MHT CET 2023 9th May Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Identify monodentate ligand from the following. 2. Identify linear polymer from the following. 3. What is the conductivity of $$0.05 ~\mathrm{M} ~\mathrm{BaCl}_2$$ solution if its molar conductivity is $$220 ~\Omega^{- 4. Which from following polymers is grouped in the category of elastomers? 5. Which element from following exhibits diagonal relationship with beryllium? 6. What is the stock notation of Manganese dioxide? 7. A reaction, $$\mathrm{Ni}_{(\mathrm{s})}+\mathrm{Cu}_{(\mathrm{(M)})}^{+} \rightarrow \mathrm{Ni}_{(\mathrm{IM})}^{+}+\m 8. What volume of ammonia is formed when $$10 ~\mathrm{dm}^3$$ dinitrogen reacts with $$30 ~\mathrm{dm}^3$$ dihydrogen at s 9. What is the number of moles of $$\mathrm{sp}^2$$ hybrid carbon atoms present in $$\mathrm{n}$$ moles of isopentane? 10. Find solubility of $$\mathrm{PbI}_2$$ if its solubility product is $$7.0 \times 10^{-9}$$. 11. Identify the product formed when vapours of 2-methylpropan-2-ol are passed over hot copper. 12. Calculate the rate constant of first order reaction if the concentration of the reactant decreases by $$90 \%$$ in 30 mi 13. What different elements are found in baryte? 14. Identify the product '$$B$$' in the following reaction. Cumene $$\mathrm{\mathrel{\mathop{\kern0pt\longrightarrow} \limi 15. Which of the following on reaction with ammoniacal silver nitrate forms silver precipitate? 16. Identify an aromatic, mixed, 3$$^\circ$$ amine from following. 17. For $$\mathrm{NaCl}_{(\mathrm{s})}$$ enthalpy of solution is $$4 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ and lattice enthalpy 18. Which from following statements regarding transition elements is NOT CORRECT? 19. A solution of $$8 \mathrm{~g}$$ of certain organic compound in $$2 ~\mathrm{dm}^3$$ water develops osmotic pressure $$0. 20. What is the value of $$\Delta H-\Delta U$$ for the following reaction? $$2 \mathrm{C}_{(\mathrm{s})}+3 \mathrm{H}_{2(\ma 21. Which from the following compound solutions in water of equal concentration has electrical conductivity nearly same as d 22. What is the $$\mathrm{pH}$$ of a solution containing $$2.2 \times 10^{-6} \mathrm{M}$$ hydrogen ions? 23. Which of the following statements is NOT true about Rutherford atomic model? 24. What is IUPAC name of propylene glycerol? 25. Identify the CORRECT decreasing order of melting point of cluster of sodium atoms depending on size. 26. Which from the following coordinate complexes contains anionic and neutral ligands in it? 27. Which among the following is allylic halide? 28. Which of the following compounds has the highest boiling point? 29. A solution of nonvolatile solute is obtained by dissolving $$1 \mathrm{~g}$$ in $$100 \mathrm{~g}$$ solvent, decreases i 30. What is the IUPAC name of allylamine? 31. What is the wave number of photon emitted during transition from orbit, $$\mathrm{n}=4$$ to $$\mathrm{n}=2$$ in hydrogen 32. Which from following is a CORRECT bond line formula of $$\mathrm{HO}\left(\mathrm{CH}_2\right)_3 \mathrm{CH}\left(\mathr 33. Identify the carbon atoms of $$\alpha$$-glucose and $$\beta$$-fructose forming glycosidic linkage in sucrose. 34. Calculate the molar mass of an element having density $$21 \mathrm{~g} \mathrm{~cm}^{-3}$$ that forms fcc unit cell $$\l 35. Which of the following is the SI unit of coefficient of viscosity? 36. Which from following metal has ccp crystal structure? 37. Identify the reagent '$$A$$' used in the following conversion. Ethyl bromide $$\stackrel{\mathrm{A}}{\longrightarrow}$$ 38. What is the concentration of $$\left[\mathrm{H}_3 \mathrm{O}^{+}\right]$$ ion in $$\mathrm{mol} ~\mathrm{L}^{-1}$$ of $$ 39. Which group elements from following are called as chalcogens? 40. What is the number of electrons around sulfur in $$\mathrm{H}_2 \mathrm{SO}_4$$ molecule? 41. An ideal gas expands by $$1.5 \mathrm{~L}$$ against a constant external pressure of $$2 \mathrm{~atm}$$ at $$298 \mathrm 42. The rate law for the reaction $$\mathrm{A}+\mathrm{B} \rightarrow$$ product is given by rate $$=k[A][B]$$ Calculate $$[A 43. Which among the following has the lowest boiling point? 44. Find the average rate of formation $$\mathrm{O}_{2(\mathrm{~g})}$$ in the following reaction. $$\begin{aligned} & 2 \mat 45. Which among the following reactions occurs by breaking of $$\mathrm{C}-\mathrm{O}$$ bond in alcohol? 46. Which among the following gases exhibits very low solubility in water at room temperature? 47. Identify the trisaccharide from following. 48. Identify the element from following having six unpaired electrons in observed electronic configuration? 49. Find the radius of metal atom in simple cubic unit cell having edge length 334.7 pm? 50. Which of the following colloids is NOT a gel?

