MHT CET 2024 11th May Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Identify the major product ( $99 \%$ ) formed when $\left(\mathrm{CH}_3\right)_3 \mathrm{CH}$ is treated with $\mathrm{B 2. Which among the following pair of properties are intensive? 3. Which of the following equations gives angular momentum of an electron in a stationary orbit? 4. Which element from following has lowest ionization enthalpy $\left(\mathrm{IE}_1\right)$ ? 5. Which alkyl halide has highest bond enthalpy of $\mathrm{C}-\mathrm{X}$ bond? 6. Calculate van't Hoff factor (i) of 0.2 m aqueous solution of an electrolyte if it freezes at $-0.660 \mathrm{~K} .\left( 7. Identify reagent used for preparation of benzophenone from benzonitrile? 8. Which of the following is an elementary reaction? 9. Which compound from following contains N atom in its ring? 10. 2 moles of an ideal gas expands isothermally from $5 \mathrm{dm}^3$ to $10 \mathrm{dm}^3$ at a constant external pressur 11. What is the wave number of lowest transition associated with Lyman series? 12. Vapour pressure of a pure solvent is 550 mm of Hg . By addition of a non volatile solute it decreases to 510 mm of Hg . 13. Identify the product obtained when excess of benzoyl chloride is treated with dimethyl cadmium. 14. Rate constant of a reaction, $$ 2 \mathrm{NO}_2 \mathrm{Cl}_{2(\mathrm{~g})} \longrightarrow 2 \mathrm{NO}_{2(\mathrm{~ 15. Which from following compounds is obtained when glucose is heated with HI for longer time? 16. In Haber's process of production of ammonia, $\mathrm{K}_2 \mathrm{O}$ is used as 17. An ideal gas expands against constant external pressure of 2 bar from 5 lit to 8 lit and absorbs 10 kJ of heat. What is 18. Which of the following compounds follows octet rule? 19. Identify the type of hybridization present in $\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$. 20. Identify the false statement among the following. 21. Which from the following statement is NOT correct regarding Mendius reduction? 22. Initial concentration of reactant in a first order reaction is $0.08 \mathrm{~mol} \mathrm{~dm}^{-3}$ What concentration 23. Which from following amines has highest $\mathrm{pK}_{\mathrm{b}}$ value? 24. What is oxidation number of S in $\mathrm{SO}_3^{2-}$ ? 25. When fused NaCl undergoes electrolysis the product formed at cathode is 26. Which element from following exhibits highest number of various different possible oxidation states? 27. Which among the following has lowest boiling point? 28. A buffer solution is prepared by mixing 0.01 M HCN and 0.02 MNaCN . If $\mathrm{K}_{\mathrm{a}}$ for HCN is $6.6 \times 29. Which reagent from following is used for preparation of aliphatic aldehyde from nitriles? 30. n-type of semiconductor is formed when 31. Which from following polymer contains este linkage? 32. Which of the following element is used in photoelectric cell? 33. The resistance of conductivity cell filled with 0.1 M KCl solution is 100 ohm and conductivity is $1.70 \times 10^{-4} \ 34. What type of hybridisation is involved in central atom of hydrides of group 16 elements? 35. Which from following compounds is used to prepare a refrigerant R-22? 36. A monobasic acid is $5 \%$ dissociated in its 0.02 M solution. Calculate the dissociation constant of acid. 37. Identify product obtained in following reaction. $$ \mathrm{C}_6 \mathrm{H}_5 \mathrm{OH} \xrightarrow{\mathrm{CrO}_3} 38. Metallic silver has fcc structure. If radius of Ag atom is 144 pm . What is the edge length of unit cell? 39. Which from following polymers needs dihydric alcohol and aromatic dicarboxylic acid for its synthesis? 40. Identify fibrous protein from following. 41. Which of the following has dipole-induced dipole interaction as inter molecular force? 42. The conductivity of 0.02 M KCl solution is 0.00250 ohm $^{-1} \mathrm{~cm}^{-1}$. What is its molar conductivity? 43. Which of the following pair of compounds cannot demonstrate law of multiple proportion? 44. Which among the following P-block elements forms colourless and odourless hydride? 45. What is the number of unpaired electrons present in $\left[\mathrm{CoF}_6\right]^{3-} ?$ 46. Which from following is called as Lucas reagent? 47. Which among the following salts turns red litmus blue in its aqueous solution? 48. Which reagent from following is used in Reimer-Tiemann reaction? 49. What is the number of octahedral voids present in 0.2 mol of a compound forming hcp structure? 50. What is the percentage atom economy when formula weight of product obtained is 70 u and the sum of formula weight of rea

