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

Chemistry

1. If instantaneous rate of reaction is given as $$ -\frac{1}{\mathrm{a}} \frac{\mathrm{~d}[\mathrm{~A}]}{\mathrm{dt}}=-\f 2. Which among the following is a correct decreasing order of thermodynamic stability of the complexes? 3. Identify the process from following such that volume of system remains constant. 4. Identify the instrument used to find crystal structure from following : 5. In a solution, mole fraction of solute is 0.2 , when lowering in vapour pressure is 10 mm Hg . To get lowering of vapour 6. Which among the following is an example of one dimensional nanostructure? 7. Which among the following is an example of emulsion? 8. Which of the following solutions will not show flow of solvent in either direction when separated by semipermeable membr 9. Identify the correct stability order of following alkenes. I) $\left(\mathrm{CH}_3\right)_2 \mathrm{C}=\mathrm{C}\left(\ 10. Which of the following element in +1 oxidation state has largest ionic radius? 11. Identify the product in following reaction. Pent -3-enenitrile $\xrightarrow[\mathrm{H}_3 \mathrm{O}^{+}]{\mathrm{AlH}(\ 12. Which of the following molecules has zero dipole moment? 13. What is the concentration of an electrolyte solution to have molar conductivity of $101 \Omega^{-1} \mathrm{~cm}^2 \math 14. What is IUPAC name of following compound? 15. Which element from following is the last element of 5d-transition series? 16. The solubility of $\mathrm{CaCO}_3$ is $7 \times 10^{-5} \mathrm{~mol} \mathrm{dm}^{-3}$ at $25^{\circ} \mathrm{C}$. Wha 17. Which of the following compounds is NOT obtained at any stage of Gabriel phthalimide synthesis? 18. The solution containing $18 \mathrm{~g} \mathrm{dm}^{-3}$ glucose (molar mass 180) in water and another containing $6 \m 19. Which among following polymers is used to manufacture water pipes? 20. Identify the correct pair of molecule and the heteroatom present in it respectively from following: 21. What type of unit cell from following is common to all seven types of crystal systems? 22. If $P_1$ partial pressure of a gas and $x_1$ is its mole fraction in a mixture, then correct relation between $P_1$ and 23. Which among the following is benzylic halide? 24. Which from following statements is NOT correct regarding Bohr model? 25. Cell constant of a conductivity cell is $0.9 \mathrm{~cm}^{-1}$ and resistance shown by $\mathrm{AgNO}_3$ solution is 65 26. Which among the following minerals contains radioactive element in it? 27. The common name of Benzene-1, 2, 3-triol is 28. Rate law for a reaction is $r=k[A]^2[B]$. If rate constant is $6.25 \mathrm{~mol}^{-2} \mathrm{dm}^6 \mathrm{~s}^{-1}$, 29. Which element from following is NOT considered as transition element on the basis of electronic configuration? 30. Two moles of an ideal gas are compressed isothermally and reversibly from 40 L to 20 L at 300 K . What is the work done? 31. Identify the product ' $A$ ' obtained in following reaction. N -alkyl phthalimide $\xrightarrow{\mathrm{N}_2 \mathrm{OH} 32. Which among the following is the conjugate base of $\mathrm{HClO}_4$ ? 33. Which from following polymers contain - CO - NH - linkage in it? 34. Identify the product of ozonolysis of but-2-ene from following: 35. What is atomic radius of an element if it crystallises in BCC structure with edge length of unit cell 287 pm? 36. Identify the product ' B ' in the following reaction sequence. $$\mathrm{C}_2 \mathrm{H}_5-\mathrm{Br} \xrightarrow[\tex 37. Identify the correct statement for following reaction. $$3 \mathrm{Mg}+\mathrm{N}_2 \longrightarrow \mathrm{Mg}_3 \mathr 38. Which of the following cannot be used as standard solution for determination of cell constant of conductivity cell? 39. Which from following reagents is used in the conversion of phenol to picric acid? 40. Which element from following has largest atomic size as compared to other three? 41. Calculate the enthalpy change when 12 g carbon react with sufficient hydrogen to form methane. If enthalpy of formation 42. What type of ligand is the oxalate ion? 43. What is pH of a centimolar solution of $\mathrm{H}_2 \mathrm{SO}_4$ ? 44. What is the time needed to reduce the initial concentration of reactant to $10 \%$ in a first order reaction if its half 45. Which from following proteins acts as an enzyme to break protein to $\alpha$-amino acid? 46. Identify the orbital having highest energy from following: 47. A metal crystallises in bcc structure with edge length $4 \times 10^{-8}$. If density of unit cell is $10 \mathrm{~g} \m 48. Identify product 'B' in following reaction 49. How many molecules of carbon dioxide are formed when 0.6 g carbon is burnt in air? 50. Identify product 'B' in the following reaction. Sodium phenoxide $\xrightarrow[6 \mathrm{~atm}]{\mathrm{CO}_2, 398 \math

