MHT CET 2023 13th May Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. What is the $$\mathrm{pH}$$ of solution containing $$4.62 \times 10^{-4} \mathrm{M} \mathrm{H}^{+}$$ ions? 2. Which of the following is vinylic alcohol? 3. Which among the following is benzylic halide? 4. Which among the following is a simple ketone? 5. Identify glycosidic linkage present in maltose. 6. Which statement from following about nano-material is NOT correct? 7. Which from following species is NOT a monodentate ligand? 8. Two moles of an ideal gas expand freely and isothermally from $$5 \mathrm{~dm}^3$$ to $$50 \mathrm{~dm}^3$$. What is the 9. What is IUPAC name of following compound? 10. What is the molecular formula of an alkane if it exhibits three structural isomers? 11. What is the bond order in N$$_2^+$$? 12. Identify alkaline earth metal from following. 13. What is the molality of solution of a non-volatile solute having boiling point elevation $$7.15 \mathrm{~K}$$ and molal 14. Which from following statements about rate constant is NOT true? 15. Identify '$$B$$' in the following conversions $$\mathrm{CH}_3 \mathrm{Br} \xrightarrow{\mathrm{KCN}} A \xrightarrow{\mat 16. Find the radius of metal atom in bcc unit cell having edge length $$450 \mathrm{~pm}$$. 17. Which from following statements is true for the molecule 18. Which among the following salt solution in water is acidic in nature? 19. Which among the following is intensive and extensive properties respectively? 20. Which of the following compounds has lowest boiling point? 21. Which of the following statements is NOT true about polymorphism? 22. Which from the following expression represents molar conductivity of an electrolyte $$\mathrm{A}_2 B_3$$ type? 23. Which of the following electromagnetic radiations possesses lowest energy? 24. Which among the following is an example of branched chain polymer? 25. For the reaction, $$\mathrm{CH}_3 \mathrm{Br}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{CH}_3 \mathrm{OH}(a q)+ 26. For the reaction, $$2 A+2 B \longrightarrow 2 C+D$$, the rate law is expressed as rate $$=k[A]^2[B]$$. Calculate the rat 27. What is the molar conductivity of $$0.005 \mathrm{~M} \mathrm{~NaI}$$ solution if it's conductivity is $$6.065 \times 1 28. Which of the following is not a disaccharide? 29. Which from following is a correct decreasing order of ionisation enthalpy for different elements? 30. Which among the following salts exhibits inverse relation between it's solubility and temperature? 31. Which from following series of elements is correctly arranged according to their decreasing order of ionisation enthalpy 32. Identify the product formed by the action of $$\mathrm{H}_2(\mathrm{~g})$$ with $$\mathrm{CO}(\mathrm{g})$$ in presence 33. Calculate $$E^{\circ}$$ cell for following. $$\mathrm{Zn}(s)\left|\mathrm{Zn}^{++}(1 \mathrm{M}) \| \mathrm{Pb}^{++}(1 \ 34. Which from following elements exhibits usual tendency to undergo reduction? 35. According to reaction, $$\mathrm{Mg}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{MgCl}_2(a q)+\mathrm{H}_2(g) \uparro 36. A closed container contains mixture of non-reacting gases $$A$$ and $$B$$. Partial pressure of $$A$$ and $$B$$ are 4.5 b 37. Which from following compounds is obtained when toluene is treated with $$\mathrm{CrO}_2 \mathrm{Cl}_2$$ in presence of 38. Which of the following is NOT prepared by the action of Grignard's reagent on methanal? 39. What is the number of elements present in each series of transition element? 40. Which of the following is Wolf-Kishner reduction? 41. Calculate the wave number of photon emitted during transition from the orbit of $$n=3$$ to $$n=2$$ in hydrogen atom $$\l 42. What is the molar concentration of acetic acid if value of it's, dissociation constant is $$1.8 \times 10^{-5}$$ and deg 43. An ideal gas absorbs $$210 \mathrm{~J}$$ of heat and undergoes expansion from $$3 \mathrm{~L}$$ to $$6 \mathrm{~L}$$ aga 44. What is the molecular formula of $$p$$-toluidine? 45. If $$0.01 \mathrm{~m}$$ aqueous solution of an electrolyte freezes at $$-0.056 \mathrm{~K}$$. Calculate van't Hoff facto 46. Which element from following does NOT belong to chalcogen family? 47. What is IUPAC name of following compound? 48. Identify the monomers used to prepare novolac. 49. Calculate the volume of unit cell if an element having molar mass $$180 \mathrm{~g} \mathrm{~mol}^{-1}$$ forms fcc unit 50. Identify homoleptic complex from following.