Mathematics

1. If the slope of one of the lines represented by $$a x^2+(2 a+1) x y+2 y^2=0$$ is reciprocal of the slope of the other, t 2. In $$\triangle \mathrm{PQR}, \sin \mathrm{P}, \sin \mathrm{Q}$$ and $$\sin \mathrm{R}$$ are in A.P., then 3. The value of $$\tan ^{-1}\left(\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\right), |x| 4. If slope of a tangent to the curve $$x y+a x+b y=0$$ at the point $$(1,1)$$ on it is 2, then a - b is 5. The equation of a line, whose perpendicular distance from the origin is 7 units and the angle, which the perpendicular t 6. Let $$a, b, c$$ be the lengths of sides of triangle $$A B C$$ such that $$\frac{a+b}{7}=\frac{b+c}{8}=\frac{c+a}{9}=k$$. 7. If the mean and S.D. of the data $$3,5,7, a, b$$ are 5 and 2 respectively, then $$a$$ and $$b$$ are the roots of the equ 8. A man takes a step forward with probability 0.4 and backwards with probability 0.6 . The probability that at the end of 9. If $$\mathrm{f}^{\prime}(x)=x-\frac{5}{x^5}$$ and $$\mathrm{f}(1)=4$$, then $$\mathrm{f}(x)$$ is 10. A linguistic club of a certain Institute consists of 6 girls and 4 boys. A team of 4 members to be selected from this gr 11. Negation of the statement "The payment will be made if and only if the work is finished in time." Is 12. The equation $$x^3+x-1=0$$ has 13. If a line $$\mathrm{L}$$ is the line of intersection of the planes $$2 x+3 y+z=1$$ and $$x+3 y+2 z=2$$. If line $$\mathr 14. The range of values of $$x$$ for which $$f(x)=x^3+6 x^2-36 x+7$$ is increasing in 15. The maximum value of the function $$f(x)=3 x^3-18 x^2+27 x-40$$ on the set $$\mathrm{S}=\left\{x \in \mathbb{R} / x^2+30 16. Let $$\mathrm{p}, \mathrm{q}, \mathrm{r}$$ be three statements, then $$[p \rightarrow(q \rightarrow r)] \leftrightarrow[ 17. $$\int_\limits1^2 \frac{\mathrm{d} x}{\left(x^2-2 x+4\right)^{\frac{3}{2}}}=\frac{\mathrm{k}}{\mathrm{k}+5} \text {, the 18. The sides of a rectangle are given by the equations $$x=-2, x=4, y=-2$$ and $$y=5$$ Then the equation of the circle, who 19. $$\overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{b}}=\hat{\mathrm{j}}-\hat{ 20. The magnitude of the projection of the vector $$2 \hat{i}+\hat{j}+\hat{k}$$ on the vector perpendicular to the plane con 21. The shortest distance between the lines $$\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$$ and $$\frac{x-2}{3}=\frac{y-4}{4}= 22. If $$\bar{a}, \bar{b}$$ and $$\bar{c}$$ are any three non-zero vectors, then $$(\bar{a}+2 \bar{b}+\bar{c}) \cdot[(\bar{a 23. In $$\triangle \mathrm{ABC}$$, with usual notations, $$\mathrm{m} \angle \mathrm{C}=\frac{\pi}{2}$$, if $$\tan \left(\fr 24. If $$\int \frac{\sin x}{3+4 \cos ^2 x} \mathrm{~d} x=\mathrm{A} \tan ^{-1}(\mathrm{~B} \cos x)+\mathrm{c}$$, (where $$\m 25. Vectors $$\overline{\mathrm{a}}$$ and $$\overline{\mathrm{b}}$$ are such that $$|\overline{\mathrm{a}}|=1 ;|\overline{\m 26. If $$y$$ is a function of $$x$$ and $$\log (x+y)=2 x y$$, then the value of $$y^{\prime}(0)$$ is 27. If $$\cos 2 B=\frac{\cos (A+C)}{\cos (A-C)}$$. Then $$\tan A, \tan B, \tan C$$ are in 28. If $$\log _2 x+\log _4 x+\log _8 x+\log _{16} x=\frac{25}{36}$$ and $$x=2^{\mathrm{k}}$$ then $$\mathrm{k}$$ is 29. If $$\left|\begin{array}{ccc}\cos (A+B) & -\sin (A+B) & \cos (2 B) \\ \sin A & \cos A & \sin B \\ -\cos A & \sin A & \co 30. General solution of the differential equation $$\log \left(\frac{d y}{d x}\right)=a x+b y$$ is 31. $$\int(\sqrt{\tan x}+\sqrt{\cot x}) d x=$$ 32. If $$Z_1=2+i$$ and $$Z_2=3-4 i$$ and $$\frac{\overline{Z_1}}{\overline{Z_2}}=a+b i$$, then the value of $$-7 a+b$$ is (w 33. Let $$\alpha \in\left(0, \frac{\pi}{2}\right)$$ be fixed. If the integral $$\int \frac{\tan x+\tan \alpha}{\tan x-\tan \ 34. Two adjacent sides of a parallelogram are $$2 \hat{i}-4 \hat{j}+5 \hat{k}$$ and $$\hat{i}-2 \hat{j}-3 \hat{k}$$, then th 35. A water tank has a shape of inverted right circular cone whose semi-vertical angle is $$\tan ^{-1}\left(\frac{1}{2}\righ 36. The differential equation of all circles which pass through the origin and whose centres lie on $$\mathrm{Y}$$-axis is 37. If $$x^{\mathrm{k}}+y^{\mathrm{k}}=\mathrm{a}^{\mathrm{k}}(\mathrm{a}, \mathrm{k}>0)$$ and $$\frac{\mathrm{d} y}{\mathrm 38. The area (in sq. units) bounded by the curve $$y=x|x|, \mathrm{X}$$-axis and the lines $$x=-1$$ and $$x=1$$ is 39. The co-ordinates of the point, where the line $$\frac{x-1}{2}=\frac{y-2}{-3}=\frac{z+5}{4}$$ meets the plane $$2 x+4 y-\ 40. $$\lim _\limits{x \rightarrow 0} \frac{(1-\cos 2 x) \cdot \sin 5 x}{x^2 \sin 3 x}$$ is 41. If $$\mathrm{g}$$ is the inverse of $$\mathrm{f}$$ and $$\mathrm{f}^{\prime}(x)=\frac{1}{1+x^3}$$, then $$\mathrm{g}^{\p 42. A problem in statistics is given to three students A, B and C. Their probabilities of solving the problem are $$\frac{1} 43. Let $$A=\left[\begin{array}{ccc}1 & 1 & 1 \\ 0 & 1 & 3 \\ 1 & -2 & 1\end{array}\right], B=\left[\begin{array}{c}6 \\ 11 44. $$f(x)=\left\{\begin{array}{ll} \frac{1-\cos k x}{x^2}, & \text { if } x \leq 0 \\ \frac{\sqrt{x}}{\sqrt{16+\sqrt{x}}-4} 45. If $$\mathrm{D}, \mathrm{E}$$ and $$\mathrm{F}$$ are the mid-points of the sides $$\mathrm{BC}$$, $$\mathrm{CA}$$ and $$ 46. Two cards are drawn successively with replacement from a well shuffled pack of 52 cards, then mean of number of queens i 47. The equation of a plane, containing the line of intersection of the planes $$2 x-y-4=0$$ and $$y+2 z-4=0$$ and passing t 48. A random variable $$\mathrm{X}$$ assumes values 1, 2, 3, ....., n with equal probabilities, if $$\operatorname{var}(X)=E 49. The graphical solution set for the system of inequations $$x-2 y \leq 2,5 x+2 y \geq 10,4 x+5 y \leq 20, x \geq 0, y \ge 50. Let $$\mathrm{f}(0)=-3$$ and $$\mathrm{f}^{\prime}(x) \leq 5$$ for all real values of $$x$$. The $$\mathrm{f}(2)$$ can h

