MHT CET 2021 24th September Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Which of the following is an alkali metal? 2. The electrical conductance of unit volume (1 cm$$^3$$) of solution is called as 3. What is oxidation state of cobalt in a coordination complex if it's EAN is 36 and the value of C.N. is 6 (Given: Atomic 4. Which among the following cations will not form coloured compounds? (Atomic number $$\mathrm{Cu}=29, \mathrm{Ti}=22, \ma 5. Which of the following aldehydes is less reactive towards nucleophilic addition reaction? 6. Which of the following is an aldohexose? 7. Cannizzaro reaction is an example of 8. The solution containing $$3 \mathrm{~g}$$ urea (molar mass 60 ) per $$\mathrm{dm}^3$$ of water and another solution cont 9. Which following statement is true for vinylic halide? 10. What is the formal charge on 'N' atom in ion? 11. Identify the product 'B' in the following series of reactions. $$\mathrm{CH_3COOH+CH_3CH_2OH}$$ $$\stackrel{\mathrm{H}^{ 12. The solubility of sparingly soluble salt $$\mathrm{AB}_2$$ is $$1.0 \times 10^{-4} \mathrm{~mol} \mathrm{~dm}^{-3}$$. Wh 13. Which element from following in +3 oxidation state forms colourless compounds? 14. Which among the following compounds contains amino group? 15. What is IUPAC name of phloroglucinol? 16. In a first reaction 60% of reactant decomposes in 4.606 min. What is half life of reaction? (k = 0.1989 min$$^{-1}$$) 17. The density of chromium metal is 7 g cm$$^{-3}$$. If edge length of unit cell is 300 pm, identify the type of unit cell. 18. How many gram of H$$_2$$O are present in 0.25 mol of it? 19. Identify molecular formula of pyridine from following 20. Which of the following is a first step in mechanism of heterogenous catalysis? 21. Which of the following carboxylic acids has lowest boiling point? 22. For the reaction, $$2 \mathrm{~A}+\mathrm{B} \rightarrow 2 \mathrm{C}$$, rate of disappearance of $$\mathrm{A}$$ is $$0. 23. Which of following is an example of cross-linked polymers? 24. For isochoric process, the first law of thermodynamics can be expressed as 25. Which of the following alcohols has lowest boiling point? 26. What is the $$\mathrm{pH}$$ of $$0.005 \mathrm{~M} \mathrm{~H}_2 \mathrm{SO}_4$$ solution? 27. The solubility product expression for $$\mathrm{Ca}_3\left(\mathrm{PO}_4\right)_2$$ is represented as 28. Which among the following is NOT a feature of $$\mathrm{S}_{\mathrm{N}} 1$$ mechanism? 29. An element has $$\mathrm{BCC}$$ structure with edge length of unit cell $$600 \mathrm{~pm}$$. What is the atomic radius 30. When certain volume of gas expands against a constant external pressure of $$2.40 \times 10^5 \mathrm{~Pa}$$ at 300 $$\m 31. Which among the following pairs of electronic effect and it's example is NOT correct? 32. A certain mass of a gas occupies volume of 250 mL at 2 atm. Calculate the volume of gas if pressure is increased to 2.5 33. Vapour pressure of solution and of pure solvent are $$\mathrm{P}_1$$ and $$\mathrm{P}_1{ }^0$$ respectively. If $$\frac{ 34. Which of the following pairs of compounds is isomorphous? 35. What is internal energy change when $$62 \mathrm{~J}$$ of work is done on the system and $$128 \mathrm{~J}$$ of heat is 36. Which of the following catalyst/reagent is used to convert $$\mathrm{C} \equiv \mathrm{C}$$ triple bond to $$\mathrm{C}= 37. Which among the following reactions exhibits the reducing property of ozone? 38. Which of the following is a correct bridged name of deoxyriboseadenosine monophosphate? 39. What is IUPAC name of the following compound? 40. Which among following compounds of chlorine possesses Cl atom in highest oxidation state? 41. According to Raoult's law mole fraction of solute in solution in given by formula 42. What is maximum number of electrons accommodated in a subshell having azimuthal quantum number, $$\ell$$ = 2 ? 43. Half-life and rate constant for first order reaction are related by equation, 44. What is the conductivity of 0.02 M HCl solution if molar conductivity of the solution at 25$$^\circ$$C is 412.3 $$\Omega 45. Which among the following is a source of wool? 46. What is percentage atom economy during conversion of reactant to product if formula weight of reactants is 246 u and of 47. What is the charge required for the reduction of moles of Cu$$^{2+}$$ to Cu? 48. Which of the following amine is weakest base? 49. Which of following is NOT a redox reaction? 50. Which among the following is a correct order of increasing field strength of ligands?