Mathematics

1. If $$x d y=y(d x+y d y), y(1)=1, y(x)>0$$, then $$y(-3)$$ is 2. Slope of the tangent to the curve $$y=2 e^x \sin \left(\frac{\pi}{4}-\frac{x}{2}\right) \cos \left(\frac{\pi}{4}-\frac{x 3. If the vectors $$p \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+q \hat{\mathbf{j}}+\hat{\mathbf{ 4. A tetrahedron has vertices at $$P(2,1,3), Q(-1,1,2), R(1,2,1)$$ and $$O(0,0,0)$$, then angle between the faces $$O P Q$$ 5. Two dice are rolled. If both dice have six faces numbered $$1,2,3,5,7,11$$, then the probability that the sum of the num 6. The domain of the definition of the function $$y(x)$$ is given by the equation $$2^x+2^y=2$$ is 7. If $$\mathbf{a}=\frac{1}{\sqrt{10}}(3 \hat{\mathbf{i}}+\hat{\mathbf{k}}), \mathbf{b}=\frac{1}{7}(2 \hat{\mathbf{i}}+3 \h 8. $$y=\frac{\sqrt[3]{1+3 x} \sqrt[4]{1+4 x} \sqrt[5]{1+5 x}}{\sqrt[7]{1+7 x} \sqrt[8]{1+8 x}} \text {. Then, } \frac{d y}{ 9. Five students are selected from $$n$$ students such that the ratio of number of ways in which 2 particular students are 10. If $$\int \frac{\log \left(t+\sqrt{1+t^2}\right)}{\sqrt{1+t^2}} d t=\frac{1}{2}[g(t)]^2+c$$, (where $$c$$ is a constant 11. If $$A=\left[\begin{array}{cc}1 & \tan x \\ -\tan x & 1\end{array}\right]$$, then $$A^T \cdot A^{-1}=$$ 12. $$\mathbf{a}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\h 13. Let $$P Q R$$ be a right angled isosceles triangle, right angled at $$Q(2,1)$$. If the equation of the line $$P R$$ is $ 14. If a curve $$y=a \sqrt{x}+b x$$ passes through the point $$(1,2)$$ and the area bounded by the curve, line $$x=4$$ and $ 15. A plane is parallel to two lines whose direction ratios are $$2,0,-2$$ and $$-2,2,0$$ and it contains the point $$(2,2,2 16. If $$q$$ is false and $$p \wedge q \leftrightarrow r$$ is true, then ............ is a tautology. 17. Negation of contrapositive of statement pattern $$(p \vee \sim q) \rightarrow(p \wedge \sim q)$$ is 18. The value of $$\tan \left(\sin ^{-1}\left(\frac{3}{5}\right)+\tan ^{-1}\left(\frac{2}{3}\right)\right)$$ is 19. Variance of first $$2 n$$ natural numbers is 20. $$\int \frac{x-3}{(x-1)^3} e^x d x=$$ 21. If $$\mathbf{a}, \mathbf{b}, \mathbf{c}$$ are non-coplanar unit vectors such that $$\mathbf{a} \times(\mathbf{b} \times 22. $$\int \frac{2+\cos \frac{x}{2}}{x+\sin \frac{x}{2}} d x=$$ 23. In $$\triangle A B C$$, with usual notations, if $$\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$$, then the value of $$\ 24. If slope of the tangent to the curve $$x y+a x+b y=0$$ at the point $$(1,1)$$ on it is 2, then the value of $$3 a+b$$ is 25. If $$(3 x+2)-(5 y-3) i$$ and $$(6 x+3)+(2 y-4) i$$ are conjugates of each other, then the value of $$\frac{x-y}{x+y}$$ i 26. If $$\left(\tan ^{-1} x\right)^2+\left(\cot ^{-1} x\right)^2=\frac{5 \pi^2}{8}$$, then the value of $$x$$ is 27. The solution of $$(1+x y) y d x+(1-x y) x d y=0$$ is 28. The integral $$\int_\limits{\pi / 6}^{\pi / 3} \sec ^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x d x$$ is equal 29. $$\lim _\limits{x \rightarrow 0} \frac{\sqrt{1+x \sin x}-\sqrt{\cos x}}{\tan ^2 \frac{x}{2}}=$$ 30. $$A(1,-3), B(4,3)$$ are two points on the curve $$y=x-\frac{4}{x}$$. The points on the curve, the tangents at which are 31. Let $$f: R \rightarrow R$$ be a function such that $$f(x)=x^3+x^2 f^{\prime}(1)+x f^{\prime \prime}(2)+f^{\prime \prime 32. A radioactive substance, with initial mass $$m_0$$, has a half-life of $$h$$ days. Then, its initial decay rate is given 33. The abscissae of two points $$A$$ and $$B$$ are the roots of the equation $$x^2+2 a x-b^2=0$$ and their ordinates are ro 34. The incentre of the $$\triangle A B C$$, whose vertices are $$A(0,2,1), B(-2,0,0)$$ and $$C(-2,0,2)$$, is 35. The acute angle between the line joining the points $$(2,1,-3),(-3,1,7)$$ and a line parallel to $$\frac{x-1}{3}=\frac{y 36. A random variable $$X$$ has the probability distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td{borde 37. The shaded area in the given figure is a solution set for some system of inequations. The maximum value of the function 38. The foot of the perpendicular from the point $$(1,2,3)$$ on the line $$\mathbf{r}=(6 \hat{\mathbf{i}}+7 \hat{\mathbf{j}} 39. Water is running in a hemispherical bowl of radius $$180 \mathrm{~cm}$$ at the rate of 108 cubic decimeters per minute. 40. The solution of $$\sin x+\sin 5 x=\sin 3 x$$ in $$(0, \pi / 2)$$ are 41. If $$(1+\sqrt{1+x}) \tan x=1+\sqrt{1-x}$$, then $$\sin 4 x$$ is 42. If the sum of the mean and the variance of a binomial distribution for 5 trials is 1.8 , then the value of $$p$$ is 43. If $$I=\int \frac{e^x}{e^{4 x}+e^{2 x}+1} d x$$ and $$J=\int \frac{e^{-x}}{e^{-4 x}+e^{-2 x}+1} d x$$, then for any arbi 44. The principal value of $$\sin ^{-1}(\sin (3 \pi / 4))$$ is 45. If $$x=\log _e\left(\frac{\cos \frac{y}{2}-\sin \frac{y}{2}}{\cos \frac{y}{2}+\sin \frac{y}{2}}\right), \tan \frac{y}{2} 46. The c.d.f. $$F(x)$$ associated with p.d.f. $$f(x)$$ $$f(x)=\left\{\begin{array}{cl}12 x^2(1-x), & \text { if } 0 47. If $$f(x)$$ is continuous on its domain $$[-2,2]$$, where $$f(x)=\left\{\begin{array}{cc} \frac{\sin a x}{x}+3 & , \text 48. $$P S$$ is the median of the triangle with vertices at $$P(2,2), Q(6,-1)$$ and $$R(7,3)$$, then the intercepts on the co 49. If Rolle's theorem holds for the function $$f(x)=x^3+b x^2+a x+5$$ on $$[1,3]$$ with $$c=2+\frac{1}{\sqrt{3}}$$, then th 50. The distance of the point $$(1,6,2)$$ from the point of intersection of the line $$\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2

