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

Chemistry

1. What is the number of moles of donor atoms present in one mole oxalate ion? 2. Which from following substances acts as a base when reacted with water? 3. Which from following polymers is classified as fibres? 4. What type of solution is the iodine in air? 5. Identify ' $Y$ ' in the following reaction. $$\mathrm{CH}_3 \mathrm{Br} \xrightarrow{\mathrm{KcN}} \mathrm{X} \xrightarr 6. What is de Broglie's wavelength for a particle having mass $6.64 \times 10^{-27} \mathrm{~kg}$ moving with velocity of $ 7. Identify the product formed in the following reaction. 8. What is the IUPAC name of the following compound? 9. Calculate the pH of 0.02 M monobasic acid having $2 \%$ dissociation. 10. Which of the following molecule can form hydrogen bonding with itself? 11. Calculate the cell constant of conductivity cell containing 0.1 M KCl solution having resistance $60 \Omega$ and conduct 12. Calculate standard internal energy change for $\mathrm{OF}_{2(\mathrm{~g})}+\mathrm{H}_2 \mathrm{O}_{(\mathrm{g})} \long 13. Which of the following compounds is obtained by using Finkelstein reaction? 14. In a first order reaction $60 \%$ of the reactant converts into product in 45 minute. Calculate rate constant of the rea 15. Identify a compound having properties of tear gas. 16. Which of the following series of emission spectral lines for hydrogen observed in visible region? 17. What is the number of faraday required to produce 0.18 g aluminium at cathode during electrolysis of molten $\mathrm{AlC 18. Which pair of metal ions from following have same number of unpaired electrons? 19. Which from following compounds contains oxygen as a heteroatom? 20. What type of glycosidic linkages are developed when excess glucose is to be stored for future use in animals? 21. Calculate the relative lowering of vapour pressure if vapour pressure of pure solvent and vapour pressure of solution at 22. Which from following ligands is neutral? 23. Identify chiral molecule from following: 24. Which from following polymers is a urea-formaldehyde resin? 25. Which reagent is used in the conversion of phenol to picric acid? 26. Identify the reactivity order for halogens towards alkanes. 27. What is the total number of tetrahedral voids in 0.6 mole of compound that forms hcp structure? 28. Identify name of reaction when aldehyde or ketone react with $\mathrm{Zn}-\mathrm{Hg} /$ conc. HCl to give alkane. 29. What products are obtained when beryllium oxide is treated separately with aq. HCl and aq. NaOH solutions respectively? 30. Calculate internal energy change of a system if work done by the system is 8 J and heat supplied to it is 40 J . 31. Identify basic oxide from following. 32. Calculate the solubility product of sparingly soluble salt BA at $27^{\circ} \mathrm{C}$ if its solubility is $1.8 \time 33. Which of the following conversions is Hofmann Elimination reaction? 34. For the reaction, $$\mathrm{CH}_3 \mathrm{Br}_{(\mathrm{aq})}+\mathrm{OH}_{(\mathrm{aq})}^{-} \longrightarrow \mathrm{C 35. Identify the product X in the following reaction. Ethanoyl chloride $\xrightarrow{\mathrm{H}_2 \mathrm{O}} \mathrm{X}$ 36. Which of the following is allylic alcohol? 37. Identify positively charged sol from the following. 38. Calculate the number of unit cells in 0.4 g metal if the product of density and volume of unit cell is $1.2 \times 10^{- 39. What is the major product obtained when tert-butyl bromide is heated with silver fluoride? 40. Which from following equations represents a correct relationship between standard cell potential and equilibrium constan 41. What is the total number of particles present in base centred unit cell? 42. Which of the following equation relates temperature of a reaction with $\Delta \mathrm{H}^{\circ}$ and $\Delta \mathrm{S 43. Calculate the molality of solution if its depression in freezing point is 0.18 K . $\left[\mathrm{K}_{\mathrm{f}}=1.6 \m 44. For the reaction, $$\mathrm{H}_{2(g)}+\mathrm{Br}_{2(8)} \longrightarrow 2 \mathrm{HBr}_{(\mathrm{g})}, \mathrm{r}=\math 45. Identify an actinoid element from following. 46. What is the oxidation number of Mn in $\mathrm{MnO}_4^{-}$? 47. What is the number of electrons present in antibonding orbitals of $\mathrm{N}_2$ molecule according to molecular orbita 48. Which from following is a largest size nanomaterial? 49. Which from following nitrogen bases of nucleic acids is derived from purine? 50. Calculate mass in kg of 2.5 mole ammonia.

