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

Chemistry

1. How many amino acids are linked together by $(\mathrm{n}-1)$ amide bonds? 2. What is the percentage by mass of oxygen in NaOH ? (Atomic mass of $\mathrm{Na}=23 \mathrm{u}, \mathrm{O}=16 \mathrm{u}, 3. For the reaction $$\begin{aligned} & 2 \mathrm{NO}_{(\mathrm{s})}+2 \mathrm{H}_{2(\mathrm{~g})} \longrightarrow \mathrm{ 4. Identify the alloy used for construction of gas turbine engines. 5. Calculate the partial pressure exerted by dioxygen from a mixture of $32 \mathrm{~g} \mathrm{O}_2, 80 \mathrm{~g} \mathr 6. What is IUPAC name of following compound? 7. Which among the following is ferromagnetic substance? 8. What is $\mathrm{O}-\mathrm{O}$ bond length in ozone molecule? 9. Find the number of electrons that generate 1 coulomb charge? 10. Which among the following statements is NOT true about rate constant? 11. Calculate the oxidation number of Cr in $\mathrm{CrO}_4^{2-}$ ion and $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ respecti 12. Identify the monomer used to obtain a polymer that resembles the wool. 13. Which from following is a correct stability order of complex formed by metal ions if the ligand remains same? 14. Aldol condensation reaction is 15. What is the numerical difference in molar masses of second and third member of a homologous series? 16. What is the number of chiral carbon atoms present in 2-chloro-3,4-dimethylhexane? 17. Which of the following is a primary amine? 18. The $\mathrm{E}_{\text {cell }}^{+}$of $\mathrm{Cu}_{(\mathrm{s})}\left|\mathrm{Cu}_{(\mathrm{1M})}^{++} \| \mathrm{Ag}_ 19. Conjugate acid of $\mathrm{NH}_2^{-}$and $\mathrm{NH}_3$ are respectively 20. Calculate the value of $\Delta G$ for the following reaction. $\mathrm{N}_2 \mathrm{O}_{4(\mathrm{~g})} \longrightarrow 21. Calculate the radius of first orbit of $\mathrm{Li}^{++}$. 22. Which from following polymers (trade name) is used to obtain paints? 23. What is the number of electrons lost by Cr in a complex $\left[\mathrm{Cr}(\mathrm{CO})_6\right]$ ? 24. Identify the reagent ' R ' used in the following reaction. Ketone $\xrightarrow{\mathbf{R}}$ Semicarbazone 25. Identify alkadiene molecule from following. 26. Identify the product obtained in the following reaction. $$\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Br}+\mathrm{CH}_3 \mathrm 27. Identify the reagent R used in following conversion? tert-butyl bromide $\xrightarrow{\mathrm{R}}$ Isobutylene 28. Calculate the mass of ' Ca ' deposited at cathode by passing 0.8 ampere current through molten $\mathrm{CaCl}_2$ in 60 m 29. What is the expected value of $\Delta T_f$ for $1.25 \mathrm{~m} \mathrm{CaCl}_2$ solution if 1.25 m sucrose solution ha 30. Calculate Henry's law constant if solubility of gas in water at $25^{\circ} \mathrm{C}$ is $5.14 \times 10^{-4} \mathrm{ 31. What is the total number of orbitals present in N shell? 32. What is value of percent atom economy when reactants having sum of formula weight 78 u results in the formation of a pro 33. Identify the product formed in the following reaction. $\mathrm{CH_3CH_2MgBr}$ $$\mathrm{\mathrel{\mathop{\kern0pt\longr 34. Which from following is a mineral of copper? 35. Identify dispersed phase and dispersion medium in fog respectively. 36. Ethers when dissolved in cold concentrated sulfuric acid forms, 37. Calculate the total volume occupied by all atoms in simple cubic unit cell if radius of atom is $3 \times 10^{-8} \mathr 38. Under similar conditions enthalpy of freezing is exactly opposite to 39. A buffer solution is prepared by mixing $0.2 \mathrm{~M} \mathrm{~NH} \mathrm{O}_4 \mathrm{OH}$ and $1 \mathrm{~M} \math 40. A solution of nonvolatile solute is obtained by dissolving 0.8 g in $0.3 \mathrm{dm}^3$ water has osmotic pressure 0.2 a 41. Which of the following molecules is an example of sp hybridization? 42. A first order reaction takes 40 minute for $20 \%$ decomposition. Calculate its rate constant. 43. What is the number of moles of water molecules present in a mole of carnallite? 44. What is the number of amino acids present in single turn of $\alpha$-helix of protein? 45. Which from following compounds is obtained as by product in synthesis of sodium carbonate by Solvay process? 46. Which of the following compounds is NOT a phenol? 47. A compound is formed by two elements A and B. The atoms of element B form ccp structure. The atoms of A occupy $\frac{1} 48. Which of the following isomers of $\mathrm{C}_4 \mathrm{H}_9 \mathrm{Br}$ is a chiral molecule? 49. The dissociation constant of a weak monobasic acid is $3.2 \times 10^{-4}$. Calculate the degree of dissociation in its 50. 100 ml of $\mathrm{H}_{2(\mathrm{~g})}$ and 100 ml of $\mathrm{Cl}_{2(\mathrm{~g})}$ were allowed to react at 1 bar pres

