MHT CET 2023 10th May Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. What is the calculated value of spin only magnetic moment in terms of BM if only one unpaired electron is present in a s 2. Which of the following is tertiary allylic alcohol? 3. Identify the solvent used in bromination of phenol to obtain 2,4,6-tribromophenol. 4. How many moles of nitrogen atoms are present in $$8 \mathrm{~g}$$ of ammonium nitrate? (Molar mass of ammonium nitrate $ 5. Identify the elements undergoing reduction and oxidation respectively in the following redox reaction. $$3 \mathrm{H}_3 6. Which of the following is tricarboxylic acid? 7. Find the radius of an atom in fcc unit cell having edge length $$393 \mathrm{pm}$$. 8. Which from following is a CORRECT decreasing order of ionization enthalpies of different elements? 9. A gas absorbs $$200 \mathrm{~J}$$ heat and expands by $$500 \mathrm{~cm}^3$$ against a constant external pressure $$2 \t 10. Identify a copolymer from following. 11. Find the average rate of formation of $$\mathrm{NO}_{2(\mathrm{~g})}$$, in following reaction. $$\begin{aligned} & 2 \ma 12. Calculate the rate constant for the first order reaction, $$\mathrm{A} \rightarrow \mathrm{B}$$ if the rate of reaction 13. Identify the product obtained when benzonitrile is reduced by stannous chloride in presence of hydrochloric acid followe 14. Find solubility in terms of $$\mathrm{mol} \mathrm{~L}^{-1}$$ if solubility product of silver bromide is $$6.4 \times 10 15. What happens when solution of an electrolyte is diluted? 16. The solubility of a gas in a liquid is directly proportional to the pressure of the gas over the solution. Identify the 17. Weak acid HX has dissociation constant $$1 \times 10^{-5}$$. Calculate the percent dissociation in its $$0.1 \mathrm{M}$ 18. Calculate the $$\mathrm{pH}$$ of a buffer solution containing $$0.01 ~\mathrm{M}$$ salt and $$0.004 \mathrm{~M}$$ weak a 19. Which among the following is vinylic halide? 20. Which from following compounds is obtained when carbon dioxide gas bubbled through slaked lime solution? 21. Calculate the number of atoms present in unit cell of an element having molar mass $$190 \mathrm{~g} \mathrm{~mol}^{-1}$ 22. What is the solubility of a gas in water at $$25^{\circ} \mathrm{C}$$ if partial pressure is $$0.18 \mathrm{~atm}$$ ? $$ 23. What is the radius of fourth orbit of $$\mathrm{Be}^{+++}$$ ? 24. What is the number of unpaired electrons in $$\mathrm{NO}$$ molecule? 25. Identify the glycosidic linkage present in lactose. 26. Which from following statements is TRUE about $$\mathrm{CH}_3 \mathrm{CH}\left(\mathrm{NH}_2\right) \mathrm{CH}_2 \mathr 27. Which of the following is obtained as product when ethylene reacts with oxygen in presence of $$\mathrm{Pd} / \mathrm{Al 28. What is the position of transition elements from $$\mathrm{Sc}$$ to $$\mathrm{Zn}$$ in long form of periodic table? 29. Which from following elements is most abundant on earth? 30. What is the volume of 1 mole real gas at STP $$\left(V_0=22.4 \mathrm{~dm}^3\right)$$, if compressibility factor of real 31. Identify the product obtained when isopropyl bromide is reacted with metallic sodium in dry ether. 32. Which of the following is general representation of Grignard reagent? 33. Which among the following statements is NOT true about high density polythene? 34. What is osmotic pressure of solution of $$1.7 \mathrm{~g} \mathrm{~CaCl}_2$$ in $$1.25 \mathrm{~dm}^3$$ water at $$300 \ 35. Which among the following pair of properties is intensive? 36. Identify the molecular formula of an alkane that exhibits only two different structural isomers. 37. An organic compound '$$\mathrm{A}$$' on reaction with $$\mathrm{PCl}_3$$ gives an alkyl chloride having formula $$\mathr 38. Identify tetrasaccharide from following. 39. What type of ligand does the ethylenediamine is? 40. What is angular momentum of an electron in fourth orbit of hydrogen atom? 41. Which from following complexes is heteroleptic? 42. Calculate $$E_{\text {cell }}^{\circ}$$ in which following reaction occurs. $$\mathrm{Mg}_{(\mathrm{s})}+2 \mathrm{Ag}_{ 43. Identify CORRECT decreasing order of solubilities of alcohols, alkanes and amines in water having comparable molar mass. 44. Which of the following characteristic properties is NOT true for crystalline solid? 45. Time required for $$90 \%$$ completion of a first order reaction is '$$x$$' minute. Calculate the time required to compl 46. Identify '$$A$$' in the following reaction: A $$\mathrm{\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{ether}^{LiAl{ 47. Which of the following reagents is used in Gatterman-Koch formylation of arene? 48. Identify the last step in wet chemical synthesis of nanomaterial. 49. Calculate the conductivity of $$0.02 \mathrm{~M}$$ electrolyte solution if its molar conductivity $$407.2 \Omega^{-1} \m 50. If $$8.84 \mathrm{~kJ}$$ heat is liberated for formation of $$3 \mathrm{~g}$$ ethane, calculate its $$\triangle_{\mathrm