Mathematics

1. The number of arrangements, of the letters of the word MANAMA in which two M's do not appear adjacent, is 2. A random variable $X$ has the following probability distribution .tg {border-collapse:collapse;border-spacing:0;} .tg 3. $$\int \frac{x+1}{x\left(1+x \mathrm{e}^x\right)^2} \mathrm{dx}=$$ 4. An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half of the quantity of ice me 5. Contrapositive of the statement 'If two numbers are not equal, then their squares are not equal', is 6. If $\mathrm{f}:[1, \infty) \rightarrow[2, \infty)$ is given by $\mathrm{f}(x)=x+\frac{1}{x}$ then $\mathrm{f}^{-1}(x)$ e 7. The angles of a triangle are in the ratio $5: 1: 6$, then ratio of the smallest side to the greatest side is 8. Let $y=y(x)$ be the solution of the differential equation $x \frac{\mathrm{~d} y}{\mathrm{~d} x}+y=x \log x,(x>1)$ If $2 9. The area (in sq. units) of the region bounded by $y-x=2$ and $x^2=y$ is equal to 10. Let $\bar{a}, \bar{b}$ and $\bar{c}$ be three unit vectors such that $\overline{\mathrm{a}} \times(\overline{\mathrm{b}} 11. $\lim _\limits{x \rightarrow 0} \frac{x \tan 2 x-2 x \tan x}{(1-\cos 2 x)^2}$ is 12. If $y=\mathrm{a} \log x+\mathrm{b} x^2+x$ has its extreme values at $x=-1$ and $x=2$, then the value of $\left(\frac{a}{ 13. If $\hat{a}=\frac{1}{\sqrt{10}}(3 \hat{i}+\hat{k})$ and $\hat{b}=\frac{1}{7}(2 \hat{i}+3 \hat{j}-6 \hat{k})$, then the v 14. If $\mathrm{f}(x)=\log _{x^2}(\log x)$, then at $x=\mathrm{e}, \mathrm{f}^{\prime}(x)$ has the value 15. If $\mathrm{I}=\int_0^{\frac{\pi}{4}} \log (1+\tan x) \mathrm{d} x$, then value of $\mathrm{I}$ is 16. The parametric equations of the circle $x^2+y^2-\mathrm{a} x-b y=0$ are 17. The curve $y=a x^3+b x^2+c x+5$ touches the X - axis at $(-2,0)$ and cuts the Y -axis at a point Q where its gradient is 18. A variable plane passes through the fixed point $(3,2,1)$ and meets $X, Y$ and $Z$ axes at points $A$, B and C respectiv 19. The value of $\sin \left(\cos ^{-1}\left(-\frac{1}{3}\right)-\sin ^{-1}\left(\frac{1}{3}\right)\right)$ is 20. Let $\overline{\mathrm{a}}, \overline{\mathrm{b}}$, and $\overline{\mathrm{c}}$ be three non-zero vectors such that no t 21. Let $\mathrm{A}, \mathrm{B}$ and C be three events, which are pairwise independent and $\bar{E}$ denote the complement o 22. A production unit makes special type of metal chips by combining copper and brass. The standard weight of the chip must 23. The distance of the point $(1,-5,9)$ from the plane $x-y+z=5$ measured along the line $x=y=\mathrm{z}$ is __________ uni 24. If $\mathrm{f}(x)=1+x ; \mathrm{g}(x)=\log x$, then $\int \mathrm{g}(\mathrm{f}(x)) \mathrm{d} x$ is equal to 25. The general solution of $\sin x+\cos x=1$ is 26. In a $\triangle \mathrm{PQR}, \mathrm{m} \angle \mathrm{R}=\frac{\pi}{2}$. If $\tan \left(\frac{\mathrm{P}}{2}\right)$ a 27. If for some $\alpha \in \mathbb{R}$, the lines $\mathrm{L}_1: \frac{x+1}{2}=\frac{y-2}{-1}=\frac{z-1}{1}$ and $\mathrm{L 28. $$\int \cos (\log x) \mathrm{d} x=$$ 29. If $\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$ are non-coplanar unit vectors such that $\overl 30. The joint equation of pair of lines through the origin, each of which makes an angle of $30^{\circ}$ with Y -axis, is 31. Let $f(x)=\left\{\begin{array}{cc}\frac{1-\cos 4 x}{x^2} & , x0\end{array}\right.$ If $\mathrm{f}(x)$ is continuous at $ 32. The number of solutions of $\tan x+\sec x=2 \cos x$ in $[0,2 \pi]$ is 33. The maximum value of the function $\mathrm{f}(\mathrm{x})=2 \mathrm{x}^3-15 x^2+36 x-48$ on the set $A=\left\{x / x^2+20 34. The number of unit vectors perpendicular to $\overline{\mathrm{a}}=(1,1,0)$ and $\overline{\mathrm{b}}=(0,1,1)$ is 35. If the normal to the curve $y=\mathrm{f}(x)$ at the point $(3,4)$ makes an angle of $\left(\frac{3 \pi}{4}\right)$ with 36. $$ \int \frac{2 x+5}{\sqrt{7-6 x-x^2}} d x=A \sqrt{7-6 x-x^2}+B \sin ^{-1}\left(\frac{x+3}{4}\right)+\mathrm{c} $$ (whe 37. A straight line L through the point $(3,-2)$ is inclined at an angle of $60^{\circ}$ to the line $\sqrt{3} x+y=1$. If L 38. If $y(x)$ is the solution of the differential equation $(x+2) \frac{\mathrm{d} y}{\mathrm{~d} x}=x^2+4 x-9, x \neq-2$ an 39. If the sides of a triangle $a, b, c$ are in A.P., then with usual notations, a $\cos ^2 \frac{\mathrm{C}}{2}+\mathrm{c} 40. A random variable x takes the values $0,1,2$, $3, \ldots$ with probability $\mathrm{P}(\mathrm{X}=x)=\mathrm{k}(x+1)\lef 41. If $A\left[\begin{array}{ll}2 & 1 \\ 7 & 4\end{array}\right]$ then $\left(A^2-5 A\right)^{-1}$ is 42. The following statement $(\mathrm{p} \rightarrow \mathrm{q}) \rightarrow((\sim \mathrm{p} \rightarrow \mathrm{q}) \right 43. Let $\omega=-\frac{1}{2}+\mathrm{i} \frac{\sqrt{3}}{2}, \mathrm{i}=\sqrt{-1}$, then the value of $\left|\begin{array}{cc 44. Let f be twice differentiable function such that $\mathrm{f}^{\prime \prime}(x)=-\mathrm{f}(x), \mathrm{f}^{\prime}(x)=\ 45. Let $P(3,2,6)$ 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}+\hat 46. Let $\mathrm{f}(x)=\frac{x}{\sqrt{\mathrm{a}^2+x^2}}-\frac{\mathrm{d}-x}{\sqrt{\mathrm{~b}^2+(\mathrm{d}-x)^2}}, x \in \ 47. If the vectors $\overline{\mathrm{a}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{b}}=2 \hat 48. If $y=(\sin x)^{\tan x}$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to 49. If for some $x \in \mathbb{R}^{+} \cup\{0\}$, the frequency distribution of the marks obtained by 20 students in a test 50. One hundred identical coins, each with probability p , of showing up heads are tossed once. If $0