Physics

1. A sample of oxygen gas and a sample of hydrogen gas both have the same mass, same volume and the same pressure. The rati 2. If two planets have their radii in the ratio $$x: y$$ and densities in the ratio $$m: n$$, then the acceleration due to 3. An excited hydrogen atom emits a photon of wavelength $$\lambda$$ in returning to ground state. The quantum number $$n$$ 4. There is hole of area $$A$$ at the bottom of a cylindrical vessel. Water is filled to a height $$h$$ and water flows out 5. The number of turns in the primary and the secondary of a transformer are 1000 and 3000 , respectively. If $$80 \mathrm{ 6. The ratio of magnetic field at the centre of the current carrying circular loop and magnetic moment is $$X$$. When both 7. Light of wavelength $$5000 \mathop A\limits^o$$ is incident normally on a slit. The first minimum of the diffraction pat 8. When two tuning forks are sounded together, 5 beats per second are heard. One of the forks is in unison with $$0.97 \mat 9. The work done in rotating a dipole placed parallel to the electric field through $$180^{\circ}$$ is W. So, the work done 10. When an electron is excited from its 4 th orbit to 5 th stationary orbit, the change in the angular momentum of electron 11. The Boolean expression for the following combination is 12. Under the influence of force $$F_1$$ the body oscillates with a period $$T_1$$ and due to another force $$F_2$$ body osc 13. The internal energy of a monoatomic ideal gas molecule is 14. A gas at pressure $$p_0$$ is contained in a vessel. If the masses of all the molecules are halved and their velocities a 15. The equation of a progressive wave is $$Y=a \sin 2 \pi\left(n t-\frac{x}{5}\right)$$. The ratio of maximum particle velo 16. For an adiabatic process, which one of the following is wrong statement? 17. A mine is located at depth $$R / 3$$ below earth's surface. The acceleration due to gravity at that depth in mine is ($$ 18. A $$10 \mathrm{~m}$$ long wire of resistance $$20 \Omega$$ is connected in series with a battery of emf $$3 \mathrm{~V}$ 19. A group of lamps having total power rating of $$1000 \mathrm{~W}$$ is supplied by an AC voltage of $$E=200 \sin \left(31 20. At a particular angular frequency, the reactance of capacitor and that of inductor is same. If the angular frequency is 21. A metal disc of radius $$R$$ rotates with an angular velocity $$\omega$$ about an axis perpendicular to its plane passin 22. A mass $$M$$ is suspended from a light spring. An additional mass $$M_1$$ added extends the spring further by a distance 23. The path difference between two identical light waves at a point $$Q$$ on the screen is $$3 \mu \mathrm{m}$$. If wavelen 24. If the maximum efficiency of a full wave rectifier is $$x \%$$ and that of half-wave rectifier is $$y \%$$, then the rel 25. Two bodies $$A$$ and $$B$$ start from the same point at the same instant and move along a straight line. body $$A$$ move 26. A small steel ball is dropped from a height of $$1.5 \mathrm{~m}$$ into a glycerine jar. The ball reaches the bottom of 27. In a parallel plate capacitor with air between the plates, the distance $$d$$ between the plates is changed and the spac 28. A ray of light passes through an equilateral prism such that the angle of incidence $$(i)$$ is equal to angle of emergen 29. The radii of curvature of both the surfaces of a convex lens of focal length $$f$$ and power $$P$$ are equal. One of the 30. A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring balance reads $$ 31. In a $$L$$-$$R$$ circuit the inductive reactance is equal to the resistance $R$ in the circuit. An emf $$E=E_0 \cos \ome 32. Four identical uniform solid spheres each of same mass $$M$$ and radius $$R$$ are placed touching each other as shown in 33. A transverse wave strike against a wall, 34. A circular current carrying coil has radius $$R$$. The magnetic induction at the centre of the coil is $$B_C$$. The magn 35. In the electric field due to a charge $$Q$$, a charge $$q$$ moves from point $$A$$ to $$B$$. The work done is ( $$\varep 36. Of the two slits producing interference in Young's experiment, one is covered with glass so that light intensity passing 37. Magnetic shielding is done by surrounding the instrument to be protected from magnetic field by 38. In the given figure, the equivalent capacitance between points A and B is 39. If work done in blowing a soap bubble of volume $$V$$ is $$W$$, then the work done in blowing the bubble of volume $$2 \ 40. Which one of the following is based on convection? 41. A simple spring has length $$l$$ and force constant $$K$$. It is cut in to two springs of length $$l_1$$ and $$l_2$$ suc 42. A closed pipe and an open pipe have their first overtone equal in frequency. Then, the lengths of these pipe are in the 43. A conductor $$10 \mathrm{~cm}$$ long is moves with a speed $$1 \mathrm{~m} / \mathrm{s}$$ perpendicular to a field of st 44. Dual nature of light is exhibited by 45. A carnot engine operates with source at $$227^{\circ} \mathrm{C}$$ and sink at $$27^{\circ} \mathrm{C}$$. If the source 46. Doping of a semiconductor (with small impurity atoms) generally changes the resistivity as follows. 47. A stone is projected at angle $$\theta$$ with velocity $$u$$. If it executes nearly a circular motion at its maximum poi 48. When radiations of wavelength $$\lambda$$ is incident on a metallic surface the stopping potential required is $$4.8 \ma 49. A thin uniform $$\operatorname{rod} A B$$ of mass $$m$$ and length $$l$$ is hinged at one end $$A$$ to the ground level. 50. Only $$4 \%$$ of the total current in the circuit passes through a galvanometer. If the resistance of the galvanometer i