Physics

1. Light of wavelength ',$$\lambda$$' is incident on a slit of width '$$\mathrm{d}$$'. The resulting diffraction pattern is 2. Two S.H.Ms. are represented by equations $$\mathrm{y}_1=0.1 \sin \left(100 \pi \mathrm{t}+\frac{\pi}{3}\right)$$ and $$\ 3. A film of soap solution is formed between two straight parallel wires of length $$10 \mathrm{~cm}$$ each separated by $$ 4. An ideal gas in a container of volume 500 c.c. is at a pressure of $$2 \times 10^{+5} \mathrm{~N} / \mathrm{m}^2$$. The 5. A gas at N.T.P. is suddenly compressed to onefourth of its original volume. If $$\gamma=1.5$$, then the final pressure i 6. A particle of mass '$$\mathrm{m}$$' moves along a circle of radius '$$r$$' with constant tangential acceleration. If K.E 7. An e.m.f. $$E=4 \cos (1000 t)$$ volt is applied to an LR circuit of inductance $$3 \mathrm{~mH}$$ and resistance $$4 ~\O 8. In the reverse biasing of a p-n junction diode : 9. When a charge of $$3 ~\mathrm{C}$$ is placed in uniform electric field, it experiences a force of $$3000 \mathrm{~N}$$. 10. A soap bubble of radius '$$R$$' is blown. After heating a solution, a second bubble of radius '$$2 \mathrm{R}$$' is blow 11. In a transistor, in common emitter configuration, the ratio of power gain to voltage gain is 12. A galvanometer of resistance $$20 ~\Omega$$ gives a deflection of 5 divisions when $$1 \mathrm{~mA}$$ current flows thro 13. The equation of simple harmonic progressive wave is given by $$y=a \sin 2 \pi(b t-c x)$$. The maximum particle velocity 14. Five current carrying conductors meet at a point '$$\mathrm{O}$$' as shown in figure. The magnitude and direction of the 15. An alternating voltage of frequency '$$\omega$$' is induced in electric circuit consisting of an inductance '$$L$$' and 16. A gas is compressed at a constant pressure of $$50 \mathrm{~N} / \mathrm{m}^2$$ from a volume of $$10 \mathrm{~m}^3$$ to 17. The reactance of capacitor at $$50 \mathrm{~Hz}$$ is $$5 \Omega$$. If the frequency is increased to $$100 \mathrm{~Hz}$$ 18. Stationary waves can be produced in 19. The pressure exerted by an ideal gas at a particular temperature is directly proportional to 20. If a ray of light in denser medium strikes a rarer medium at angle of incidence $$i$$, the angles of reflection and refr 21. A spring has a certain mass suspended from it and its period for vertical oscillations is '$$T_1$$'. The spring is now c 22. When photons of energies twice and thrice the work function of a metal are incident on the metal surface one after other 23. A simple pendulum of length $$2 \mathrm{~m}$$ is given a horizontal push through angular displacement of $$60^{\circ}$$. 