MHT CET 2024 10th May Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Which from following is NOT a dihydric compound? 2. Calculate the volume of unit cell if an element having molar mass $92 \mathrm{~g} \mathrm{~mol}^{-1}$ that forms bcc str 3. Which of the following ethers is gaseous at room temperature? 4. A gas occupies $11.2 \mathrm{~dm}^3$ at 105 kPa What is the volume if pressure is increased to 210 kPa ? 5. For a zero order reaction, $\mathrm{A} \longrightarrow$ product, concentration of A decreases from $1.2 \mathrm{~mol~dm} 6. What is the volume of oxygen required for complete combustion of 0.25 mole of methane at S.T.P.? 7. What type of solution the alloy is? 8. Which from following is NOT a salient feature of Watson and Crick model for DNA? 9. Which of the following is NOT true about order of a reaction? 10. Calculate solubility $\left(\mathrm{moldm}^{-3}\right)$ of a sparingly soluble electrolyte AB at 298 K if its solubility 11. Which from following alkyl substituted alkenes is most stable? 12. In an ionic solid equal number of cations and anions are missing from their regular positions in the crystal lattice cre 13. Which from following compounds is a trihydric alcohol? 14. Which of the following compounds is recovered in solvay's process when $\mathrm{NH}_4 \mathrm{Cl}$ is treated with slake 15. What is the shape of bromine pentafluoride? 16. What type of colloid is the soap lather? 17. Which compound from following has highest boiling point? 18. Which from following statements is NOT true for nucleic acids? 19. Which of the following units of electrical measurement is not equivalent to 1 Siemen? 20. What is the oxidation number of carbon in $\mathrm{K}_2 \mathrm{C}_2 \mathrm{O}_4 ?$ 21. What type of isomerism is exhibited by $\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right] \mathrm{Cl}_3$ an 22. Which of the following groups exhibits (+)R effect? 23. Identify the product 'B' obtained in following reaction. $\mathrm{R}-\mathrm{C} \equiv \mathrm{N} \xrightarrow[\mathrm{H 24. Which of the following is radius of first orbit of He$^+$ ? 25. Identify heteroleptic complex from following. 26. Calculate rate constant of first order reaction if concentration of reactant decreases by $90 \%$ in 30 minute? 27. Identify the correct decreasing order of $\mathrm{pK}_{\mathrm{b}}$ values of compounds from following. 28. Identify the instrument used to find the structure of surface of material. 29. Which of the following equations indicates increase in entropy? 30. Which from following statements is true about internal energy? 31. What is the molar mass of product hydrocarbon when 2 moles of methyl bromide reacts with large excess of sodium in dry e 32. What is the order of ease of dehydrohalogenation of alkyl halides? 33. Identify the product obtained in following reaction. $\mathrm{C}_6 \mathrm{H}_6 \xrightarrow[\text { Anhyd. } \mathrm{Al 34. Which of the following molecule has bond order 2 ? 35. Identify rare earth element from following. 36. 0.2 molal aqueous solution of KCl freezes at $-0.680^{\circ} \mathrm{C}$. Calculate van't Hoff factor for this solution. 37. 0.1 molal aqueous solution of glucose boils at $100.16^{\circ} \mathrm{C}$. What is boiling point of 0.5 molal aqueous s 38. Identify a polymer obtained from $\beta$-hydroxybutyric acid and $\beta$-hydroxyvaleric acid. 39. A conductivity cell dipped in 0.05 MKCl has resistance 600 ohm. If conductivity is $0.0012 \mathrm{ohm}^{-1} \mathrm{~cm 40. 2 moles of an ideal gas are expanded isothermally and reversibly from 20 L to 40 L at 300 K . Calculate work done. ( $\m 41. Identify the product P of following reaction. $$\mathrm{CH}_3 \mathrm{OH}+\mathrm{CH}_3 \mathrm{MgX} \longrightarrow \ma 42. Calculate number of atoms per unit cell of an element having molar mass $92.0 \mathrm{~g} \mathrm{~mol}^{-1}$ and densit 43. What is the product obtained when phenylethene is treated with $\mathrm{KMnO}_4$ in dilute $\mathrm{H}_2 \mathrm{SO}_4$ 44. What is the pH of $10^{-8} \mathrm{M~HCl}$ solution? 45. What is the oxidation state of iodine in $\mathrm{I}_2 \mathrm{Cl}_6$ ? 46. Chlorine exists in two isotopic forms ${ }^{35} \mathrm{Cl},{ }^{37} \mathrm{Cl}$. If average atomic mass of chlorine is 47. Which element from following has completely filled f-orbital in observed and expected electronic configuration? 48. Which from following monomers is used to obtain polymer represented as 49. What is the conductivity of 0.05 M KCl solution if cell constant is $1.32 \mathrm{~cm}^{-1}$ and resistance is 528 ohm? 50. Which of the following substances conducts electricity?