Mathematics

1. The value of $$\mathrm{c}$$ for the function $$\mathrm{f}(x)=\log x$$ on [$$1$$, e] if LMVT can be applied, is 2. The three ships namely A, B and C sail from India to Africa. If the odds in favour of the ships reaching safely are $$2: 3. If $$\mathrm{p}$$ and $$\mathrm{q}$$ are true statements and $$\mathrm{r}$$ and $$\mathrm{s}$$ are false statements, the 4. If the sum of mean and variance of a Binomial Distribution is $$\frac{15}{2}$$ for 10 trials, then the variance is 5. If $$(\bar{a} \times \bar{b}) \times \bar{c}=-5 \bar{a}+4 \bar{b}$$ and $$\bar{a} \cdot \bar{b}=3$$, then the value of $ 6. The plane through the intersection of planes $$x+y+z=1$$ and $$2 x+3 y-z+4=0$$ and parallel to $$\mathrm{Y}$$-axis also 7. Let $$\mathrm{f}(x)=\mathrm{e}^x-x$$ and $$\mathrm{g}(x)=x^2-x, \forall x \in \mathrm{R}$$, then the set of all $$x \in 8. Let $$f$$ be a differentiable function such that $$\mathrm{f}(1)=2$$ and $$\mathrm{f}^{\prime}(x)=\mathrm{f}(x)$$, for a 9. The joint equation of a pair of lines passing through the origin and making an angle of $$\frac{\pi}{4}$$ with the line 10. Two sides of a square are along the lines $$5 x-12 y+39=0$$ and $$5 x-12 y+78=0$$, then area of the square is 11. The value of $$\int \frac{\mathrm{d} x}{x^2\left(x^4+1\right)^{\frac{3}{4}}}$$ is 12. $$\int \frac{5 \tan x}{\tan x-2} \mathrm{~d} x=x+\mathrm{a} \log |\sin x-2 \cos x|+\mathrm{c},$$ (where $$c$$ is a const 13. Let $$\mathrm{S}=\left\{\mathrm{t} \in \mathrm{R} / \mathrm{f}(x)=|x-\pi|\left(\mathrm{e}^{|x|}-1\right) \sin |x|\right. 14. The domain of the function $$\mathrm{f}(x)=\sin ^{-1}\left(\frac{|x|+5}{x^2+1}\right)$$ is $$(-\infty,-a] \cup[a, \infty 15. The perpendicular distance of the origin from the plane $$x-3 y+4 z-6=0$$ is 16. The area bounded by the $$\mathrm{X}$$-axis and the curve $$y=x(x-2)(x+1)$$ is 17. Let $$\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$$ and $$\mathrm{g}: \mathrm{R} \rightarrow \mathrm{R}$$ be continuou 18. If $$\bar{p}=\hat{i}+\hat{j}+\hat{k}$$ and $$\bar{q}=\hat{i}-2 \hat{j}+\hat{k}$$. Then a vector of magnitude $$5 \sqrt{3 19. The value of $$\frac{{ }^{10} \mathrm{C}_{\mathrm{r}}}{{ }^{11} \mathrm{C}_{\mathrm{r}}}$$, when both the numerator and 20. The general solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}+\left(\frac{3 x^2}{1+x^3}\right) 21. If $$y$$ is a function of $$x$$ and $$\log (x+y)=2 x y$$, then $$\frac{d y}{d x}$$ at $$x=0$$ is 22. The displacement '$$\mathrm{S}$$' of a moving particle at a time $$t$$ is given by $$S=5+\frac{48}{t}+t^3$$. Then its ac 23. If $$\bar{a}$$ and $$\bar{b}$$ are two unit vectors such that $$\bar{a}+2 \bar{b}$$ and $$5 \bar{a}-4 \bar{b}$$ are perp 24. The value of $$\tan ^{-1}(1)+\cos ^{-1}\left(-\frac{1}{2}\right)+\sin ^{-1}\left(-\frac{1}{2}\right)$$ is 25. $$\int_\limits 