Mathematics

1. If $\mathrm{g}(x)=[\mathrm{f}(2 \mathrm{f}(x)+2)]^2$ and $\mathrm{f}(0)=-1, \mathrm{f}^{\prime}(0)=1$ then $g^{\prime}(0 2. If $\tan ^{-1}\left(\frac{1}{4}\right)+\tan ^{-1}\left(\frac{2}{9}\right)=\frac{1}{2} \cos ^{-1} x$, then $x$ is 3. The shaded area in the given figure is a solution set for some system of inequalities. The maximum value of the function 4. If $z_1=5-2 i$ and $z_2=3+i$, where $i=\sqrt{-1}$, then $\arg \left(\frac{z_1+z_2}{z_1-z_2}\right)$ is 5. The co-ordinates of the foot of the perpendicular from the point $(0,2,3)$ on the line $\frac{x+3}{5}=\frac{y+1}{2}=\fra 6. The slope of tangent at $(x, y)$ to a curve passing through $\left(1, \frac{\pi}{4}\right)$ is $\frac{y}{x}-\cos ^2 \fra 7. If $\cos ^{-1}\left(\frac{12}{13}\right)+\sin ^{-1}\left(\frac{3}{5}\right)=\sin ^{-1} \mathrm{P}$, then the value of $P 8. The rate of change of the volume of a sphere with respect to its surface area, when its radius is 2 cm , is _________ $\ 9. In a triangle $\mathrm{ABC}, l(\mathrm{AB})=\sqrt{23}$ units, $l(\mathrm{BC})=3$ units, $l(\mathrm{CA})=4$ units, then $ 10. Truth values of $\mathrm{p} \rightarrow \mathrm{r}$ is F and $\mathrm{p} \leftrightarrow \mathrm{q}$ is F . Then the tru 11. Water is being poured at the rate of $36 \mathrm{~m}^3 / \mathrm{min}$ into a cylindrical vessel, whose circular base is 12. A line having direction ratios $1,-4,2$ intersects the lines $\frac{x-7}{3}=\frac{y-1}{-1}=\frac{z+2}{1}$ and $\frac{x}{ 13. $\int \frac{x^2-4}{x^4+9 x^2+16} \mathrm{dx}=\tan ^{-1}(\mathrm{f}(x))+\mathrm{c}$ (where c is a constant of integration 14. If $\overline{\mathrm{a}}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ and $\overline{\mathrm{b}}=2 \hat{i}+3 15. Let $A=\left[\begin{array}{cc}1 & 2 \\ -1 & 4\end{array}\right]$ and $A^{-1}=\alpha \mathrm{I}+\beta \mathrm{A}, \alpha, 16. $$\lim _\limits{y \rightarrow 0} \frac{\sqrt{1+\sqrt{1+y^4}}-\sqrt{2}}{y^4}=$$ 17. If $\overline{\mathrm{a}}$ is perpendicular to $\bar{b}$ and $\bar{c},|\bar{a}|=2$, $|\overline{\mathrm{b}}|=3,|\overlin 18. The mean and variance of seven observations are 8 and 16 respectively. If five of the observations are $2,4,10,12,14$, t 19. If $y=\tan ^{-1}\left(\frac{2+3 x}{3-2 x}\right)+\tan ^{-1}\left(\frac{4 x}{1+5 x^2}\right)$, then $\frac{d y}{d x}=$ 20. If $\mathrm{f}(x)=\frac{a \sin x+b \cos x}{c \sin x+d \cos x}$ is decreasing for all $x$ then 21. If a discrete random variable X is defined as follows $\mathrm{P}[\mathrm{X}=x]=\left\{\begin{array}{cl}\frac{\mathrm{k} 22. If $\bar{a}=2 \hat{i}-\hat{j}+\hat{k}, \bar{b}=\hat{i}+\hat{j}-2 \hat{k}$ and $\bar{c}=4 \hat{i}-2 \hat{j}+\hat{k}$, the 23. Numbers are selected at random, one at a time from two digit numbers $10,11,12 \ldots ., 99$ with replacement. An event 24. The function $y(x)$ represented by $x=\sin t$, $y=a