MHT CET 2024 16th May Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Identify the angle $\mathrm{O}-\mathrm{S}-\mathrm{O}$ in $\mathrm{SO}_2$ molecule. 2. Calculate the number of unit cells in 0.9 g metal if it forms bec structure. $\left[\rho \times \mathrm{a}^3=3 \times 10 3. Which of the following polymers need $\mathrm{HO}-\mathrm{CH}_2-\mathrm{CH}_2-\mathrm{OH}$ as one of the monomers for it 4. What is the EAN of Zn in $\left[\mathrm{Zn}\left(\mathrm{NH}_3\right)_4\right]^{2+}$ ? 5. What is molecular formula of undecane? 6. Which from following elements has completely filled 4 f orbital at expected ground state configuration? 7. Which from following compounds is NOT in gaseous phase at $25^{\circ} \mathrm{C}$ ? 8. Calculate the pH of 0.01 M sulphuric acid. 9. Identify the correct statement from following properties. 10. Which of the following is true for a reaction as per coliision theory? 11. What is the IUPAC name of following compound? 12. What is wavenumber of a radiation having wavelength $0.25 \mu \mathrm{~m}$ ? 13. What is the product of Hydroborationoxidation of but-1-ene? 14. Identify the class of $\left(\mathrm{C}_6 \mathrm{H}_5\right)_3 \mathrm{~N}$ ? 15. What is the conductivity of 0.05 M NaOH solution having resistance 31.5 ohm and cell constant $0.315 \mathrm{~cm}^{-1}$ 16. What is IUPAC name of the following compound? 17. The enthalpy of vaporisation of a liquid is $30 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and entropy of vaporisation is $75 \mat 18. Which from following polymers is used as substitute for wool? 19. Which from following complexes is having ambidentate ligand in it? 20. What is the number of moles of oxygen and number of moles of N atoms respectively present in one mole thymine? 21. Identify one dimensional nanostructure from following. 22. What is the general formula of lanthanoid hydroxide? (Consider Ln as any lanthanoid element) 23. Find the void volume of fcc unit cell in $\mathrm{cm}^3$ if the volume of fcc unit cell $1.25 \times 10^{-22} \mathrm{~c 24. Find work done on 2 mole of an ideal gas at $27^{\circ} \mathrm{C}$ if it is compressed reversibly and isothermally from 25. Rate of reaction, $\mathrm{A}+\mathrm{B} \rightarrow$ product, is $7.2 \times 10^{-2} \mathrm{moldm}^{-3} \mathrm{~s}^{- 26. Identify the product obtained when alkenes react with cold and dilute alkaline potassium permanganate. 27. Which among the following has the highest melting point? 28. What is the oxidation state of phosphorus in phosphate ion? 29. Which from the following concentrations of a weak electrolyte solution exhibits maximum molar conductivity? 30. Which among the following is NOT dicarboxylic acid? 31. What is IUPAC name of following compound? 32. Consider the following cell $\mathrm{E}^{\circ}$ cell $=1.007 \mathrm{~V}$ and $\mathrm{E}^{\circ}$ calomel $=0.242 \mat 33. Identify the substrate ' A ' in the following conversion. $$A \xrightarrow[\mathrm{H}_3 \mathrm{O}^{+}]{\mathrm{AlH}(\ma 34. Find the number of moles of sodium atoms in $6.9 \times 10^{-2} \mathrm{~kg}\left(\right.$ Atomic mass $\left.=23 \mathr 35. Identify the product ' B ' in the following sequence of recations. $$\mathrm{CH}_3 \mathrm{Br} \xrightarrow{\mathrm{KCN} 36. Which of the following elements belongs to second group and fifth period of periodic table? 37. Which among the following has lowest boiling point? 38. Which of the following species contain 20 electrons? 39. A zero order reaction has half life time of 0.2 minute. If initial concentration of reactant is $0.2 \mathrm{~mol} \math 40. Which of the following is NOT optically active compound? 41. What is the numerical value of gas constant $R$ in terms of $\mathrm{L} \mathrm{atm} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$ 42. What type of solid is the silica? 43. Which from following mixtures in water acts as a buffer? 44. Calculate van't Hoff factor of 0.15 M solution of electrolyte if it freezes at $-$0.5 K. $$\left[\mathrm{K}_{\mathrm{f}} 45. Calculate the solubility in $\mathrm{mol} \mathrm{dm}^{-3}$ of sparingly soluble salt BA if its solubility product $4.9 46. Which of the following equations gives combined relationship of Boyle's law and Charle's law? 47. What is the value of slope in Freundlich adsorption isotherm $\log \frac{\mathrm{x}}{\mathrm{m}}$ against $\log \mathrm{ 48. What is the total number of electrons present in bonding orbitals of $\mathrm{O}_2$ molecule according to molecular orbi 49. Calculate the relative lowering of vapour pressure of solution containing 46 g of non volatile solute in 162 g of water 50. Identify acidic amino acid from following (represented by using three letter symbols)