Mathematics

1. The probability that at least one of the events $$E_1$$ and $$E_2$$ occurs is 0.6. If the simultaneous occurrence of $$\ 2. $$\lim _\limits{x \rightarrow 0} \frac{\sqrt{1-\cos x^2}}{1-\cos x}=$$ 3. If $$\mathrm{A}=\left[\begin{array}{cc}\lambda & \mathrm{i} \\ \mathrm{i} & -\lambda\end{array}\right]$$ and $$\mathrm{A 4. The distance 's' in meters covered by a particle in t seconds is given by $$s=2+27 t-t^3$$. The particle will stop after 5. If the polar co-ordinates of a point are $$\left(2, \frac{\pi^{\mathrm{c}}}{4}\right)$$, then its Cartesian co-ordinates 6. $$\int e^x\left(\frac{1+\sin x}{1+\cos x}\right) d x=$$ 7. The negation of '$$\forall x \in N, x^2+x$$ is even number' is 8. $$\int_\limits2^5 2[\mathrm{x}] \mathrm{dx}=\{\text { where }[\mathrm{x}] \text { denotes the greatest integer function 9. $$\int_\limits0^\pi x \sin x \cos ^4 x d x=$$ 10. The equation of the plane which passes through (2, $$-$$3, 1) and is normal to the line joining the points (3, 4, $$-$$1 11. A committee of 5 is to be formed out of 6 men and 4 ladies. The number of ways this can be done, when at most 2 ladies a 12. In a triangle ABC with usual notations a = 2, b = 3, then value of $$\frac{\cos 2 \mathrm{~A}}{\mathrm{a}^2}-\frac{\cos 13. The particular solution of the differential equation $$\left(1+e^{2 x}\right) d y+e^x\left(1+y^2\right) d x=0$$ at $$x=0 14. If $$y=1+x e^y$$, then $$\frac{d y}{d x}=$$ 15. Two dice are thrown simultaneously. If X denotes the number of sixes, then the expectation of X is 16. If $$G(3,-5, r)$$ is the centroid of $$\triangle A B C$$, where $$A \equiv(7,-8,1), B \equiv(p, q, 5), C \equiv(q+1,5 p, 17. The acute angle between the lines $$\left(x^2+y^2\right) \sin \theta+2 x y=0$$ is 18. For any non-zero vectors $$\bar{a}, \bar{b}, \bar{c}$$, the value of $$\bar{a} \cdot[(\bar{b} \times \bar{c}) \times(\ba 19. If the lines $$\frac{2 x-4}{\lambda}=\frac{y-1}{2}=\frac{z-3}{1}$$ and $$\frac{x-1}{1}=\frac{3 y-1}{\lambda}=\frac{z-2}{ 20. The order and degree of the differential equation $$\sqrt{\frac{d y}{d x}}-4 \frac{d y}{d x}-7 x=0$$ are respectively. 21. If $$x=e^t(\sin t-\cos t)$$ and $$y=e^t(\sin t+\cos t)$$, then $$\frac{d y}{d x}$$ at $$t=\frac{\pi}{3}$$ is 22. If the lines represented by $$(k^2+2) x^2+3 x y-6 y^2=0$$ are perpendicular to each other, then the values of $$\mathrm{ 23. If $$\bar{a}=3 \hat{i}+\hat{j}-\hat{k}, \bar{b}=2 \hat{i}-\hat{j}+23 \hat{k}$$ and $$\bar{c}=7 \hat{i}-\hat{j}+23 \hat{k 24. For the set of 50 observations, the sum of their squares is 3050 , their arithmetic mean is 6. Hence the