Mathematics

1. $\int_\limits0^{\frac{\pi}{2}}|\sin x-\cos x| d x$ has the value 2. Negation of the statement "The payment will be made if and only if the work is finished in time." is 3. If $$y = {{\sin x} \over {1 + {{\cos x} \over {1 + {{\sin x} \over {1 + {{\cos x} \over {...}}}}}}}}$$, then $\frac{dy}{ 4. If $\quad \overline{\mathrm{a}}=\hat{\mathrm{i}}-\hat{\mathrm{k}}, \overline{\mathrm{b}}=x \hat{\mathrm{i}}+\hat{\mathrm 5. Let a line intersect the co-ordinate axes in points $A$ and $B$ such that the area of the triangle $O A B$ is 12 sq. uni 6. If for certain $x, 3 \cos x \neq 2 \sin x$, then the general solution of, $\sin ^2 x-\cos 2 x=2-\sin 2 x$, is 7. In a game, 3 coins are tossed. A person is paid ₹ 100$, if he gets all heads or all tails; and he is supposed to pay ₹ 4 8. The curve $x^4-2 x y^2+y^2+3 x-3 y=0$ cuts the X -axis at $(0,0)$ at an angle of 9. The abscissae of the two points A and B are the roots of the equation $x^2+2 a x-b^2=0$ and their ordinates are roots of 10. Water is running in a hemispherical bowl of radius 180 cm at the rate of 108 cubic decimeters per minute. How fast the w 11. $\mathrm{S}_1=\sum_\limits{\mathrm{r}=1}^{\mathrm{n}} \mathrm{r}, \mathrm{S}_2=\sum_\limits{\mathrm{r}=1}^{\mathrm{n}} \ 12. The numerical value of $\tan \left(2 \tan ^{-1}\left(\frac{1}{5}\right)+\frac{\pi}{4}\right)$ 13. Let $\bar{a}, \bar{b}$ and $\bar{c}$ be three vectors having magnitudes 1,1 and 2 respectively. If $\overline{\mathrm{a} 14. Area (in sq.units) lying in the first quadrant and bounded by the circle $x^2+y^2=4$ and the lines $x=0$ and $x=2$ is 15. If $A+B=\left[\begin{array}{cc}1 & \tan \frac{\theta}{2} \\ -\tan \frac{\theta}{2} & 1\end{array}\right]$ where $A$ is s 16. If, $\int \frac{d \theta}{\cos ^2 \theta(\tan 2 \theta+\sec 2 \theta)}=\lambda \tan \theta+2 \log _{\mathrm{e}}|\mathrm{ 17. The domain of definition of the function $y(x)$ is given by the equation $2^x+2^y=2$, is 18. If $\cos x \frac{\mathrm{~d} y}{\mathrm{~d} x}-y \sin x=6 x, 0 19. Equation of the plane, through the points $(-1,2,-2)$ and $(-1,3,2)$ and perpendicular to $y \mathrm{z}$ - plane, is 20. The values of $a$ and $b$, so that the function $$f(x)= \begin{cases}x+\mathrm{a} \sqrt{2} \sin x & , 0 \leq x \leq \fra 21. If $\overline{\mathrm{a}}$ and $\overline{\mathrm{c}}$ are unit vectors inclined at $\frac{\pi}{3}$ with each other and 22. If the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-1}{4}$ and $\frac{x-3}{-1}=\frac{y-\mathrm{k}}{2}=\frac{\mathrm{z}}{1} 23. A point moves along the arc of parabola $y=2 x^2$. Its abscissa increases uniformly at the rate of 2 units $/ \mathrm{se 24. If $\quad \int(2 x+4) \sqrt{x-1} \mathrm{~d} x=\mathrm{a}(x-1)^{\frac{5}{2}}+\mathrm{b}(x-1)^{\frac{3}{2}}+\mathrm{c}$, 25. If