Mathematics

1. If $$ y=[(x+1)(2 x+1)(3 x+1) \ldots \ldots \ldots(n x+1)]^2 $$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=0$ is 2. For the probability distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-sty 3. The value of $\int \frac{\mathrm{d} x}{7+6 x-x^2}$ is equal to 4. The value of $\begin{aligned} \cos \left(18^{\circ}-\mathrm{A}\right) \cos \left(18^{\circ}+\mathrm{A}\right) -\cos \lef 5. If $\int \frac{\mathrm{d} x}{1+3 \sin ^2 x}=\frac{1}{2} \tan ^{-1}(\mathrm{f}(x))+\mathrm{c}$, where c is a constant of 6. A random variable X has the following probability distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td 7. Let $f:[-1,3] \rightarrow \mathbb{R}$ be defined as $$\left\{\begin{array}{lc} |x|+[x], & -1 \leqslant xwhere $[t]$ deno 8. Let $\overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{b}}=\hat{\mathrm{i}}-\h 9. The differential equation, having general solution as $A x^2+B y^2=1$, where $A$ and $B$ are arbitrary constants, is 10. Let $z$ be a complex number such that $|z|+z=2+i$, where $i=\sqrt{-1}$, then $|z|$ is equal to 11. If $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$ are two unit vectors such that $5 \overline{\mathrm{a}}+4 \overli 12. The value of $\int \frac{\sec x \cdot \tan x}{9-16 \tan ^2 x} \mathrm{dx}$ is equal to 13. If $n(A)=4, n(B)=2$. Then the number of subsets of the set $\mathrm{A} \times \mathrm{B}$ each having at least 3 element 14. A radio active substance has half-life of $h$ days, then its initial decay rate is given by Note that at $\mathrm{t}=0, 15. If $(a+\sqrt{2} b \cos x)(a-\sqrt{2} b \cos y)=a^2-b^2$, where $\mathrm{a}>\mathrm{b}>0$, then $\frac{\mathrm{d} x}{\mat 16. Contrapositive of the statement. 'If two numbers are equal, then their squares are equal' is 17. Let A and B be $3 \times 3$ real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the syste 18. If $\mathrm{f}(x)=x^3-10 x^2+200 x-10$, then 19. The number of common tangents to the circles $x^2+y^2-x=0$ and $x^2+y^2+x=0$ is /are 20. Let $\bar{a}=2 \hat{i}+\hat{j}-2 \hat{k}$ and $\bar{b}=\hat{i}+\hat{j}$. If $\bar{c}$ is a vector such that $\overline{\ 21. The equation $\mathrm{e}^{\sin x}-\mathrm{e}^{-\sin x}=4$ has ̱_________ solutions. 22. The value of $\int \frac{d x}{5+4 \sin x}$ is equal to 23. If $p \rightarrow(q \vee r)$ is false, then the truth values of $\mathrm{p}, \mathrm{q}, \mathrm{r}$ are respectively 24. The area of the region bounded by curves $y=3 x+1, y=4 x+1$ and $x=2$ is 25. The region represented by the inequations $2 x+3 y \leqslant 18, x+y \geqslant 10, x \geqslant 0, y \geqslant 0$ is 26. Let $\mathrm{f}(x)=(x+1)^2-1, x \geqslant-1$, then the