Mathematics

1. $$\int \frac{x \mathrm{~d} x}{(x-1)^2(x+2)}=$$ 2. Let $Z$ be a complex number such that $|Z|+Z=2+i$ (where $i=\sqrt{-1})$, then $|Z|$ is equal to 3. _________ numbers greater than a million can be formed with the digits 2, 3, 0, 3, 4, 2, 3. 4. For the following shaded region, the linear constraints are 5. $$\lim _\limits{x \rightarrow 2}\left(\frac{5^x+5^{3-x}-30}{5^{3-x}-5^{\frac{x}{2}}}\right)=$$ 6. $$\begin{aligned} & \text { If } \\ & \int(7 x-2) \sqrt{3 x+2} \mathrm{~d} x=\mathrm{A}(3 x+2)^{\frac{5}{2}}+\mathrm{B}( 7. If $y=\sin ^{-1}\left(\frac{\log x^2}{1+(\log x)^2}\right)$, then $\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)_{\mat 8. If $f(x)=\left\{\begin{array}{cc}\frac{a}{2}(x-|x|) & , \\ 0, & \text { for } x0\end{array}\right.$ is continuous at $x= 9. The p.m.f. of a random variable X is given by $$\begin{aligned} \mathrm{P}[\mathrm{X}=x] & =\frac{\binom{5}{x}}{2^5}, \t 10. If $\mathrm{f}(x)=(1+x)\left(1+x^2\right)\left(1+x^4\right)\left(1+x^8\right)$, then $f^{\prime}(1)=$ 11. $$\int_\limits{0.2}^{3.5}[x] \mathrm{d} x=$$ (where $[x]=$ greatest integer not greater than $x$ ) 12. Let $\mathrm{p}, \mathrm{q}$ and r be the statements $\mathrm{p}: \mathrm{X}$ is an equilateral triangle $\mathrm{q}: \m 13. The bacteria increase at the rate proportional to the number of bacteria present. If the original number N doubles in 8 14. If $\mathrm{f}(x)=x^3-6 x^2+9 x+3$ is monotonically decreasing function, then $x$ lies in 15. If $[x]^2-5[x]+6=0$, where $[x]$ denotes the greatest integer function, then 16. The perpendicular distance of the origin from the plane $2 x+y-2 z-18=0$ is 17. Let p : A man is judge. $\mathrm{q}: \mathrm{He}$ is honest. The inverse of $p \rightarrow q$ is 18. If equation of normal to the curve $x=\sqrt{t}$, $y=\mathrm{t}-\frac{1}{\sqrt{\mathrm{t}}}$ at $\mathrm{t}=4$ is 19. If three fair coins are tossed, then variance of number of heads obtained, is 20. The plane $2 x+3 y+4 z=1$ meets $X$-axis in $A$, Y -axis in B and Z -axis in C . Then the centroid of $\triangle A B C$ 21. If $x^2+y^2=\mathrm{t}+\frac{1}{\mathrm{t}}, x^4+y^4=\mathrm{t}^2+\frac{1}{\mathrm{t}^2}$, then $\frac{\mathrm{d} y}{\ma 22. The general solution of $\frac{\mathrm{d} y}{\mathrm{~d} x}+\sin \left(\frac{x+y}{2}\right)=\sin \left(\frac{x-y}{2}\rig 23. If $A$ and $B$ are two independent events such that $\mathrm{P}\left(\mathrm{A}^{\prime}\right)=0.75, \mathrm{P}(\mathrm 24. If the lines $\frac{x+1}{-10}=\frac{y+k}{-1}=\frac{z-4}{1} \quad$ and $\frac{x+10}{-1}=\frac{y+1}{-3}=\frac{z-1}{4}$ int 25. The approximate value of $(3.978)^{\frac{3}{2}}$ is 26. The value of $\tan ^{-1}\left\{\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right\}+\frac{1}{2} \cos ^{-1} x$ is 27. Let $\overline{\mathrm{a}}, \overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ be three non-zero vectors such that no tw 28. In an experiment with 15 observations for $x$, the following results were available $\sum x^2=2830, \sum x=170$. One obs 29. The area of the region lying in the first quadrant by $y=4 x^2, x=0, y=2, y=4$ is 30. The equation of the line passing through the point $(3,1,2)$ and perpendicular to the lines $\frac{x-1}{1}=\frac{y-2}{2} 31. Let $A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right]$ and $B=\left[\begin{array}{l}4 \ 32. If $\bar{x}=\frac{\bar{b} \times \bar{c}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}, \bar{y}= 33. If in a triangle $A B C$, with usual notations, the angles are in A.P. and $b: c=\sqrt{3}: \sqrt{2}$, then angle $\mathr 34. The rate of change of the volume of a sphere with respect to its surface area, when its radius is 2 cm , is 35. If angle $\theta$ in $[0,2 \pi]$ satisfies both the equations $\cot \theta=\sqrt{3}$ and $\sqrt{3} \sec \theta+2=0$, the 36. The area of the triangle with vertices $(1,2,0)$, $(1,0,2)$ and $(0,3,1)$ is 37. The particular solution of the differential equation, $x y \frac{\mathrm{~d} y}{\mathrm{~d} x}=x^2+2 y^2$ when $y(1)=0$ 38. The equation of the tangent to the circle, given by $x=5 \cos \theta, y=5 \sin \theta$ at the point $\theta=\frac{\pi}{3 39. The joint equation of two lines through the origin, each making an angle with measure of $30^{\circ}$ with the positive 40. With usual notations, if the lengths of the sides of a triangle are $7 \mathrm{~cm}, 4 \sqrt{3} \mathrm{~cm}$ and $\sqrt 41. If the volume of tetrahedron whose vertices are $A \equiv(1,-6,10), B \equiv(-1,-3,7), C \equiv(5,-1, k)$ and $D \equiv( 42. If the slope of one of the lines given by $\mathrm{K} x^2+6 x y+y^2=0$ is three times the order, then the value of $K$ i 43. $$ \cos ^3\left(\frac{\pi}{8}\right) \cos \left(\frac{3 \pi}{8}\right)+\sin ^3\left(\frac{\pi}{8}\right) \sin \left(\fra 44. If $\bar{a}$ and $\bar{b}$ are two unit vectors such that $5 \bar{a}+4 \bar{b}$ and $\bar{a}-2 \bar{b}$ are perpendicula 45. The value of $\int \frac{\cos ^3 x}{\sin ^2 x+\sin x} \mathrm{~d} x$ is 46. Let $\mathrm{P} \equiv(-5,0), \mathrm{Q} \equiv(0,0)$ and $\mathrm{R} \equiv(2,2 \sqrt{3})$ be three points. Then the eq 47. $$\cos \left[\sin ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)\right]=$$ 48. If $x \in[-1,1]$, then the value of $\int \mathrm{e}^{\sin ^{-1} x}\left(\frac{x+\sqrt{1-x^2}}{\sqrt{1-x^2}}\right) \mat 49. The probability that a person who undergoes a bypass surgery will recover is 0.6 . the probability that of the six patie 50. The distance ' $s$ ' in meters covered by a body in $t$ seconds is given by $s=3 t^2-8 t+5$. The body will stop after