standard deviat 25. If $$y=2 x$$ is a chord of circle $$x^2+y^2-10 x=0$$, then the equation of circle with this chord as diameter is 26. If $$\sin ^2 x+\cos ^2 y=1$$, then $$\frac{d y}{d x}=$$ 27. If $$f(x)=2\{x\}+5 x$$, where $$\{x\}$$ is fractional part function, then $$f(-1.4)$$ is 28. The curve $$y=a x^3+b x^2+c x+5$$ touches $$X$$-axis at $$P(-2,0)$$ and cuts $$Y$$-axis at a point $$Q$$, where its grad 29. The area of the region bounded by the curve $$y=2 x-x^2$$ and X-axis is 30. The equation of a line with slope $$-\frac{1}{\sqrt{2}}$$ and makes an intercept of $$2 \sqrt{2}$$ units on negative dir 31. If $$\mathrm{\frac{3+2i}{1+i}=\frac{1}{2}(x+iy)}$$, then x $$-$$ y = 32. If the angle between the vectors $$\overline{\mathrm{a}}=2 \lambda^2 \hat{\mathrm{i}}+4 \lambda \hat{\mathrm{j}}+\hat{\m 33. A population P grew at the rate given by the equation $$\frac{dP}{dt}=0.5P$$, then the population will become double in 34. If $$A=\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$$, and $$A(\operatorname{adj} A)=k 35. $$\int \cos ^3 x e^{\log (\sin x)^2} d x=$$ 36. The probability distribution of a random variable X is .tg {border-collapse:collapse;border-spacing:0;} .tg td{border- 37. If $$\mathrm{p}$$ : It is raining. $$\mathrm{q}$$ : Weather is pleasant then simplified form of the statement "It is not 38. If $$\mathrm{f}(\mathrm{x})=\mathrm{x}, \quad$$ for $$\mathrm{x} \leq 0$$ $$=0,\quad$$ for $$x>0$$, then the function $$ 39. A fair coin is tossed for a fixed number of times. If probability of getting 7 heads is equal to probability of getting 40. The region represented by the inequalities $$x \geq 6, y \geq 3,2 x+y \geq 10, x \geq 0, y \geq 0$$ is 41. IF $$A X=B$$, where $$A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right], X=\left[\begin{ 42. $$\int \frac{d x}{e^x+e^{-x}+2}=$$ 43. The co-ordinates of the points on the line $$\frac{x+2}{1}=\frac{y-1}{2}=\frac{z+1}{-2}$$ at a distance of 12 units from 44. The value of $$\tan ^{-1} 2+\tan ^{-1} 3$$ is 45. If $$\bar{a}+\bar{b}, \bar{b}+\bar{c}, \bar{c}+\bar{a}$$ are coterminus edges of a parallelopiped, then its volume is 46. The differential equation of all parabolas whose axis is $$y$$-axis, is 47. The minimum value of the function f(x) = x log x is 48. The general solution of the differential equation $$\frac{d y}{d x}=\tan \left(\frac{y}{x}\right)+\frac{y}{x}$$ is 49. $$\tan \mathrm{A}+2 \tan 2 \mathrm{~A}+4 \tan 4 \mathrm{~A}+8 \cot 8 \mathrm{~A}=$$ 50. If the vector equation of the plane $$\bar{r}=(2 \hat{i}+\hat{k})+\lambda \hat{i}+\mu(\hat{i}+2 \hat{j}-3 \hat{k})$$ in