e^{t \sqrt{2}}+b e^{t \sqrt{2}}, t \in\left(\frac{-\pi}{2}, \frac{\p 25. The value of $\cos 20^{\circ}+2 \sin ^2 55^{\circ}-\sqrt{2} \sin 65^{\circ}$ is 26. If $[x]$ denotes the greatest integer function, then $$\int_\limits0^5 x^2[x] d x=$$ 27. If the function $f$ defined on $\left(\frac{\pi}{6}, \frac{\pi}{3}\right)$ by $$f(x)=\left\{\begin{array}{cc} \frac{\sqr 28. $$\int \cos ^{\frac{-3}{7}} x \cdot \sin ^{\frac{-11}{7}} x d x=$$ 29. If $\bar{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k}, \quad \bar{b}=b_1 \hat{i}+b_2 \hat{j}+b_3 \hat{k}$, $\bar{c}=c_1 \hat{i 30. The domain of the function $\mathrm{f}(x)=\frac{\sin ^{-1}(x-3)}{\sqrt{9-x^2}}$ is 31. If $\bar{a}=2 \hat{i}+2 \hat{j}+3 \hat{k}, \quad \bar{b}=-\hat{i}+2 \hat{j}+\hat{k}$ and $\bar{c}=3 \hat{i}+\hat{j}$ are 32. The area (in sq. units) bounded between the parabolas $x^2=\frac{y}{4}$ and $x^2=9 y$ and the line $y=2$ is 33. A plane makes positive intercepts of unit length on each of $X$ and $Y$ axis. If it passes through the point $(-1,1,2)$ 34. The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 35. One end of the diameter of the circle $x^2+y^2-6 x-5 y-1=0$ is $(-1,3)$, then the equation of the tangent at the other e 36. If $\tan ^{-1}\left(\frac{x+1}{x-1}\right)+\tan ^{-1}\left(\frac{x-1}{x}\right)=\tan ^{-1}(-7)$, then $x$ is equal to 37. The equation of the normal to the curve $y=x \log x$ parallel to $2 x-2 y+3=0$ is 38. $$\int \frac{\mathrm{e}^{\tan ^{-1} x}}{1+x^2}\left[\left(\sec ^{-1} \sqrt{1+x^2}\right)^2+\cos ^{-1}\left(\frac{1-x^2}{ 39. The equation of plane through the point $(2,-1,-3)$ and parallel to lines $\frac{x-1}{3}=\frac{y+2}{2}=\frac{z}{-4}$ and 40. The co-ordinates of the foot of perpendicular, drawn from the point $(-2,3)$ on the line $3 x-y-1=0$ are 41. The value of $\tan ^{-1}(-\sqrt{3})-\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)+\cos ^{-1}\left(\frac{-1}{2}\right)$ is 42. The general solution of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}=y \tan x-y^2 \sec x$ is 43. If $\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$ are three vectors such that $\overline{\mathrm{ 44. Two friends A and B apply for a job in the same company. The probabilities of A getting selected is $\frac{2}{5}$ and th 45. If $P_1$ and $P_2$ are perpendicular distances (in units) from point $(2,-1)$ to the pair of lines $2 x^2-5 x y+2 y^2=0$ 46. $$\int \frac{x^3-7 x+6}{x^2+3 x} \mathrm{~d} x=$$ 47. The cumulative distribution function of a discrete random variable X is given by .tg {border-collapse:collapse;border- 48. A five digit number divisible by 3 is to be formed using the digits $0,1,2,3,4,5$ without repetition, then the total num 49. The statement $\sim(p \leftrightarrow \sim q)$ is 50. If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha \log |x|+\beta x^2+x$, then