Physics

1. For a particle moving in vertical circle, the total energy at different positions along the path [The motion is under gr 2. When the number of turns in a coil is doubled without any change in the length of the coil, its self-inductance 3. A small particle carrying a negative charge of $1.6 \times 10^{-19} \mathrm{C}$ is suspended in equilibrium between two 4. Two spheres $S_1$ and $S_2$ have same radii but temperatures $T_1$ and $T_2$ respectively. Their emissive power is same 5. The acceleration due to gravity at the surface of the planet is same as that at the surface of the earth, but the densit 6. A big water drop is formed by the combination of ' $n$ ' small water droplets of equal radii. The ratio of the surface e 7. An inductance of $\frac{300}{\pi} \mathrm{mH}$, a capacitance of $\frac{1}{\pi} \mathrm{mF}$ and a resistance of $20 \Om 8. A simple pendulum of length ' $L$ ' has mass ' $M$ ' and it oscillates freely with amplitude ' $A$ '. At extreme positio 9. In Fraunhofer diffraction pattern, slitwidth is 0.5 mm and screen is at 2 m away from the lens. If wavelength of light u 10. A bullet is fired on a target with velocity V . Its velocity decreases from V to $\mathrm{V} / 2$. When it penetrates 30 11. Following combination of gates is equivalent to 12. A boat is moving due east in a region where the earth's magnetic field is $3.6 \times 10^{-5} \mathrm{~N} / \mathrm{Am}$ 13. In the following electrical network, the value of I is 14. An inclined plane makes an angle $30^{\circ}$ with horizontal. A solid sphere rolls down from the top of the inclined pl 15. An ink mark is made on a piece of paper. A glass slab of thickness ' $t$ ' is placed on it. The ink mark appears to be r 16. The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (a) second to first en 17. The magnetic flux near the axis and inside the air core solenoid of length 80 cm carrying current ' I ' is $1.57 \times 18. Two identical light waves having phase difference $\phi$ propagate in same direction. When they superpose, the intensity 19. Two gases A and B having same initial state ( $\mathrm{P}, \mathrm{V}, \mathrm{n}, \mathrm{T}$ ). Now gas A is compresse 20. If ' $\mathrm{n}_{\mathrm{c}}$ ' and ' $\mathrm{n}_{\mathrm{h}}$ ' are the number of electrons and number of holes respe 21. The frequency of two tuning forks A and B are respectively $1.4 \%$ more and $2.6 \%$ less than that of the tuning fork 22. With an alternating voltage source frequency ' f ', inductor ' $L$ ', capacitor ' $C$ ' and resistance ' $R$ ' are conne 23. When three capacitors of equal capacities are connected in parallel and one of the same capacity, capacitor is connected 24. Two vessels separately contain two ideal gases A and B at the same temperature, pressure of A being twice that of B . Un 25. The depth 'd' at which the value of acceleration due to gravity becomes $\frac{1}{n-1}$ times the value at the earth's s 26. If the frequency of incident radiation $(\nu)$ is increased, keeping other factors constant, the stopping potential ( $\ 27. A resonance tube closed at one end is of height 1.5 m . A tuning fork of frequency 340 Hz is vibrating above the tube. W 28. Water rises in a capillary tube of radius ' $r$ ' up to height ' $h$ '. The mass of water in capillary is ' $m$ '. The m 29. Charges $3 \mathrm{Q}, \mathrm{q}$ and Q are placed along x -axis at positions $\mathrm{x}=0, \mathrm{x}=\frac{1}{3}$ an 30. A bar magnet has length 4 cm , cross-sectional area $2 \mathrm{~cm}^2$ and magnetic moment $6 \mathrm{Am}^2$. The intens 31. At the poles of earth, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator of earth 32. A particle performing S.H.M. starts from equilibrium position and its time period is 12 second. After 2 seconds its velo 33. For a light ray to undergo total internal reflection ( $\mathrm{i}=$ angle of incidence, $\mathrm{i}_{\mathrm{c}}=$ crit 34. With gradual increase in frequency of an a.c. supply, the impedance of an LCR series circuit 35. Two parallel plate air capacitors of same capacity ' C ' are connected in series to a battery of emf ' $E$ '. Then one o 36. Assuming that the earth is revolving around the sun in circular orbit of radius R , the angular momentum is directly pro 37. With what velocity an observer should move relative to a stationary source so that a sound of triple the frequency of so 38. Two long straight parallel wires are separated by a distance '2d'. Each wire carries a current 'I' in the same direction 39. If 'T' is the half life of a radioactive substance then its instantaneous rate of change of activity is proportional to 40. An insulated container contains a diatomic gas of molar mass ' m '. The container is moving with velocity ' $V$ ', if it 41. The current drawn from the battery in the given network is (Internal resistance of the battery is negligible) 42. Rails of material of steel are laid with gaps to allow for thermal expansion. Each track is 10 m long, when laid at temp 43. If the potential difference used to accelerate electrons is doubled. By what factor does the deBroglie wavelength $(\lam 44. In an adiabatic process for an ideal gas, the relation between the universal gas constant ' $R$ ' and specific heat at c 45. A p-n junction diode cannot be used 46. A particle performs linear S.H.M. at a particular instant, velocity of the particle is ' $u$ ' and acceleration is ' $\m 47. For the velocity-time graph shown in the figure below, the distance covered by the body in last two second of its motion 48. The coefficient of mutual induction is 2 H and induced e.m.f. across secondary is 2 kV Current in the primary is reduced 49. The work done in blowing a soap bubble of radius $R$ is $W_1$ at room temperature. Now the soap solution is heated. From 50. When the same monochromatic ray of light travels through glass slab and through water, the number of waves in glass slab