Physics

1. A current 'I' produces a magnetic flux '$$\phi$$' per turn in a coil of '$$n$$' turns. Self inductance of the coil is '$ 2. A rejector circuit is the resonant circuit in which 3. A light of wavelength '$$\lambda$$' and intensity '$$\mathrm{I}$$' falls on photosensitive material. If '$$\mathrm{N}$$' 4. The current drawn from the battery in the given network is (Internal resistance of the battery is negligible) 5. The moment of inertia of a thin uniform rod of mass 'M' and length 'L' about an axis passing through a point at a distan 6. A current $$I=10 \sin (100 \pi t)$$ ampere, is passed in a coil which induces a maximum emf $$5 \pi$$ volt in neighbouri 7. The average density of the earth is [g is acceleration due to gravity] 8. Two bar magnets '$$\mathrm{P}$$' and '$$\mathrm{Q}$$' are kept in uniform magnetic field '$$\mathrm{B}$$' with magnetic 9. Which one of the following is NOT a correct expression for an ideal gas? [$$\mathrm{C_p}=$$ Molar specific heat of a gas 10. The molecular masses of helium and oxygen are 4 and 32 respectively. The ratio of r.m.s. speed of helium at 327$$^\circ$ 11. Which one of the following p-V diagram is correct for an isochoric process: 12. A magnetic dipole of magnetic moment $$\mathrm{M}$$, is freely suspended in a magnetic field of induction B. The minimum 13. In series LCR circuit, at resonance the peak value of current will be [$$\mathrm{E_0}$$ is peak emf, R is resistance, $$ 14. A particle is moving along the circular path with constant speed and centripetal acceleration 'a'. If the speed is doubl 15. The displacement of a particle performing S.H.M. is given by $$x=5 \sin (3 t+3)$$, where $$x$$ is in $$\mathrm{cm}$$ and 16. A cylindrical tube open at both ends has fundamental frequency 'n' in air. The tube is dipped vertically in water so tha 17. In the following electrical network, the value of 1 is 18. The half life of a radioactive substance is 30 minute. The time taken between 40% decay and 85% decay of the same radioa 19. Two monochromatic beams of intensities I and 4 I respectively are superposed to form a steady interference pattern. The 20. Three charges each of $$+1 \mu \mathrm{C}$$ are placed at the corners of an equilateral triangle. If the repulsive force 21. Velocity of sound waves in air is '$$\mathrm{V}$$' $$\mathrm{m} / \mathrm{s}$$. For a particular sound wave in air, path 22. Choose the correct statement. In conductors 23. For a transistor, the current ratio $$\alpha_{\mathrm{dc}}=\frac{69}{70}$$, the current gain $$\beta_{\mathrm{dc}}$$ is 24. 'n' small drops of same size fall through air with constant velocity $$5 \mathrm{~cm} / \mathrm{s}$$. They coalesce to f 25. The depth from the surface of the earth of radius $$\mathrm{R}$$, at which acceleration due to gravity will be $$60 \%$$ 26. A body of mass 'm' is moving with speed 'V' along a circular path of radius 'r'. Now the speed is reduced to $$\frac{V}{ 27. The path difference between two interfering light waves meeting at a point on the screen is $$\left(\frac{57}{2}\right) 28. Pressure inside two soap bubbles are 1.01 atm and 1.03 atm. The ratio between their volumes is (Pressure outside the soa 29. The length and diameter of a metal wire used in sonometer is doubled. The fundamental frequency will change from 'n' to 30. An alternating e.m.f. is $$\mathrm{e}=\mathrm{e}_0 \sin \omega \mathrm{t}$$. In what time the e.m.f. will have half its 31. A ray of light is incident on one face of an equilateral glass prism having refractive index $$\sqrt{2}$$. It produces t 32. The input a.c. voltage of frequency $$60 \mathrm{~Hz}$$ is applied to half-wave rectifier and also to full-wave rectifie 33. Three point masses, each of mass 'm' are kept at the corners of an equilateral triangle of side 'L'. The system rotates 34. A closed organ pipe and an open organ pipe of same length produce 2 beats per second when they are set into vibrations t 35. A rectangular loop $$\mathrm{PQMN}$$ with movable arm $$\mathrm{PQ}$$ of length $$12 \mathrm{~cm}$$ and resistance $$2 \ 36. Assume that for solar radiation, surface temperature of the sun is $$6000 \mathrm{~K}$$. If Wien's constant 'b' is $$2.8 37. The kinetic energy of a light body and a heavy body is same. Which one of them has greater momentum? 38. Four electric charges $$+\mathrm{q},+\mathrm{q},-\mathrm{q}$$ and $$-\mathrm{q}$$ are placed in order at the corners of 39. White light consists of wavelengths from $$480 \mathrm{~nm}$$ to $$672 \mathrm{~nm}$$. What will be the wavelength range 40. A metal sphere cools at the rate of $$1.5^{\circ} \mathrm{C} / \mathrm{min}$$ when its temperature is $$80^{\circ} \math 41. The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (i) second to first en 42. The length of the seconds pendulum is lm on earth. If the mass and diameter of the planet is 1.5 times that of the earth 43. A solenoid 2 m long and 4 cm in diameter has 4 layers of windings of 1000 turns each and carries a current of 5 A. What 44. A particle of charge 'q' and mass 'm' moves in a circular orbit of radius 'r' with angular speed '$$\omega$$'. The ratio 45. A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to 46. In a photoelectric experiment, a graph of maximum kinetic energy $$(\mathrm{KE}_{\text {max }})$$ against the frequency 47. If the work done in blowing a soap bubble of volume '$$\mathrm{V}$$' is '$$\mathrm{W}$$', then the work done in blowing 48. A monochromatic ray of light travels through glass slab and water column. The number of waves in glass slab of thickness 49. Capacitors of capacities $$\mathrm{C}_1, \mathrm{C}_2$$ and $$\mathrm{C}_3$$ are connected in series. If the combination 50. A monoatomic gas is suddenly compressed to $$(1 / 8)^{\text {th }}$$ of its initial volume adiabatically. The ratio of t