0^\pi \frac{x \tan x}{\sec x+\cos x} d x= $$ 26. If $$\tan ^{-1} a+\tan ^{-1} b+\tan ^{-1} c=\pi$$, then which of the following statement is true? 27. If $$\mathrm{f}(x)=\frac{4}{x^4}\left[1-\cos \frac{x}{2}-\cos \frac{x}{4}+\cos \frac{x}{2} \cdot \cos \frac{x}{4}\right] 28. Two lines $$\frac{x-3}{1}=\frac{y+1}{3}=\frac{z-6}{-1}$$ and $$\frac{x+5}{7}=\frac{y-2}{-6}=\frac{z-3}{4} \quad$$ inters 29. The value of $$\int \frac{\left(x^2-1\right) d x}{x^3 \sqrt{2 x^4-2 x^2+1}}$$ is 30. The shaded area in the figure given below is a solution set of a system of inequations. The minimum value of objective f 31. If $$\overline{\mathrm{a}}=\mathrm{m} \overline{\mathrm{b}}+\mathrm{nc}$$, where $$\overline{\mathrm{a}}=4 \hat{\mathrm{ 32. In a game, 3 coins are tossed. A person is paid ₹ 7 /-, if he gets all heads or all tails; and he is supposed to pay ₹ 3 33. $$\int \mathrm{e}^x\left(1-\cot x+\cot ^2 x\right) \mathrm{d} x=$$ 34. The parametric equations of the circle $$x^2+y^2+2 x-4 y-4=0$$ are 35. In a triangle $$\mathrm{ABC}$$, with usual notations, if $$\mathrm{c}=4$$, then value of $$(a-b)^2 \cos ^2 \frac{C}{2}+( 36. $$\lim _\limits{x \rightarrow a} \frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}}=$$ 37. If $$B=\left[\begin{array}{ccc}3 & \alpha & -1 \\ 1 & 3 & 1 \\ -1 & 1 & 3\end{array}\right]$$ is the adjoint of a $$3 \t 38. If $$x=3 \tan \mathrm{t}$$ and $$y=3 \sec \mathrm{t}$$, then the value of $$\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}$$ at 39. A fair die is tossed twice in succession. If $$\mathrm{X}$$ denotes the number of sixes in two tosses, then the probabil 40. The negation of the statement pattern $$\sim s \vee(\sim r \wedge s)$$ is equivalent to 41. If the volume of tetrahedron, whose vertices are with position vectors $$\hat{i}-6 \hat{j}+10 \hat{k},-\hat{i}-3 \hat{j} 42. The argument of $$\frac{1+i \sqrt{3}}{\sqrt{3}+i}, i=\sqrt{-1}$$ is 43. If $$y=\tan ^{-1}\left(\frac{\log \left(\frac{\mathrm{e}}{x^2}\right)}{\log \left(e x^2\right)}\right)+\tan ^{-1}\left(\ 44. If the surface area of a spherical balloon of radius $$6 \mathrm{~cm}$$ is increasing at the rate $$2 \mathrm{~cm}^2 / \ 45. The value of $$\alpha$$, so that the volume of parallelopiped formed by $$\hat{i}+\alpha \hat{j}+\hat{k}, \hat{j}+\alpha 46. In a certain culture of bacteria, the rate of increase is proportional to the number of bacteria present at that instant 47. If $$x, y, z$$ are in A.P. and $$\tan ^{-1} x, \tan ^{-1} y$$ and $$\tan ^{-1} z$$ are also in A.P., then 48. Mean and variance of six observations are 8 and 16 respectively. If each observation is multiplied by 3, then new varian 49. The differential equation of all circles, passing through the origin and having their centres on the $$\mathrm{X}$$-axis 50. $$\int_\limits0^1 \cos ^{-1} x d x=$$