Mathematics

1. Let $A=\left[\begin{array}{ll}x & 1 \\ 1 & 0\end{array}\right], x \in \mathbb{R}^{+}$and $A^4=\left[a_{i j}\right]_2$. I 2. The proposition $(\sim p) \vee(p \wedge \sim q)$ is equivalent to 3. In a triangle ABC , with usual notations, $2 \mathrm{ac} \sin \left(\frac{\mathrm{A}-\mathrm{B}+\mathrm{C}}{2}\right)$ i 4. If $\frac{x^2}{\mathrm{a}}+\frac{2 x y}{\mathrm{~h}}+\frac{y^2}{\mathrm{~b}}=0$ represents a pair of straight lines and 5. If $\overline{\mathrm{a}}, \overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ are unit coplanar vectors, then the scalar 6. If a random variable X has the following probability distribution values .tg {border-collapse:collapse;border-spacing: 7. Let the vectors $\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$ be such that $|\bar{a}|=2,|\bar{b} 8. If the sum of the deviations of 50 observations from 30 is 50 , then the mean of these observations is 9. The general solution of the equation $\sqrt{3} \cos \theta+\sin \theta=\sqrt{2}$ is 10. If $\sin ^{-1}\left(\frac{x}{5}\right)+\operatorname{cosec}^{-1}\left(\frac{5}{4}\right)=\frac{\pi}{2}$, then the value 11. A random variable X takes the values $0,1,2,3$ and its mean is 1.3 . If $\mathrm{P}(\mathrm{X}=3)=2 \mathrm{P}(\mathrm{X 12. Let $\overline{\mathrm{a}}, \overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ be three non-zero vectors such that no tw 13. The equation of the plane, passing through the intersection of the planes $x+y+z=1$ and $2 x+3 y-z+4=0$ and parallel to 14. If $\mathrm{f}(1)=1, \mathrm{f}^{\prime}(1)=3$, then the derivative of $\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f 15. If $\left[\begin{array}{lll}\overline{\mathrm{a}} \times \overline{\mathrm{b}} & \overline{\mathrm{b}} \times \overline{ 16. The value of $\lim _\limits{x \rightarrow 0}\left((\sin x)^{\frac{1}{x}}+\left(\frac{1}{x}\right)^{\sin x}\right)$, wher 17. If $\theta$ denotes the acute angle between the curves $y=10-x^2$ and $y=2+x^2$, at a point of the intersection, then $| 18. If $y=a \log x+b x^2+x$ has its extremum values at $x=-1$ and $x=2$, then 19. Let $P=\{\theta / \sin \theta-\cos \theta=\sqrt{2} \cos \theta\}$ and $Q=\{\theta / \sin \theta+\cos \theta=\sqrt{2} \si 20. A line with positive direction cosines passes through the point $\mathrm{P}(2,-1,2)$ and makes equal angles with co-ordi 21. Let $\mathrm{f}(x)=\frac{1-\tan x}{4 x-\pi}, x \neq \frac{\pi}{4}, x \in\left[0, \frac{\pi}{2}\right]$. $f(x)$ is contin 22. The value of $\int_\limits{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\sin ^2 x}{1+2^x} d x$ is 23. The area (in sq. units) of the region described by $\left\{(x, y) / y^2 \leq 2 x\right.