24. The force acting on the electron in hydrogen atom (Bohr' theory) is related to the principle quantum number '$$n$$' as 25. If the frequency of the input voltage is $$50 \mathrm{~Hz}$$, applied to a (a) half wave rectifier and (b) full wave rec 26. Periodic time of a satellite revolving above the earth's surface at a height equal to radius of the earth '$$R$$' is [ $ 27. The wavelength of light for the least energetic photons emitted in the Lyman series of the hydrogen spectrum is nearly [ 28. In Young's double slit experiment, the wavelength of light used is '$$\lambda$$'. The intensity at a point is '$$\mathrm 29. The side of a copper cube is $$1 \mathrm{~m}$$ at $$0^{\circ} \mathrm{C}$$. What will be the change in its volume, when 30. If current '$$I$$' is flowing in the closed circuit with collective resistance '$$R$$', the rate of production of heat e 31. Two coils $$\mathrm{A}$$ and $$\mathrm{B}$$ have mutual inductance 0.008 $$\mathrm{H}$$. The current changes in the coil 32. A thin rod of length $$L$$ has magnetic moment $$M$$ when magnetised. If rod is bent in a semicircular arc what is magne 33. A fluid of density '$$\rho$$' and viscosity '$$\eta$$' is flowing through a pipe of diameter '$$d$$', with a velocity '$ 34. In Young's double slit experiment, the fringe width is $$2 \mathrm{~mm}$$. The separation between the $$13^{\text {th }} 35. 10 A current is flowing in two straight parallel wires in the same direction. Force of attraction between them is $$1 \t 36. Consider a planet whose density is same as that of the earth but whose radius is three times the radius '$$R$$' of the e 37. When a certain metal surface is illuminated with light of frequency $$v$$, the stopping potential for photoelectric curr 38. If the length of an open organ pipe is $$33.3 \mathrm{~cm}$$, then the frequency of fifth overtone is [Neglect end corre 39. A transparent glass cube of length $$24 \mathrm{~cm}$$ has a small air bubble trapped inside. When seen normally through 40. The temperature of an ideal gas is increased from $$27^{\circ} \mathrm{C}$$ to $$927^{\circ} \mathrm{C}$$. The r.m.s. sp 41. A disc of radius $$R$$ and thickness $$\frac{R}{6}$$ has moment of inertia I about an axis passing through its centre an 42. A charge '$$q$$' moves with velocity '$$v$$' through electric (E) as well as magnetic field (B). Then the force acting o 43. A parallel combination of two capacitors of capacities '$$2 ~\mathrm{C}$$' and '$$\mathrm{C}$$' is connected across $$5 44. Consider the following statements $$\mathrm{A}$$ and $$\mathrm{B}$$. Identify the correct choice in the given answers. A 45. The charges $$2 \mathrm{q},-\mathrm{q},-\mathrm{q}$$ are located at the vertices of an equilateral triangle. At the circ 46. The magnetic field at a point $$\mathrm{P}$$ situated at perpendicular distance '$$R$$' from a long straight wire carryi 47. A particle at rest starts moving with constant angular acceleration $$4 ~\mathrm{rad} / \mathrm{s}^2$$ in circular path. 48. If the end correction of an open pipe is $$0.8 \mathrm{~cm}$$, then the inner radius of that pipe is 49. The mutual inductance (M) of the two coils is $$3 ~\mathrm{H}$$. The self inductances of the coils are $$4 ~\mathrm{H}$$ 50. A particle is vibrating in S.H.M. with an amplitude of $$4 \mathrm{~cm}$$. At what displacement from the equilibrium pos