the angles $\mathrm{A}, \mathrm{B}$ and C of a triangle ABC are in the ratio $2: 3: 7$ respectively, then the sides a 26. The value of $\left(1+\cos \frac{\pi}{8}\right)\left(1+\cos \frac{3 \pi}{8}\right)\left(1+\cos \frac{5 \pi}{8}\right)\le 27. The value of $\tan ^{-1}\left(\tan \frac{7 \pi}{6}\right)$ is 28. In a Binomial distribution consisting of 5 independent trials, probabilities of exactly 1 and 2 successes are 0.4096 and 29. The function to be maximized is given by $Z=3 x+2 y$. The feasible region for this function is the shaded region given b 30. If the line, $\frac{x-3}{2}=\frac{y+2}{1}=\frac{z+4}{3}$ lies in the plane, $\ell x+m y-z=9$, then $\ell^2+m^2$ is equal 31. $$\int \frac{\sqrt{x}}{x+1} d x=$$ 32. The equation of the normal to the curve $y=x \log x$, which is parallel to the line $2 x-2 y+3=0$, is 33. $$\int \frac{1+\sin (\log x)}{1+\cos (\log x)} d x=$$ 34. If $\mathrm{w}=\frac{-1+i \sqrt{3}}{2}$, where $\mathrm{i}=\sqrt{-1}$, then the value of $\left(3+w+3 w^2\right)^4$ is 35. If $|\overline{\mathrm{a}}|=2,|\overline{\mathrm{~b}}|=3$ and $\overline{\mathrm{a}}, \overline{\mathrm{b}}$ are mutuall 36. If $y$ is a function of $x$ and $\log (x+y)=2 x y$, then the value of $y^{\prime}(0)$ is 37. A random variable X has the following probability distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td 38. If $y=a x^{n+1}+b x^{-n}$, then $x^2 \frac{d^2 y}{d x^2}=$ 39. Let $\bar{A}, \bar{B}, \bar{C}$ be vectors of lengths 3 units, 4 units, 5 units respectively. let $\bar{A}$ be perpendic 40. The approximate value of $x^3-2 x^2+3 x+2$ at $x=2.01$ is 41. The general solution of $\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{x+y+1}{x+y-1}$ is 42. There are three events $\mathrm{A}, \mathrm{B}, \mathrm{C}$, one of which must and only one can happen. The odds are 8: 43. Let $\bar{a}, \bar{b}$ and $\bar{c}$ be three non-zero vectors such that no two of them are collinear and $(\overline{\m 44. If $\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=\pi$ and $x^2+y^2+z^2+k x y z=1$, then k is 45. A radio-active substance has a half-life of h days, then its initial decay rate is given by (where radio-active substanc 46. The inverse of $p \rightarrow(q \rightarrow r)$ is logically equivalent to 47. If the line $\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}$ lies in the plane $x+3 y-\alpha z+\beta=0$, then $(\alpha, \bet 48. Mean and variance of six observations are 6 and 12 respectively. If each observation is multiplied by 3, then new varian 49. Words of length 10 are formed by using the letters A, B, C, D, E, F, G, H, I, J. Let $x$ be number of such words where n 50. $\triangle \mathrm{OAB}$ is formed by the lines $x^2-4 x y+y^2=0$ and the line $A B$. The equation of line $A B$ is $2 x