$ and $\left.y \geq(4 x-1)\right\ 24. Let $y=y(x)$ be the solution of the differential equation $(x \log x) \frac{d y}{d x}+y=2 x \log x(x \geq 1)$ then $y(\m 25. The set of all points, for which $f(x)=x^2 e^{-x}$ strictly increases, is 26. Range of the function $\mathrm{f}(x)=\frac{x^2+x+2}{x^2+x+1}, x \in \mathbb{R}$ is 27. Let $S$ be a non-empty subset of $\mathbb{R}$. Consider the following statement: p : There is a rational number $x \in \ 28. The number of values of $x$ in the interval $(0,5 \pi)$ satisfying the equation $3 \sin ^2 x-7 \sin x+2=0$ 29. If the vectors $\overline{A B}=3 \hat{i}+4 \hat{k}$ and $\overline{A C}=5 \hat{i}-2 \hat{j}+4 \hat{k}$ are the sides of 30. The equation of the circle, concentric with the circle $2 x^2+2 y^2-6 x+8 y+1=0$ and double of its area is 31. If $y=\sec \left(\tan ^{-1} x\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=1$ is equal to 32. Eight chairs are numbered 1 to 8 . Two women and three men wish to occupy one chair each. First the women choose chairs 33. If the distance between the plane Ax-2y+z $=\mathrm{d}$ and the plane containing the lines $\frac{x-1}{2}=\frac{y-2}{3}= 34. Maximum value of $Z=100 x+70 y$ Subject to $2 x \geq 4, y \leq 3, x+y \leq 8, x, y \geq 0$ is 35. Three persons $\mathrm{P}, \mathrm{Q}$ and R independently try to hit a target. If the probabilities of their hitting th 36. If $\bar{a}$ and $\bar{b}$ are two unit vectors such that $\bar{a}+2 \bar{b}$ and $5 \overline{\mathrm{a}}-4 \overline{\ 37. Let the function $g:(-\infty, \infty) \rightarrow\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ be given by $g(u)=2 \tan ^{ 38. The length of the projection of the line segment joining the points $(5,-1,4)$ and $(4,-1,3)$ on the plane $x+y+z=7$ is 39. If $f(x)=\frac{\sin ^2 \pi x}{1+\pi^x}$, then $\int(f(x)+f(-x)) d x$ is equal to 40. Suppose that the points $(h, k),(1,2)$ and $(-3,4)$ lie on the line $l_1$. If a line $l_2$ passing through the points $( 41. If $\int \frac{\mathrm{d} x}{\cos ^3 x \sqrt{2 \sin 2 x}}=(\tan x)^A+C(\tan x)^B+\mathrm{k}$ where k is a constant of in 42. The maximum value of $\left(\cos \alpha_1\right) \cdot\left(\cos \alpha_2\right) \ldots .\left(\cos \alpha_n\right)$ und 43. If $\frac{\mathrm{d} y}{\mathrm{~d} x}=y+3, y+3>0$ and $y(0)=2$, then $y(\log 2)$ is equal to 44. The assets of a person are reduced in his business such that the rate of reduction is proportional to the square root of 45. If $f(1)=1, f^{\prime}(1)=5$, then the derivative of $\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f}(x))^2$ at $x=1$ 46. The abscissa of the point on the curve $y=\mathrm{a}\left(\mathrm{e}^{\frac{x}{a}}+\mathrm{e}^{-\frac{x}{a}}\right)$ whe 47. The integral $\int \frac{2 x^3-1}{x^4+x} \mathrm{~d} x$ is equal to 48. Let $\mathrm{z}=x+\mathrm{i} y$ be a complex number, where $x$ and $y$ are integers and $i=\sqrt{-1}$. Then the area of 49. If $\int \frac{\log \left(t+\sqrt{1+t^2}\right)}{\sqrt{1+t^2}} d t=\frac{1}{2}(g(t))^2+c$ where c is a constant of integ 50. A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one by one, with replacement, then the vari