set $\left\{x / f(x)=f^{-1}(x)\right\}$ is 27. The probability, that a year selected at random will have 53 Mondays, is 28. Let $\mathrm{L}_1: \frac{x+2}{5}=\frac{y-3}{2}=\frac{\mathrm{z}-6}{1}$ and $\mathrm{L}_2: \frac{x-3}{4}=\frac{y+2}{3}=\f 29. A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is corre 30. The perpendicular distance from the origin to the plane containing the two lines $\frac{x+2}{3}=\frac{y-2}{5}=\frac{z+5} 31. The number of integral values of k for which the equation $7\cos x+5\sin x=2k+1$ has a solution, is 32. The value of integral $\int_\limits{-2}^0\left(x^3+3 x^2+3 x+5+(x+1) \cos (x+1)\right) d x$ is equal to 33. If $x=2 \cos \theta-\cos 2 \theta$ and $y=2 \sin \theta-\sin 2 \theta$, then $\frac{\mathrm{d}^2 y}{d x^2}$ is equal to 34. $2 \pi-\left(\sin ^{-1} \frac{4}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{16}{65}\right)$ is equal to 35. If two sides of a square are $4 x+3 y-20=0$ and $4 x+3 y+15=0$, then the area of the square is 36. Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area 37. Let $a, b, c$ be three non-zero real numbers such that the equation $\sqrt{3} \mathrm{a} \cos x+2 b \sin x=c$, $x \in\le 38. Let $P(2,1,5)$ be a point in space and $Q$ be a point on the line $\bar{r}=(\hat{i}-\hat{j}+2 \hat{k})+\mu(-3 \hat{i}+\h 39. $$\lim _\limits{x \rightarrow \frac{\pi}{2}} \frac{\left(1-\tan \left(\frac{x}{2}\right)\right)(1-\sin x)}{\left(1+\tan 40. A ladder 5 m in length is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall 41. If the equation $\cos ^4 \theta+\sin ^4 \theta+\lambda=0$ has real solutions for $\theta$, then $\lambda$ lies in the in 42. The equation of the tangent to the parabola $y^2=8 x$, which is parallel to the line $4 x-y+3=0$ is 43. The centroid of tetrahedron with vertices $\mathrm{P}(5,-7,0), \mathrm{Q}(\mathrm{a}, 5,3), \mathrm{R}(4,-6, b)$ and $\m 44. The approximate value of $3^{2.001}$, if $\log 3=1.0986$ is 45. If the vectors $\overline{\mathrm{a}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{b}}=2 \hat 46. If $\bar{u}, \bar{v}$ and $\bar{w}$ are three non-coplanar vectors, then $(\bar{u}+\bar{v}-\bar{w}) \cdot[(\bar{u}-\bar{ 47. The value of $k$, if the slope of one of the lines given by $4 x^2+k x y+y^2=0$ is four times that of the other, is give 48. The differential equation of $y=\mathrm{e}^x\left(\mathrm{a}+\mathrm{bx}+x^2\right)$ is 49. The mean of the numbers $a, b, 8,5,10$ is 6 and the variance is $6.8$ . Then which of the following gives possible value 50. Let $\overline{\mathrm{u}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}, \overline{\mathrm{v}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}$ a