Physics

1. A particle performing S.H.M. with maximum velocity ' $V$ '. If the amplitude double and periodic time is made, $\left(\f 2. A circular arc of radius r carrying current ' I ' subtends an angle $\frac{\pi}{8}$ at its entre. The radius of a metal 3. The moment of inertia of uniform circular disc is maximum about an axis perpendicular to the disc and passing through po 4. An inductor coil of inductance $L$ is divided into two parts and both parts are connected in parallel. The net inductanc 5. If the momentum of a body of mass ' $m$ ' is increased by $20 \%$ then its kinetic energy increases by 6. Seven capacitors each of capacitance $2 \mu \mathrm{~F}$ are connected in a configuration to obtain an effective capacit 7. An e.m.f. $E=E_0 \cos \omega t$ is applied to the $L-R$ circuit. The inductive reactance is equal to the resistance ' $R 8. The radius and mean density of the planet are four times as that of the earth. The ratio of escape velocity at the earth 9. A black sphere has radius $R$ whose rate of radiation is E at temperature T . If radius is made half and temperature 4 T 10. If the ionisation energy for the hydrogen atom is 13.6 eV , then the energy required to excite it from the ground state 11. A closed pipe containing a liquid showed a pressure $P_1$ by gauge. When the valve was opened, pressure was reduced to $ 12. In a diffraction pattern due to single slit of width ' $a$ ', the first minimum is observed at an angle $30^{\circ}$ whe 13. A ray of light is incident on a medium of refractive index ' $\mu$ ' at an angle of incidence ' $i$ '. On refraction in 14. The pipe open at both ends and pipe closed at one end have same length and both are vibrating in fundamental mode. Air c 15. Two ideal diodes are connected to a battery as shown in the circuit. The current supplied by the battery is 16. In biprism experiment, if $5^{\text {th }}$ bright band with wavelength $\lambda_1$ coincides with $6^{\text {th }}$ dar 17. Ordinary bodies P and Q radiate maximum energy with wavelength difference $3 \mu \mathrm{~m}$. The absolute temperature 18. A lead bullet moving with velocity ' V ' strikes a wall and stops. If $75 \%$ of its energy is converted into heat, then 19. In photoelectric effect, the photocurrent 20. The average force applied on the wall of a closed container depends as $\mathrm{T}^{\mathrm{x}}$ where T is the temperat 21. Four electric charges $+\mathrm{q},+\mathrm{q},-\mathrm{q}$ and -q are placed in order at the corners of a square of sid 22. Electron of mass ' $m$ ' and charge ' $q$ ' is travelling with speed ' $v$ ' along a circular path of radius ' $R$ ' at 23. Two coils have a mutual inductance 0.003 H . The current changes in the first coil according to equation $I=I_0 \sin \om 24. What is the output Y in the following circuit, when all the three inputs A, B, C are first 'zero' and then 'one'? 25. Two sound waves having displacements $x_1=2 \sin (1000 \pi t)$ and $x_2=3 \sin (1006 \pi t)$, when interfere, produce 26. A completely filled water tank of height ' $h$ ' has a hole at the bottom. The total pressure of the bottom is 4 H and a 27. A series resonant circuit consists of inductor ' $L$ ' of negligible resistance and a capacitor ' $C$ ' which produces r 28. Let ' $l_1$ ' be the length of simple pendulum. Its length changes to ' $l_2$ ' to increase the periodic time by $20 \%$ 29. When the listener moves towards stationary source with velocity ' $\mathrm{V}_1$ ', the apparent frequency of emitted no 30. Which of the following graphs between pressure and volume correctly show isochoric process? 31. A ring and a disc roll on horizontal surface without slipping with same linear velocity. If both have same mass and tota 32. In potentiometer experiment, cells of e.m.f. $E_1$ and $E_2$ are connected in series $\left(E_1>E_2\right)$ the balancin 33. A solid metallic sphere of radius ' $R$ ' having moment of inertia '$I$' about diameter is melted and recast into a soli 34. In young's double slit experiment, the $\mathrm{n}^{\text {th }}$ maximum of wavelength $\lambda_1$ is at a distance of 35. For a particle in uniform circular motion 36. Using Bohr's model, the orbital period of electron in hydrogen atom in $\mathrm{n}^{\text {th }}$ orbit is ( $\mathrm{m} 37. Initial pressure and volume of a gas are ' P ' and ' $V$ ' respectively. First its volume is expanded to ' 4 V ' by isot 38. In the following graph of flux density versus magnetizing force, coercivity and retentivity are respectively represented 39. Two identical capacitors have the same capacitance ' $C$ '. One of them is charged to potential $\mathrm{V}_1$ and other 40. A small planet is revolving around a very massive star in a circular orbit of radius ' $R$ ' with a period of revolution 41. A metal sphere of radius R, density $\rho_1$ moves with terminal velocity $\mathrm{V}_1$ through a liquid of density $\s 42. In the circuit, current flowing through the circuit is 43. Two point charges +10 q and -4 q are located at $\mathrm{x}=0$ and $\mathrm{x}=\mathrm{L}$ respectively. What is the loc 44. If the potential difference used to accelerate electrons is increased four times, by what factor does the de-Broglie wav 45. When the string is stretched between two rigid supports, under certain tension and vibrated 46. Simple microscope is used to see the object first in blue light and then a red light. Due to the change from blue to red 47. The inductive reactance of a coil is ' $R$ ' $\Omega$. If inductance of a coil is tripled and frequency of a.c supply is 48. A musical instrument X produces sound waves of frequency n and amplitude A. Another musical instrument $Y$ produces soun 49. In the block diagram of simple rectifier circuit, from a variable a.c. voltage, constant d.c. voltage is obtained. The c 50. The current in LR circuit if reduced to half What will be the energy stored in it?

