MHT CET 2021 23rd September Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Which of the following statements about tropone is true? 2. Edge length of unit cell of BCC structure is 352 pm. What is radius of the atom? 3. What is the constant external pressure of an ideal gas when expanded from $$2 \times 10^{-2} \mathrm{~m}^3$$ to $$3 \tim 4. The conductivity of $$0.012 \mathrm{~M} \mathrm{~NaBr}$$ solution is $$2.67 \times 10^{-4} \mathrm{~S} \mathrm{~cm}^{-1} 5. How many molecules of ammonia gas are present in 67.2 dm$$^3$$, measured at S.T.P.? 6. What is the formal charge on 'C' atom in ? 7. Identify 2-propoxy benzene from following : 8. Identify the chiral molecule from the following: 9. Which among the followings is an allylic halide? 10. Which among the following salts undergoes hydrolysis? 11. What is the SI unit of density? 12. What is value of spin only magnetic moment of $$\mathrm{Ni}(\mathrm{Z}=28)$$ in +2 oxidation state? 13. IUPAC name of the compound $$(\mathrm{CH}_3)_4 \mathrm{C}$$ is 14. What is IUPAC name of catechol? 15. At $$298 \mathrm{~K}, 0.1 \mathrm{M}$$ solution of acetic acid is $1.34 \%$ ionized. What is the dissociation constant o 16. During a process, system absorbs $$710 \mathrm{~J}$$ of heat and increases the internal energy by $$460 \mathrm{~J}$$. W 17. For simple cubic crystal edge length is expressed as 18. Identify the use of mixture of $$\mathrm{Ar}$$ and $$\mathrm{N}_2$$ from following. 19. Which of the following is an alkali metal? 20. During the electrolysis of fused $$\mathrm{NaCl}$$, the product obtained at anode is 21. Identify product B in following reaction. Propanone $$\xrightarrow{\mathrm{Ba}(\mathrm{OH})_2} \mathrm{~A} \xrightarrow[ 22. Which among the following oxides is acidic in nature? 23. The units of monosaccharides present in raffinose are 24. Identify the protein present in nail. 25. Identify the products of following reaction : $$\mathrm{C}_6 \mathrm{H}_5 \mathrm{COOC}_2 \mathrm{H}_5 \xrightarrow[\tex 26. An element is found to crystallize with $$\mathrm{BCC}$$ structure having density $$8.55 \mathrm{~g} \mathrm{~cm}^{-3}$$ 27. Which of the following elements in their respective oxidation states does not develop spin only magnetic moment? [$$\mat 28. What is IUPAC name of $$[\mathrm{Co}(\mathrm{H}_2 \mathrm{O})(\mathrm{NH}_3)_5] \mathrm{I}_3$$ ? 29. What is effective atomic number of $$\mathrm{Pt}$$ in $$\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)_4\right]^{2+}$$ ? (G 30. Which among following compounds is a secondary amine? 31. What is vapour pressure of a solution containing $$1 \mathrm{~mol}$$ of a non-volatile solute in $$36 \mathrm{~g}$$ of w 32. $$\mathrm{pH}$$ of soft drink is 3.6. Calculate the concentration of hydrogen ions in it. 33. Which of the following solutions behaves nearly as an ideal solution? 34. Identify monomers used for manufacturing of Terylene? 35. What is the frequency of yellow light having wavelength $$580 \mathrm{~nm}$$ ? 36. Which of the following equations represents integrated rate law for zero order reaction? 37. The IUPAC name of following compound is 38. Identify the compound formed from elements X, Y, Z having oxidation state +2, +5, $$-$$2 respectively. 39. Which of the following statements is true for adsorption? 40. Which of following compounds does not undergo vinyl polymerization? 41. Identify the hetero atom and number of double bonds respectively present in furan? 42. Identify compound A from following reaction. $$\mathrm{A}+\mathrm{C}_2 \mathrm{H}_5 \mathrm{MgBr} \xrightarrow[\text { e 43. How many hydrogen atoms are bonded to ammonium ion during solvation? 44. What is the weight of $$\mathrm{Al}$$ deposited at cathode when 1 ampere current is passed through molten $$\mathrm{AlCl 45. Ammonia and oxygen react at high temperature as $$4 \mathrm{NH}_{3(\mathrm{~g})}+5 \mathrm{O}_{2(\mathrm{~g})} \longrigh 46. Which among the following is NOT an intensive property? 47. Which of the following represents integrated rate law equation for gas phase first order reaction, $$\mathrm{A}_{(\mathr 48. The solution containing $$6 \mathrm{~g}$$ urea (molar mass 60 ) per $$\mathrm{dm}^3$$ of water and another solution cont 49. Which of following is used for synthesis of adipic acid enzymatically by Drath and Frost? 50. Identify the product formed when ethyl benzene reacts with nitric acid.