Physics

1. An electric dipole will have minimum potential energy when it subtends an angle $$\left[\begin{array}{l} \cos 0^{\circ}= 2. A particle is performing S.H.M. about its mean position with an amplitude ' $a$ ' and periodic time ' $T$ '. The speed o 3. In case of photoelectric effect, the graph of measured stopping potential $\left(\mathrm{V}_0\right)$ against frequency 4. Critical angle of light passing from glass to air is minimum for wavelength of 5. What is the pressure of hydrogen in a cylinder of volume 10 litre if its total energy of translation is $7.5 \times 10^3 6. A particle ' $A$ ' has charge ' $+q$ ' and a particle ' $B$ ' has charge ' $+4 q$ '. Each has same mass ' $m$ '. When t 7. When 100 V d.c. is applied across a solenoid, a current of 1 A flows in it. When 100 a.c. is applied across it, the curr 8. When n-p-n junction transistor is used as an amplifier in common emitter mode, 9. An infinitely long straight conductor carrying current 'I' is bent in a shape as shown in figure. The radius of the circ 10. A piece of wood has length, breadth and height, ' $a$ ', ' $b$ ' and ' $c$ ' respectively. Its relative density, is ' $d 11. Assuming that junction diode is ideal, the current in arrangement shown in figure 12. Four thin metal rods each of mass ' $M$ ' and length ' $L$ ', are welded end to end to form a square. The moment of iner 13. Considering interference between two sources of intensities ' I ' and ' 4 I ', the intensity at a point where the phase 14. If number of turns per unit length in a solenoid is tripled, the self inductance of solenoid will 15. $A$ sphere ' $A$ ' of radius ' $R$ ' has a charge ' $Q$ ' on it. The field at point B outside the sphere is ' $E$ '. Now 16. Two rain drops of same radius are falling through air each with a steady speed of $5 \mathrm{~cm} / \mathrm{s}$. If the 17. Which of the following statements is NOT true? 18. In a hydrogen atom in its ground state, the first Bohr orbit has radius $r_1$. The electron's orbital speed becomes one- 19. ' $N$ ' molecules of gas $A$, each having mass ' $m$ ' and ' 2 N ' molecules of gas B , each of mass ' 2 m ' are contain 20. For a satellite moving in an orbit around the earth at height ' $h$ ' the ratio of kinetic energy to potential energy is 21. The number of turns in the primary of a transformer are 1000 and in secondary 3000. If 80 V a.c. is applied to the prima 22. A current carrying circular loop of radius ' $R$ ' and current carrying long straight wire are placed in the same plane. 23. All the springs in fig. (a), (b) and (c) are identical, each having force constant K . Mass attached to each system is ' 24. The point charges $+\mathrm{q},-\mathrm{q},-\mathrm{q},+\mathrm{q},+\mathrm{Q}$ and -q are placed at the vertices of a r 25. A $1 \mu \mathrm{~F}$ capacitor is charged to 50 V and is then discharged through 10 mH inductor of negligible resistanc 26. The phase difference between two waves giving rise to dark fringe in Young's double slit experiment is ( n is the intege 27. A capillary tube stands with its lower end dipped into liquid for which the angle of contact is $90^{\circ}$. The liquid 28. A body is projected in vertically upward direction from the surface of the earth of radius ' $R$ ' into space with veloc 29. The angular momentum of the electron in the third Bohr orbit of hydrogen atom is ' $l$ '. Its angular momentum in the fo 30. A battery of 6 V is connected to the ends of uniform wire 3 m long and of resistance $100 \Omega$. The difference of pot 31. The $\mathrm{p}-\mathrm{V}$ diagram for a fixed mass of an ideal gas undergoing cyclic process is as shown in figure. AB 32. A vessel is filled with two different liquids which do not mix. One is 40 cm deep and has refractive index 1.6 and other 33. In LCR resonant circuit, the current and voltage have phase difference 34. How is the interference pattern affected when violet light replaces sodium light? 35. A lead sphere of mass ' $m$ ' falls in viscous liquid with terminal velocity $\mathrm{V}_0$. Another lead sphere of mass 36. Two cylinders A and B fitted with piston contain equal amount of an ideal diatomic as at temperature ' T ' K . The pisto 37. A photoelectric surface is illuminated successively by monochromatic light of Wavelength $\lambda$ and $(\lambda / 3)$. 38. A metal rod having coefficient of linear expansion $2 \times 10^{-5} /^{\circ} \mathrm{C}$ is 0.75 m long at $45^{\circ} 39. If the two waves of same amplitude, having frequencies 340 Hz and 335 Hz , are moving in same direction, then the time i 40. A closely wound coil of 100 turns and of crosssection $1 \mathrm{~cm}^2$ has coefficient of self inductance 1 mH . The m 41. A particle of mass ' $m$ ' is performing uniform circular motion along a circular path of radius ' $r$ '. Its angular mo 42. Kirchhoff's second law is based on the law of conservation of 43. A moving body with mass ' $\mathrm{m}_1$ ' strikes a stationary mass ' $\mathrm{m}_2$ '. What should be the ratio $\frac 44. The frequency of the third overtone of a pipe of length ' $L_{\mathrm{c}}$ ', closed at one end is same as the frequency 45. For the following digital logic circuit, the correct truth-table is 46. The ratio of the velocity of sound in hydrogen gas $\left(\gamma=\frac{7}{5}\right)$ to that in helium gas $\left(\gamma 47. Moment of inertia of a disc about an axis passing through its centre and perpendicular to its plane is 'I'. The ratio of 48. Two cars start from a point at the same time in a straight line and their positions are represented by $x_1(t)=a t+b t^2 49. Magnetic field at the centre of a circular loop of area ' $A$ ' is ' $B$ '. The magnetic moment of the loop will be 50. A wire of length ' $L$ ' and linear density ' $m$ ' is stretched between two rigid supports with tension ' $T$ '. It is