MHT CET 2024 10th May Morning Shift

MCQ (Single Correct Answer)

-0

If $A+B=\left[\begin{array}{cc}1 & \tan \frac{\theta}{2} \\ -\tan \frac{\theta}{2} & 1\end{array}\right]$ where $A$ is symmetric and $B$ is skew-symmetric matrix, then the matrix $\left(A^{-1} B+A B^{-1}\right)$ at $\theta=\frac{\pi}{6}$ is given by

$\left[\begin{array}{cc}1 & 2 \sqrt{3} \\ 2 \sqrt{3} & 1\end{array}\right]$

$\left[\begin{array}{cc}-1 & -2 \sqrt{3} \\ 2 \sqrt{3} & 1\end{array}\right]$

$\left[\begin{array}{cc}0 & 2 \sqrt{3} \\ 2 \sqrt{3} & 0\end{array}\right]$

$\left[\begin{array}{cc}0 & -2 \sqrt{3} \\ 2 \sqrt{3} & 0\end{array}\right]$

MHT CET 2024 10th May Morning Shift

MCQ (Single Correct Answer)

-0

If, $\int \frac{d \theta}{\cos ^2 \theta(\tan 2 \theta+\sec 2 \theta)}=\lambda \tan \theta+2 \log _{\mathrm{e}}|\mathrm{f}(\theta)|+\mathrm{c}$ (where c is a constant of integration), then the ordered pair $(\lambda,|f(\theta)|)$ is equal to

$(1,|1+\tan \theta|)$

$(1,1-1-\tan \theta \mid)$

$(-1,|1+\tan \theta|)$

$(-1,|1-\tan \theta|)$

MHT CET 2024 10th May Morning Shift

MCQ (Single Correct Answer)

-0

The domain of definition of the function $y(x)$ is given by the equation $2^x+2^y=2$, is

$0< x \leq 1$

$0 \leq x \leq 1$

$-\infty< x \leq 0$

$-\infty< x<1$

MHT CET 2024 10th May Morning Shift

MCQ (Single Correct Answer)

-0

If $\cos x \frac{\mathrm{~d} y}{\mathrm{~d} x}-y \sin x=6 x, 0

$y=\cos x+3 x^2+\mathrm{c}$, where c is a constant of integration.

$y+\cos x=3 x^2+\mathrm{c}$, where c is a constant of integration.

$y=3 x^2 \cos x+\cos x$, where c is a constant of integration.

$y \cdot \cos x=3 x^2+\mathrm{c}$, where c is a constant of integration.

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