Physics

1. A thin uniform metal rod of mass ' $M$ ' and length ' $L$ ' is swinging about a horizontal axis passing through its end. 2. When the number of turns in a coil are made 3 times without any change in the length of the coil, its self inductance be 3. When a system is taken from state ' $a$ ' to state ' $c$ ' along a path abc, it is found that $\mathrm{Q}=80 \mathrm{cal 4. The driver of a car travelling with a speed ' $V_1$ ' $\mathrm{m} / \mathrm{s}$ towards a wall sounds a siren of frequen 5. When a mercury drop of radius ' $R$ ' splits up into 1000 droplets of radius ' $r$ ', the change in surface energy is ( 6. Two different logic gates giving output ' 1 ' for the inputs $(1,0)$ and then for $(0,1)$ are 7. An open organ pipe of length ' $l$ ' is sounded together with another open organ pipe of length $\left(l+l_1\right)$ in 8. When a coil is connected to a d.c. source of e.m.f. 12 volt; then the current of 4 A flows in it . If the same coil is c 9. The ratio of work done by an ideal rigid diatomic gas to the heat supplied by the gas in an isobaric process is 10. A galvanometer has resistance $80 \Omega$ and it is shunted with resistance $20 \Omega$. If $20 \%$ of the main current 11. The weights of an object are measured in a coal mine of depth ' $h_1$ ', then at sea level of height ' $h_2$ ' and lastl 12. The angle of contact between glass and water is $0^{\circ}$ and water rises in a glass capillary upto 6 cm (Surface tens 13. In double slit experiment, instead of taking slits of equal widths, one slit is made twice as wide as the other. Then in 14. Two parallel wires separated by distance 'b' are carrying equal current ' $I$ ' in the same direction. The force per uni 15. In an a.c. circuit, the reactance of a coil is $\sqrt{3}$ times its resistance. The phase difference between the voltage 16. Three thin rods, each of mass ' $M$ ' and length ' $L$ ' are placed along $\mathrm{X}, \mathrm{Y}$ and Z axes which are 17. For a symmetric (equilateral) prism, the prism formula can be written as 18. The internal energy of an ideal diatomic gas corresponding to volume ' $V$ ' and pressure ' P ' is 2.5 PV. The gas expan 19. Two photons having energies twice and thrice the work function of metal are incident one after another on the metal surf 20. If a unit positive charge is shifted from a region of low potential to a region of high potential, then the electric pot 21. Magnetic induction produced at the centre of a circular loop of radius ' $R$ ' carrying a current is ' B '. The magnetic 22. The pulleys and strings shown in figure are smooth and of negligible mass. For the system to remain in equilibrium, angl 23. In biprism experiment, the fringe width is 0.6 mm . The distance between $6^{\text {th }}$ dark fringe and $8^{\text {th 24. A radioactive substance has half-life of 60 minute. During 3 hour, the amount of substance decayed would be 25. A horizontal platform with a small object placed on it executes a linear S.H.M. in the vertical direction. The amplitude 26. In Young's double slit experiment, 'I' is the minimum intensity and ' $I_1$ ' is the intensity at a point where the path 27. For a ray of light, the critical angle is minimum, when it travels from 28. Four moles of hydrogen, two moles of helium and one mole of water vapour form an ideal gas mixture. $\left[C_{\mathrm{v} 29. Electrons are accelerated through a potential difference of 16 kV . If the potential difference is increased to 64 kV , 30. Starting from mean position, a body oscillates simple harmonically with a period ' $T$ '. After what time will its kinet 31. Two solenoids of equal number of turns have their lengths as well as radii in the same ratio $1: 3$. The ratio of their 32. In an extrinsic n-type semiconductor, the free electrons donated by the impurity atoms occupy energy levels in 33. If the angular velocity of a body rotating about the given axis increases by $20 \%$, then its kinetic energy of rotatio 34. Two progressive waves $Y_1=\sin 2 \pi\left(\frac{t}{0 \cdot 4}-\frac{x}{4}\right)$ and $Y_2=\sin 2 \pi\left(\frac{t}{0 \ 35. The strength of magnetic field at a perpendicular distance ' $x$ ' near a long straight conductor carrying current ' I ' 36. The ratio of the areas of the electron orbits for the second excited state to the first excited state for the hydrogen a 37. Two point charges $+8 q$ and $-2 q$ are located at $\mathrm{X}=0$ (origin) and $\mathrm{X}=\mathrm{L}$ respectively. The 38. A series $\mathrm{L}-\mathrm{C}-\mathrm{R}$ circuit containing a resistance ' $R$ ' has angular frequency ' $\omega$ '. 39. Consider a long uniformly charged cylinder having constant volume charge density ' $\lambda$ ' and radius ' $R$ '. A Gau 40. Two capillary tubes A and B of the same internal diameter are kept vertically in two different liquids whose densities a 41. For a transistor, current gain $(\beta)=50$. To change the collector current by $350 \mu \mathrm{~A}$, the base current 42. A sheet of steel is 40 cm long and 5 cm broad at $0^{\circ} \mathrm{C}$. The surface area of the sheet increases by $1.4 43. When a sonometer wire vibrates in third overtone there are 44. Alternating current of peak value $\left(\frac{2}{\pi}\right)$ A flows through the primary coil of a transformer. The co 45. Three condensers of capacities ' $\mathrm{C}_1$ ', ' $\mathrm{C}_2$ ', ' $\mathrm{C}_3$ ' are connected in series with a 46. The maximum velocity of a particle, executing S.H.M. with an amplitude 7 mm is $4.4 \mathrm{~ms}^{-1}$ The period of os 47. A satellite of mass ' $m$ ' is revolving around the earth of mass ' $M$ ' in an orbit of radius ' $r$ ' with constant an 48. A cell balances against a length of 150 cm on a potentiometer wire when it is shunted by a resistance of $5 \Omega$. But 49. A quantity of heat ' $Q$ ' is supplied to monoatomic ideal gas which expands at constant pressure. The fraction of heat 50. A body of mass 1 kg starts from rest and moves with uniform acceleration. In 2 seconds, its velocity is $10 \mathrm{~m}

