}{2}$

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

MHT CET 2024 15th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\cot ^{-1}(\sqrt{\cos \alpha})-\tan ^{-1}(\sqrt{\cos \alpha})=x$, then the value of $\sin x$ is

$\cot ^2\left(\frac{\alpha}{2}\right)$

$\tan ^2\left(\frac{\alpha}{2}\right)$

$\tan \alpha$

$\cot \left(\frac{\alpha}{2}\right)$

MHT CET 2024 15th May Evening Shift

MCQ (Single Correct Answer)

-0

If $[x]^2-5[x]+6=0$, where $[\cdot]$ denotes the greatest integer function, then

$x \in(2,4]$

$x \in[2,4]$

$x \in[2,4)$

$x \in(2,4)$

MHT CET 2024 15th May Evening Shift

MCQ (Single Correct Answer)

-0

The value of the integral $\int_0^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}} \mathrm{dx}$ is

$\frac{\pi}{4}$

$\frac{\pi}{2}$

$\frac{\pi}{8}$

$2 \pi$

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