Mathematics

1. The vectors $$\overrightarrow{\mathrm{AB}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}}$$ and $$\overrightarrow{\mathrm{AC}}=5 2. The principal solutions of $$\cot x=\sqrt{3}$$ are 3. The area of the region included between the parabolas $$y^2=8 x$$ and $$x^2=8 y$$, is 4. "If two triangles are congruent, then their areas are equal." is the given statement, then the contrapositive of the inv 5. Radium decomposes at the rate proportional to the amount present at any time. If $$\mathrm{P} \%$$ of amount disappears 6. The minimum value of the objective function $$z=4 x+6 y$$ subject to $$x+2 y \geq 80,3 x+y \geq 75, x, y \geq 0$$ is 7. The joint equation of pair of lines through the origin and having slopes $$(1+\sqrt{2})$$ and $$\frac{1}{(1+\sqrt{2})}$$ 8. If $$4 a b=3 h^2$$, then the ratio of slopes of the lines represented by $$a x^2+2 h x y+b y^2=0$$ is 9. If $$A=\left[\begin{array}{ccc}5 & 6 & 3 \\ -4 & 3 & 2 \\ -4 & -7 & 3\end{array}\right]$$, then cofactors of all element 10. A man is known to speck truth 3 out of 4 times. He throws a die and reports that it is 6. Then the probability that it i 11. If $$\bar{a}=2 \hat{i}+3 \hat{j}-\hat{k}, \bar{b}=-\hat{i}+2 \hat{j}-4 \hat{k}$$ and $$\bar{c}=\hat{i}+\hat{j}-2 \hat{k} 12. The differential equation obtained by eliminating A and B from $$y=A \cos \omega t+B \sin \omega t$$ 13. The Cartesian equation of a plane which passes through the points $$\mathrm{A}(2,2,2)$$ and making equal nonzero interce 14. If $$y=x \tan y$$, then $$\frac{d y}{d x}=$$ 15. $$\int_\limits0^\pi \frac{1}{4+3 \cos x} d x=$$ 16. The distance between the lines $$3 x+4 y=9$$ and $$6 x+8 y=15$$ is 17. The equation of common tangent to the circles $$x^2+y^2-4 x+10 y+20=0$$ and $$x^2+y^2+8 x-6 y-24=0$$ is 18. The radius of a circular plate is increasing at the rate of $$0.01 \mathrm{~cm} / \mathrm{sec}$$, when the radius is $$1 19. The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face i 20. The particular solution of the differential equation $$y(1+\log x) \frac{d x}{d y}-x \log x=0$$ when $$x=e, y=e^2$$ is 21. If $$\mathrm{G}(\overline{\mathrm{g}}), \mathrm{H}(\overline{\mathrm{h}})$$ and $$\mathrm{P}(\overline{\mathrm{p}})$$ ar 22. The co-ordinates of the foot of the perpendicular drawn from the point $$2 \hat{i}-\hat{j}+5 \hat{k}$$ to the line $$\ve 23. Which of the following matrices are invertible? $$\begin{aligned} & \mathrm{A}=\left[\begin{array}{cc} 2 & 3 \\ 10 & 15 24. If $${ }^{11} \mathrm{C}_4+{ }^{11} \mathrm{C}_5+{ }^{12} \mathrm{C}_6+{ }^{13} \mathrm{C}_7={ }^{14} \mathrm{C}_5$$, th 25. $$\int \sec ^{-1} x d x=$$ 26. If the standard deviation of data is 12 and mean is 72, then coefficient of variation is 27. If $$x=a(\theta+\sin \theta)$$ and $$y=a(1-\cos \theta)$$ then $$\left(\frac{d^2 y}{d x^2}\right)_{at~ \theta=\pi / 2}=$ 28. If $$\sin (y+z-x), \sin (z+x-y)$$ and $$\sin (x+y-z)$$ are in AP, then 29. The negation