Physics

1. A circular coil of resistance ' $R$ ', area ' $A$ ', number of turns ' N ' is rotated about its vertical diameter with a 2. The linear speed of a particle at the equator of the earth due to its spin motion is ' V '. The linear speed of the part 3. Three point masses, each of mass ' $m$ ' are placed at the corners of an equilateral triangle of side ' $L$ '. The momen 4. In the second orbit of hydrogen atom, the energy of an electron is ' $E$ '. In the third orbit of helium atom, the energ 5. The graph shows the variation of voltage ' V ' across the plates of two capacitors $A$ and $B$ versus increase in charge 6. The bob of a pendulum of length ' $l$ ' is pulled aside from its equilibrium position through an angle ' $\theta$ ' and 7. On the surface of the liquid in equilibrium, molecules of the liquid possess 8. An optician makes spectacles having a combination of a convex lens of focal length 40 cm in contact with a concave lens 9. A ray of light travelling through a rarer medium is incident at very small angle ' $i$ ' on a glass slab and after refra 10. Kinetic energy of a proton is equal to energy $E$ of a photon. Let ' $\lambda_1$ ' be the de-Broglie wavelength of proto 11. An inductance of 2 mH , a condenser of $20 \mu \mathrm{~F}$ and a resistance of $50 \Omega$ are connected in series to a 12. Two sound waves having frequencies 250 Hz and 256 Hz superimpose to produce beat wave. The resultant beat wave has inten 13. A body travelling with uniform acceleration crosses two points A and B with velocities $20 \mathrm{~m} / \mathrm{s}$ and 14. During an experiment, an ideal gas is found to obey an additional law $\mathrm{VP}^2=$ constant. The gas is initially at 15. To get the truth table shown from the following logic circuit, the logic gate G should be 16. In an $L C R$ circuit, if ' $V$ ' is the effective value of the applied voltage, $V_R$ is the voltage across ' $R$ ', ' 17. Two objects of masses ' $m_1$ ' and ' $m_2$ ' are moving in the circles of radii ' $r_1$ ' and ' $r_2$ ' respectively. T 18. A hollow cylinder has charge ' $q$ ' $C$ within it. If ' $\phi$ ' is the electric flux associated with the curved 19. A water drop is divided into 8 equal droplets. The pressure difference between the inner and outer side of the big drop 20. An arc of a circle of radius ' $R$ ' subtends an angle $\frac{\pi}{2}$ at the centre. It carries a current $I$. The magn 21. The Boolean expression for the given combination of logic gates is 22. A body performing uniform circular motion of radius ' $R$ ' has frequency ' $n$ '. Its centripetal acceleration per unit 23. A solenoid having 400 turns per metre has a core of a material with relative permeability 400. When a current of 0.5 A i 24. Three identical metal balls each of radius ' $r$ ' are placed such that an equilateral triangle is formed when centres o 25. Two identical galvanometers are converted into an ammeter and into milliammeter. For the same current, the value of shun 26. A boy weighs 72 N on the surface of earth. The gravitational force on a body due to earth at a height equal to half the 27. In a single slit diffraction experiment, for a wavelength of light ' $\lambda$ ', half-angular width of the principle ma 28. The first operation involved in a Carnot cycle is 29. Temperature remaining constant, the pressure of gas is decreased by $20 \%$. The percentage change in volume 30. A plane mirror is placed at the bottom of a tank containing a liquid of refractive index ' $\mu$ ', ' $p$ ' is a small o 31. A light bulb connected in series with a capacitor and an a.c. source is glowing with a certain brightness. On reducing t 32. A pipe 60 cm long and open at both the ends produces harmonics. Which harmonic mode of pipe resonates a 2.2 KHz source? 33. A point source of light is used in a photoelectric effect. If the source is removed farther from the emitting metal, the 34. The kinetic energy of a particle, executing simple harmonic motion is 16 J when it is in mean position. If amplitude of 35. At certain temperature, $\operatorname{rod} \mathrm{A}$ and $\operatorname{rod} \mathrm{B}$ of different materials have 36. A liquid drop having surface energy ' $E$ ' is spread into 512 droplets of same size. The final surface energy of the dr 37. Two radioactive substances A and B have decay constants ' $5 \lambda$ ' and ' $\lambda$ ' respectively. At $\mathrm{t}=0 38. A monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in changing the internal energy 39. A source and listener are both moving towards each other with speed $\frac{\mathrm{V}}{10}$. (where V is speed of sound) 40. The ratio of the specific heats $\frac{C_p}{C_v}=\gamma$, in terms of degrees of freedom ( n ) is 41. In a double slit experiment, the distance between slits is increased 10 times, whereas their distance from screen is hal 42. If a transformer of an audio amplifier has output impedance $8000 \Omega$ and the speaker has input impedance $8 \Omega$ 43. A particle performs linear S.H.M. At a particular instant, velocity of the particle is ' $u$ ' and acceleration is ' $\a 44. Two uniform strings A and B made of steel are made to vibrate under the same tension. If first overtone of A is equal to 45. ' $n$ ' small drops of same size are charged to ' $V$ ' volt each. If they coalesce to form a single large drop, then i 46. Air capacitor has capacitance ' $\mathrm{C}_1$ '. The space between two plates of capacitor is filled with two dielectri 47. A coil is wound on a core of rectangular crosssection. If all the linear dimensions of the core are increased by a facto 48. When a small amount of impurity atoms are added to semiconductor, then generally its resistivity 49. A current 'I' flows in anticlockwise direction in a circular arc of a wire having $\left(\frac{3}{4}\right)^{\text {th 50. When a resistance of $200 \Omega$ is connected in series with a galvanometer of resistance ' $G$ ', its range is ' $V$ '