Physics

1. Two trains, each $$30 \mathrm{~m}$$ long are travelling in opposite directions with velocities $$5 \mathrm{~m} / \mathrm 2. The fundamental frequency of air column in pipe 'A' closed at one end is in unison with second overtone of an air column 3. In Young's double slit experiment, the two slits are 'd' distance apart. Interference pattern is observed on a screen at 4. A black body radiates maximum energy at wavelength '$$\lambda$$' and its emissive power is 'E' Now due to change in temp 5. In meter bridge experiment, null point was obtained at a distance '$$l$$' from left end. The values of resistances in th 6. The magnetic field at the centre of a circular coil of radius '$$R$$', carrying current $$2 A$$ is '$$B_1$$'. The magnet 7. If a capacitor of capacity $$900 ~\mu \mathrm{F}$$ is charged to $$100 \mathrm{~V}$$ and its total energy is transferred 8. The equation of wave is $$Y=6 \sin$$ $$\left(12 \pi t-0.02 \pi x+\frac{\pi}{3}\right)$$ where '$$x$$' is in $$m$$ and '$ 9. With an alternating voltage source of frequency '$$f$$', inductor '$$L$$', capacitor '$$C$$' and resistance '$$R$$' are 10. A pure $$\mathrm{Si}$$ crystal has $$4 \times 10^{28}$$ atoms per $$\mathrm{m}^3$$. It is doped by 1 ppm concentration o 11. A mass '$$\mathrm{M}$$' moving with velocity '$$\mathrm{V}$$' along $$\mathrm{X}$$-axis collides and sticks to another m 12. Which of the following graphs between pressure (P) and volume (V) correctly shows isochoric changes? 13. A galvanometer has resistance '$$\mathrm{G}$$' and range '$$\mathrm{V} g$$'. How much resistance is required to read vol 14. '$$n$$' number of liquid drops each of radius '$$r$$' coalesce to form a single drop of radius '$$R$$'. The energy relea 15. What is the moment of inertia of the electron moving in second Bohr orbit of hydrogen atom? [ $$\mathrm{h}=$$ Planck's c 16. At critical temperature, the surface tension of liquid is 17. Two wires $$2 \mathrm{~mm}$$ apart supply current to a $$100 \mathrm{~V}, 1 \mathrm{~kW}$$ heater. The force per metre b 18. A solenoid of 500 turns/m is carrying a current of 3 A. Its core is made of iron which has relative permeability 5001. T 19. The ratio of the velocity of the electron in the first Bohr orbit to that in the second Bohr orbit of hydrogen atom is 20. The capacitive reactance of a capacitor '$$C$$' is $$\mathrm{X} \Omega$$. Both, the frequency of a.c. supply and capacit 21. A $$100 \mathrm{~mH}$$ coil carries a current of $$1 \mathrm{~A}$$. Energy stored in the form of magnetic field is 22. A metal rod $$2 \mathrm{~m}$$ long increases in length by $$1.6 \mathrm{~mm}$$, when heated from $$0^{\circ} \mathrm{C}$ 23. Assume that an electric field $$\mathrm{E}=30 \mathrm{x}^2 \hat{\mathrm{i}}$$ exists in space. If '$$\mathrm{V}_0$$' is 24. Two dielectric slabs having dielectric constant '$$\mathrm{K}_1$$' and '$$\mathrm{K}_2$$' of thickness $$\frac{\mathrm{d 25. The output of an 'OR' gate is connected to both the inputs of a 'NAND' gate. The combination will serve as 26. Which one of the operations of $$\mathrm{n}-\mathrm{p}-\mathrm{n}$$ transistor differs from that of $$p-n-p$$ transistor 27. A hollow metal pipe is held vertically and bar magnet is dropped through it with its length along the axis of the pipe. 28. A metal sphere of mass '$$m$$' and density '$$\sigma_1$$' falls with terminal velocity through a container containing li 29. Two uniform wires of same material are vibrating under the same tension. If the first overtone of first wire is equal to 30. A body is projected vertically from earth's surface with velocity equal to half the escape velocity. The maximum height 31. A ball of mass '$$\mathrm{m}$$' is dropped from a height '$$\mathrm{s}$$' on a horizontal platform fixed at the top of a 32. In the circuit given below, the current through inductor is $$0.9 \mathrm{~A}$$ and through the capacitor is $$0.6 \math 33. A body is executing a linear S.H.M. Its potential energies at the displacement '$$\mathrm{x}$$' and '$$\mathrm{y}$$' are 34. We have a jar filled with gas characterized by parameters $$\mathrm{P}, \mathrm{V}, \mathrm{T}$$ and another jar B fille 35. Two spheres each of mass '$$M$$' and radius $$\frac{R}{2}$$ are connected at the ends of massless rod of length '$$2 R$$ 36. If the potential difference used to accelerate electrons is doubled, by what factor does the de-Broglie wavelength assoc 37. A simple harmonic progressive wave is represented by $$y=A \sin (100 \pi t+3 x)$$. The distance between two points on th 38. An insulated container contains a monoatomic gas of molar mass '$$\mathrm{m}$$'. The container is moving with velocity ' 39. To get three images of a single object, the angle between the two plane mirrors should be 40. A parallel beam of monochromatic light falls normally on a single narrow slit. The angular width of the central maximum 41. For the diagram shown, the resistances between points A and B when ideal diode D is forward biased is '$$R_1$$' and that 42. The maximum kinetic energy of the photoelectrons varies 43. Light waves from two coherent sources arrive at two points on a screen with path difference of zero and $$\frac{\lambda^ 44. A uniform rope of length '$$L$$' and mass '$$m_1$$' hangs vertically from a rigid support. A block of mass '$$m_2$$' is 45. In a vessel, the ideal gas is at a pressure $$\mathrm{P}$$. If the mass of all the molecules is halved and their speed i 46. Two concentric circular coils having radii $$r_1$$ and $$r_2\left(r_2 47. A system consists of three particles each of mass '$$m_1$$' placed at the corners of an equilateral triangle of side '$$ 48. The moment of inertia of a uniform square plate about an axis perpendicular to its plane and passing through the centre 49. Two lenses of power $$-15 \mathrm{D}$$ and $$+5 \mathrm{D}$$ are in contact with each other. The focal length of the com 50. A particle performing uniform circular motion of radius $$\frac{\pi}{2} \mathrm{~m}$$ makes '$$\mathrm{x}$$' revolutions