MHT CET 2024 11th May Morning Shift

MCQ (Single Correct Answer)

-0

If the slope of one of the lines given by $\mathrm{K} x^2+6 x y+y^2=0$ is three times the order, then the value of $K$ is

$\frac{9}{4}$

$\frac{4}{9}$

$\frac{27}{4}$

$\frac{4}{27}$

MHT CET 2024 11th May Morning Shift

MCQ (Single Correct Answer)

-0

$$ \cos ^3\left(\frac{\pi}{8}\right) \cos \left(\frac{3 \pi}{8}\right)+\sin ^3\left(\frac{\pi}{8}\right) \sin \left(\frac{3 \pi}{8}\right)=$$

$\frac{1}{2 \sqrt{2}}$

$\frac{1}{\sqrt{2}}$

$\frac{1}{2}$

$\frac{\sqrt{3}}{2}$

MHT CET 2024 11th May Morning Shift

MCQ (Single Correct Answer)

-0

If $\bar{a}$ and $\bar{b}$ are two unit vectors such that $5 \bar{a}+4 \bar{b}$ and $\bar{a}-2 \bar{b}$ are perpendicular to each other, then the between $\bar{a}$ and $\bar{b}$ is

$\frac{2 \pi}{3}$

$\cos ^{-1}\left(\frac{2}{3}\right)$

$\frac{\pi}{3}$

$\cos ^{-1}\left(\frac{1}{3}\right)$

MHT CET 2024 11th May Morning Shift

MCQ (Single Correct Answer)

-0

The value of $\int \frac{\cos ^3 x}{\sin ^2 x+\sin x} \mathrm{~d} x$ is

$\log (\sin x)-\sin x+\mathrm{c}$, where c is a constant of integration.

$\log (\sin x)-\cos x+\mathrm{c}$, where c is a constant of integration.

$\log (\sin x)+\sin x+\mathrm{c}$, where c is a constant of integration.

$\log (\cos x)-\cos x+\mathrm{c}$, where c is a constant of integration.

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