MHT CET 2024 16th May Evening Shift

MCQ (Single Correct Answer)

-0

Numbers are selected at random, one at a time from two digit numbers $10,11,12 \ldots ., 99$ with replacement. An event $E$ occurs if and only if the product of the two digits of a selected number is 18 . If four numbers are selected, then probability that the event E occurs at least 3 times is

$\frac{87}{90^4}$

$\frac{348}{90^4}$

$87\left(\frac{4}{90}\right)^4$

$\left(\frac{4}{10}\right)^4$

MHT CET 2024 16th May Evening Shift

MCQ (Single Correct Answer)

-0

The function $y(x)$ represented by $x=\sin t$, $y=a e^{t \sqrt{2}}+b e^{t \sqrt{2}}, t \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$ satisfies the equation $\left(1-x^2\right) y^{\prime \prime}-x y^{\prime}=\mathrm{k} y$, then the value of k is k is

$-$1

MHT CET 2024 16th May Evening Shift

MCQ (Single Correct Answer)

-0

The value of $\cos 20^{\circ}+2 \sin ^2 55^{\circ}-\sqrt{2} \sin 65^{\circ}$ is

$-$1

$\frac{1}{2}$

MHT CET 2024 16th May Evening Shift

MCQ (Single Correct Answer)

-0

If $[x]$ denotes the greatest integer function, then $$\int_\limits0^5 x^2[x] d x=$$

$\frac{244}{3}$