MHT CET 2023 10th May Evening Shift

MCQ (Single Correct Answer)

-0

The value of $$\int \frac{\mathrm{d} x}{x^2\left(x^4+1\right)^{\frac{3}{4}}}$$ is

$$\left(\frac{x^4+1}{x^4}\right)^{\frac{1}{4}}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$\left(x^4+1\right)^{\frac{1}{4}}+c$$, where $$\mathrm{c}$$ is a constant of integration.

$$-\left(x^4+1\right)^{\frac{1}{4}}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$-\left(\frac{x^4+1}{x^4}\right)^{\frac{1}{4}}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

MHT CET 2023 10th May Evening Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{5 \tan x}{\tan x-2} \mathrm{~d} x=x+\mathrm{a} \log |\sin x-2 \cos x|+\mathrm{c},$$ (where $$c$$ is a constant of integration), then the value of $$a$$ is

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

MHT CET 2023 10th May Evening Shift

MCQ (Single Correct Answer)

-0

Let $$\mathrm{S}=\left\{\mathrm{t} \in \mathrm{R} / \mathrm{f}(x)=|x-\pi|\left(\mathrm{e}^{|x|}-1\right) \sin |x|\right.$$ is not differentiable at $$\mathrm{t}\}$$, then $$\mathrm{S}$$ is

$$\phi$$ (an empty set)

$$\{0\}$$

$$\{\pi\}$$

$$\{0, \pi\}$$

MHT CET 2023 10th May Evening Shift

MCQ (Single Correct Answer)

-0

The domain of the function $$\mathrm{f}(x)=\sin ^{-1}\left(\frac{|x|+5}{x^2+1}\right)$$ is $$(-\infty,-a] \cup[a, \infty)$$. Then a is equal to

$$\frac{\sqrt{17}}{2}+1$$

$$\frac{\sqrt{17}-1}{2}$$

$$\frac{1+\sqrt{17}}{2}$$

$$\frac{\sqrt{17}}{2}-1$$