MHT CET 2023 9th May Evening Shift

MCQ (Single Correct Answer)

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Let $$\alpha \in\left(0, \frac{\pi}{2}\right)$$ be fixed. If the integral $$\int \frac{\tan x+\tan \alpha}{\tan x-\tan \alpha} \mathrm{d} x=\mathrm{A}(x) \cos 2 \alpha+\mathrm{B}(x) \sin 2 \alpha+\mathrm{c},$$ (where $$\mathrm{c}$$ is a constant of integration), then functions $$\mathrm{A}(x)$$ and $$\mathrm{B}(x)$$ are respectively

$$x+\alpha$$ and $$\log |\sin (x+\alpha)|$$.

$$x-\alpha$$ and $$\log |\sin (x-\alpha)|$$.

$$x-\alpha$$ and $$\log |\cos (x-\alpha)|$$.

$$x+\alpha$$ and $$\log |\sin (x-\alpha)|$$.

MHT CET 2023 9th May Evening Shift

MCQ (Single Correct Answer)

-0

Two adjacent sides of a parallelogram are $$2 \hat{i}-4 \hat{j}+5 \hat{k}$$ and $$\hat{i}-2 \hat{j}-3 \hat{k}$$, then the unit vector parallel to its diagonal is

$$\frac{3}{7} \hat{\mathrm{i}}-\frac{6}{7} \hat{\mathrm{j}}+\frac{2}{7} \hat{\mathrm{k}}$$

$$\frac{2}{7} \hat{\mathrm{i}}-\frac{6}{7} \hat{\mathrm{j}}+\frac{3}{7} \hat{\mathrm{k}}$$

$$\frac{6}{7} \hat{\mathrm{i}}-\frac{2}{7} \hat{\mathrm{j}}+\frac{3}{7} \hat{\mathrm{k}}$$

$$\frac{1}{7} \hat{\mathrm{i}}+\frac{1}{7} \hat{\mathrm{j}}-\frac{3}{7} \hat{\mathrm{k}}$$

MHT CET 2023 9th May Evening Shift

MCQ (Single Correct Answer)

-0

A water tank has a shape of inverted right circular cone whose semi-vertical angle is $$\tan ^{-1}\left(\frac{1}{2}\right)$$. Water is poured into it at constant rate of 5 cubic meter/minute. The rate in meter/ minute at which level of water is rising, at the instant when depth of water in the tank is $$10 \mathrm{~m}$$ is

$$\frac{1}{5 \pi}$$

$$\frac{1}{15 \pi}$$

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

$$\frac{1}{10 \pi}$$

MHT CET 2023 9th May Evening Shift

MCQ (Single Correct Answer)

-0

The differential equation of all circles which pass through the origin and whose centres lie on $$\mathrm{Y}$$-axis is

$$\left(x^2-y^2\right) \frac{\mathrm{d} y}{\mathrm{~d} x}-2 x y=0$$

$$\left(x^2-y^2\right) \frac{\mathrm{d} y}{\mathrm{~d} x}+2 x y=0$$

$$\left(x^2-y^2\right) \frac{\mathrm{d} y}{\mathrm{~d} x}+x y=0$$

$$\left(x^2-y^2\right) \frac{\mathrm{d} y}{\mathrm{~d} x}-x y=0$$