MHT CET 2024 15th May Morning Shift

MCQ (Single Correct Answer)

-0

$$\lim _\limits{x \rightarrow \frac{\pi}{2}} \frac{\left(1-\tan \left(\frac{x}{2}\right)\right)(1-\sin x)}{\left(1+\tan \left(\frac{x}{2}\right)\right)(\pi-2 x)^3}$$ is

$\frac{1}{32}$

$\frac{1}{8}$

$\frac{1}{16}$

MHT CET 2024 15th May Morning Shift

MCQ (Single Correct Answer)

-0

A ladder 5 m in length is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall, at the rate of $2 \mathrm{~m} / \mathrm{sec}$. How fast is the height on the wall decreasing when the foot of the ladder is 4 m away from the wall?

$\frac{4}{3} \mathrm{~m} / \mathrm{sec}$

$\frac{2}{3} \mathrm{~m} / \mathrm{sec}$

$\frac{5}{3} \mathrm{~m} / \mathrm{sec}$

$\frac{8}{3} \mathrm{~m} / \mathrm{sec}$

MHT CET 2024 15th May Morning Shift

MCQ (Single Correct Answer)

-0

If the equation $\cos ^4 \theta+\sin ^4 \theta+\lambda=0$ has real solutions for $\theta$, then $\lambda$ lies in the interval

$\left(-\frac{5}{4},-1\right)$

$\left[-\frac{3}{2},-\frac{5}{4}\right]$

$\left(-\frac{1}{2},-\frac{1}{4}\right]$

$\left[-1,-\frac{1}{2}\right]$