MHT CET 2021 24th September Evening Shift

MCQ (Single Correct Answer)

-0

$$\int \cos ^3 x e^{\log (\sin x)^2} d x=$$

$$ \frac{\sin ^3 x}{3}-\sin ^5 x+c $$

$$ \frac{\sin ^3 x}{3}-\frac{\sin ^5 x}{5}+c $$

$$ \frac{\sin ^3 x}{3}+\frac{\sin ^5 x}{5}+c $$

$$ \sin ^3 x+\sin ^5 x+c $$

MHT CET 2021 24th September Evening Shift

MCQ (Single Correct Answer)

-0

The probability distribution of a random variable X is

$$\mathrm{X=x}$$	1	2	3	.........	$$\mathrm{n}$$
$$\mathrm{P(X=x)}$$	$$\mathrm{\frac{1}{n}}$$	$$\mathrm{\frac{1}{n}}$$	$$\mathrm{\frac{1}{n}}$$	.........	$$\mathrm{\frac{1}{n}}$$

then Var(X) =

$$ \frac{\mathrm{n}^2-1}{12} $$

$$\frac{n^2-n}{6}$$

$$\frac{n^2-n}{12}$$

$$\frac{\mathrm{n}^2-1}{6}$$

MHT CET 2021 24th September Evening Shift

MCQ (Single Correct Answer)

-0

If $$\mathrm{p}$$ : It is raining.

$$\mathrm{q}$$ : Weather is pleasant

then simplified form of the statement "It is not true, if it is raining then weather is not pleasant" is

It is not raining or weather is pleasant.

It is raining or weather is not pleasant.

It is raining and the weather is pleasant.

MHT CET 2021 24th September Evening Shift

MCQ (Single Correct Answer)

-0

If $$\mathrm{f}(\mathrm{x})=\mathrm{x}, \quad$$ for $$\mathrm{x} \leq 0$$

$$=0,\quad$$ for $$x>0$$, then the function $$f(x)$$ at $$x=0$$ is

not continuous and not differentiable.

not continuous but differentiable.

continuous but not differentiable.

continuous and differentiable.

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