MHT CET 2023 13th May Evening Shift

MCQ (Single Correct Answer)

-0

If $$I=\int \frac{e^x}{e^{4 x}+e^{2 x}+1} d x$$ and $$J=\int \frac{e^{-x}}{e^{-4 x}+e^{-2 x}+1} d x$$, then for any arbitrary constant $$C$$, than the value of $$J-I$$ equals

$$\frac{1}{2} \log \left|\left(\frac{e^{4 x}-e^{2 x}+1}{e^{4 x}+e^{2 x}+1}\right)\right|+C$$

$$\frac{1}{2} \log \left|\left(\frac{e^{2 x}+e^x+1}{e^{2 x}-e^x+1}\right)\right|+C$$

$$\frac{1}{2} \log \left|\left(\frac{e^{2 x}-e^x+1}{e^{2 x}+e^x+1}\right)\right|+C$$

$$\frac{1}{2} \log \left|\left(\frac{e^{4 x}+e^{2 x}+1}{e^{4 x}-e^{2 x}+1}\right)\right|+C$$

MHT CET 2023 13th May Evening Shift

MCQ (Single Correct Answer)

-0

The principal value of $$\sin ^{-1}(\sin (3 \pi / 4))$$ is

$$\pi / 4$$

$$-\pi / 4$$

$$3 \pi / 4$$

$$5 \pi / 4$$

MHT CET 2023 13th May Evening Shift

MCQ (Single Correct Answer)

-0

If $$x=\log _e\left(\frac{\cos \frac{y}{2}-\sin \frac{y}{2}}{\cos \frac{y}{2}+\sin \frac{y}{2}}\right), \tan \frac{y}{2}=\sqrt{\frac{1-t}{1+t}}$$ Then, $$\left(y_1\right)_{t=1 / 2}$$ has the value

$$1 / 2$$

$$-1 / 2$$

$$1 / 4$$

$$-1 / 4$$

MHT CET 2023 13th May Evening Shift

MCQ (Single Correct Answer)

-0

The c.d.f. $$F(x)$$ associated with p.d.f. $$f(x)$$

$$f(x)=\left\{\begin{array}{cl}12 x^2(1-x), & \text { if } 0< x <1 \\ 0 ; & \text { otherwise }\end{array}\right.$$ is

$$F(x)=4 x^3+3 x^4$$

$$F(x)=4 x^3-3 x^4$$

$$F(x)=-4 x^3-3 x^4$$