Physics

1. The materials having negative magnetic susceptibility are 2. In most liquids, with rise in temperature, surface tension of a liquid 3. Two identical capacitors A and B are connected in series to a battery of E.M.F., 'E'. Capacitor B contains a slab of di 4. In $\mathrm{M}_{\mathrm{O}}$ is the mass of an oxygen isotope ${ }_8 \mathrm{O}^{17}$ and $\mathrm{M}_{\mathrm{p}}$ and 5. Two point charges $+8 q$ and $-2 q$ are located at $x=0$ and $x=\mathrm{L}$ respectively. The location of a point on the 6. When an electron orbiting in hydrogen atom in its ground state jumps to higher excited state, the de-Broglie wavelength 7. A graph of magnetic flux $(\phi)$ versus current (I) is shown for 4 different inductors $\mathrm{P}, \mathrm{Q}, \mathrm 8. The magnetic induction along the axis of a toroidal solenoid is independent of 9. Optical path of a particular ray of light has travelled a distance of 3 cm in flint glass is same as that on travelling 10. A string is under tension of 180 N and mass per unit length $2 \times 10^{-3} \mathrm{Kg} / \mathrm{m}$. It produces two 11. Two spheres of equal masses, one of which is a thin spherical shell and the other solid sphere, have the same moment of 12. Assuming the expression for the pressure exerted by the gas, it can be shown that pressure is 13. A particle executing S.H.M. has velocities ' $\mathrm{V}_1$ ' and ' $\mathrm{V}_2$ ' at distances ' $x_1$ ' and ' $x_2$ 14. The angle of incidence is found to be twice the angle of refraction when ray of light passes from vacuum into a medium o 15. The input signal given to C.E. amplifier having a voltage gain of 126 is $V_i=2 \cos \left(12 t+\frac{\pi}{3}\right)$. T 16. The figure shows the variation of photocurrent with anode potential for four different radiations. Let $\mathrm{I}_{\mat 17. When a resistance of $100 \Omega$ is connected in series with a galvanometer of resistance G , its range is V . To doubl 18. The angular separation of the central maximum in the Fraunhofer diffraction pattern is measured. The slit is illuminated 19. A particle starting from rest moves along the circumference of a circle of radius ' $r$ ' with angular acceleration ' $\ 20. If heat energy $\Delta \mathrm{Q}$ is supplied to an ideal diatomic gas, the increase in internal energy is $\Delta U$ a 21. How many times more intense is a 60 dB sound that a 30 dB sound? 22. Two loops P and Q of radii $\mathrm{R}_1$ and $\mathrm{R}_2$ are made from uniform metal wire of same material. $I_p$ an 23. The power radiated by a black body is P and it radiates maximum energy around the wavelength $\lambda_0$. Now the temper 24. Two coils P and Q each of radius R carry currents I and $\sqrt{8} \mathrm{I}$ respectively in same direction. Those coil 25. In Young's double slit experiment, intensity at a point is $\left(\frac{1}{4}\right)$ of the maximum intensity. The angu 26. The mutual inductance of two coils is 45 mH . The self-inductance of the coils are $\mathrm{L}_1=75 \mathrm{mH}$ and $\m 27. Frequency of the series limit of Balmer series of hydrogen atom of Rydberg's constant ' $R$ ' and velocity of light ' $C 28. The co-ordinates of a moving particle at any time ' $t$ ' are given by $x=\alpha t^3$ and $y=\beta t^3$ where $\alpha$ a 29. A bucket full of hot water is kept in a room. If it cools from $75^{\circ} \mathrm{C}$ to $70^{\circ} \mathrm{C}$ in $t 30. A cylinder contains water upto a height ' $H$ '. It has three orifices $\mathrm{O}_1, \mathrm{O}_2, \mathrm{O}_3$ as sho 31. In LCR series circuit, an alternating e.m.f. 'e' and current ' $i$ ' are given by equations $\mathrm{e}=160 \sin (100 \m 32. The power $(\mathrm{P})$ is supplied to a rotating body having moment of inertia ' I ' and angular acceleration ' $\alph 33. When the dielectric is placed in an external electric field, the electric field inside the dielectric is 34. A satellite is orbiting just above the surface of the planet of density ' $\rho$ ' with periodic time ' $T$ '. The quant 35. The truth table of the following circuit is 36. Two sound waves each of wavelength ' $\lambda$ ' and having the same amplitude ' $A$ ' from two source ' $\mathrm{S}_1$ 37. The potential difference $\left(V_A-V_B\right)$ between the points A and B in the given part of the circuit 38. An ideal diatomic gas is heated at constant pressure. What is the fraction of total energy applied, which increases the 39. An electric lamp connected in series with a capacitor and an a.c. source is glowing with certain brightness. On increasi 40. A series combination of $n_1$ capacitors, each of value $C_1$ is charged by a source of potential difference 6 V . Anoth 41. The speed with which the earth would have to rotate about its axis so that a person on the equator would weigh $\frac{3} 42. A simple pendulum has a periodic time ' $\mathrm{T}_1$ ' when it is on the surface of earth of radius ' $R$ '. Its perio 43. A coil of resistance $250 \Omega$ is placed in a magnetic field. If the magnetic flux $(\phi)$ linked with the coil vari 44. If the $\mathrm{p}-\mathrm{n}$ junction diode is unbiased, 45. When capillary is dipped vertically in water, rise of water in capillary is ' h '. The angle of contact is zero. Now the 46. The alternating voltage is given by $\mathrm{v}=\mathrm{v}_0 \sin \left(\omega \mathrm{t}+\frac{\pi}{3}\right)$ when wil 47. In case of system of two-particles of different masses, the centre of mass lies 48. A simple pendulum of length L has mass m and it oscillates freely with amplitude A. At extreme position, its potential e 49. A glass slab of thickness 4.8 cm is placed on the piece of paper on which an ink dot is marked. By how much distance wou 50. In ideal gas of $27^{\circ} \mathrm{C}$ is compressed adiabatically to $(8 / 27)$ of its original volume. If $\gamma=\fr