MHT CET 2024 11th May Evening Shift

MCQ (Single Correct Answer)

-0

$$ \int \frac{2 x+5}{\sqrt{7-6 x-x^2}} d x=A \sqrt{7-6 x-x^2}+B \sin ^{-1}\left(\frac{x+3}{4}\right)+\mathrm{c} $$ (where c is a constant of integration) then the value of $A+B$ is

$-$3

$-$1

MHT CET 2024 11th May Evening Shift

MCQ (Single Correct Answer)

-0

A straight line L through the point $(3,-2)$ is inclined at an angle of $60^{\circ}$ to the line $\sqrt{3} x+y=1$. If L also intersects the X -axis, then the equation of $L$ is

$y+\sqrt{3} x+2-3 \sqrt{3}=0$

$y-\sqrt{3} x+2+3 \sqrt{3}=0$

$\sqrt{3} y-x+3+2 \sqrt{3}=0$

$\sqrt{3} y+x-3+2 \sqrt{3}=0$

MHT CET 2024 11th May Evening Shift

MCQ (Single Correct Answer)

-0

If $y(x)$ is the solution of the differential equation $(x+2) \frac{\mathrm{d} y}{\mathrm{~d} x}=x^2+4 x-9, x \neq-2$ and $y(0)=0$, then $y(-4)$ is equal to

$-$1

MHT CET 2024 11th May Evening Shift

MCQ (Single Correct Answer)

-0

If the sides of a triangle $a, b, c$ are in A.P., then with usual notations, a $\cos ^2 \frac{\mathrm{C}}{2}+\mathrm{c} \cos ^2 \frac{\mathrm{~A}}{2}$ is

$\frac{3 \mathrm{a}}{2}$

$\frac{3 \mathrm{c}}{2}$

$\frac{3 b}{2}$

$\frac{\mathrm{a}+\mathrm{c}}{2}$

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