MHT CET 2024 16th May Morning Shift

MCQ (Single Correct Answer)

-0

Let $y=y(x)$ be the solution of the differential equation $(x \log x) \frac{d y}{d x}+y=2 x \log x(x \geq 1)$ then $y(\mathrm{e})$ is equal to

MHT CET 2024 16th May Morning Shift

MCQ (Single Correct Answer)

-0

The set of all points, for which $f(x)=x^2 e^{-x}$ strictly increases, is

$(0,2)$

$(2, \infty)$

$(-2,0)$

$(-\infty, \infty)$

MHT CET 2024 16th May Morning Shift

MCQ (Single Correct Answer)

-0

Range of the function $\mathrm{f}(x)=\frac{x^2+x+2}{x^2+x+1}, x \in \mathbb{R}$ is

$\left(1, \frac{7}{3}\right)$

$\left[1, \frac{7}{3}\right)$

$\left(1, \frac{7}{3}\right]$

$\left[1, \frac{7}{3}\right]$

MHT CET 2024 16th May Morning Shift

MCQ (Single Correct Answer)

-0

Let $S$ be a non-empty subset of $\mathbb{R}$. Consider the following statement:

p : There is a rational number $x \in \mathrm{~S}$ such that $x>0$.

Which of the following statements is the negation of the statement p?

There is a rational number $x \in \mathrm{~S}$ such that $x \leq 0$.

There is no rational number $x \in \mathrm{~S}$ such that $x \leq 0$.

Every rational number $x \in S$ satisfies $x \leq 0$.

$x \in \mathrm{~S}$ and $x \leq 0 \Rightarrow x$ is not a rational number.

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