of inverse of $$\sim \mathrm{p} \rightarrow \mathrm{q}$$ is 30. Let $$\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$$ and $$\overline{\mathrm{b}}=\hat{\m 31. $$\begin{aligned} & \text { If the function given by} \mathrm{f}(\mathrm{x}) \\ & =-2 \sin \mathrm{x} \quad-\pi \leq \ma 32. If $$\tan ^{-1}(2 x)+\tan ^{-1}(3 x)=\frac{\pi}{4}$$, where $$x>0$$, then $$x=$$ 33. The projection of $$\bar{a}=\hat{i}-2 \hat{j}+\hat{k}$$ on $$\bar{b}=2 \hat{i}-\hat{j}+\hat{k}$$ is 34. Let two cards are drawn at random from a pack of 52 playing cards. Let X be the number of aces obtained. Then the value 35. The order and degree of the differential equation $$\frac{d^2 y}{d x^2}=\sqrt{\frac{d y}{d x}}$$ are respectively 36. $$\int_\limits1^3\left[\tan ^{-1}\left(\frac{x}{x^2-1}\right)+\tan ^{-1}\left(\frac{x^2-1}{x}\right)\right] d x=$$ 37. If amplitude of $$(z-2-3 i)$$ is $$\frac{3 \pi}{4}$$, then locus of $$z$$ is (where $$z=x+i y$$) 38. A fair coin is tossed 100 times. The probability of getting a head for even number of times is 39. If $$\int \frac{\sqrt{x}}{x(x+1)} d x=k \tan ^{-1} m+c$$, (where c is constant of integration), then 40. The equation of tangent to the curve $$y=\sqrt{2} \sin \left(2 x+\frac{\pi}{4}\right)$$ at $$x=\frac{\pi}{4}$$, is 41. With usual notations in $$\triangle$$ABC, if $$\frac{\sin A}{\sin C}=\frac{\sin (A-B)}{\sin (B-C)}$$, then $$a^2, b^2, c 42. The general solution of the differential equation $$\cos (x+y) \frac{d y}{d x}=1$$ is 43. The derivative of the function $$\cot ^{-1}\left[(\cos 2 x)^{1 / 2}\right]$$ at $$x=\pi / 6$$ is 44. The domain of the function $$\log _{10}\left(x^2-5 x+6\right)$$ is 45. If $$\bar{a}=2 \hat{i}-\hat{j}+\hat{k}, \bar{b}=\hat{i}+2 \hat{j}-3 \hat{k}$$ and $$\bar{c}=3 \hat{i}+\lambda \hat{j}+5 46. The area of the triangle $$\mathrm{ABC}$$ is $$10 \sqrt{3} \mathrm{~cm}^2$$, angle $$\mathrm{B}$$ is $$60^{\circ}$$ and 47. If the slopes of the lines given by the equation $$a x^2+2 h x y+b y^2=0$$ are in the ratio $$5: 3$$, then the ratio $$h 48. For all real $$x$$, the minimum value of the function $$f(x)=\frac{1-x+x^2}{1+x+x^2}$$ is 49. $$\int \frac{d x}{\cos x \sqrt{\cos 2 x}}=$$ 50. If the function defined by $$f(x)=K(x-x^2)$$ if $$0

Physics

1. The moment of inertia of a body about the given axis, rotating with angular velocity 1 rad/s is numerically equal to 'P' 2. An electron in a circular orbit of radius $$0.05 \mathrm{~nm}$$ performs $$10^{14}$$ revolutions/second. What is the mag 3. A glass rod of radius '$$r_1$$' is inserted symmetrically into a vertical capillary tube of radius '$$r_2$$' ($$r_1 4. de-Broglie wavelength associated with an electron accelerated through a potential difference '$$\mathrm{V}$$' is '$$\lam 5. When the temperature of a semiconductor is increased, its resistance and electric conductivity respectively. 6. A bob of simple pendulum of mass 'm' perform $$\mathrm{SHM}$$ with amplitude '$$\mathrm{A}$$' and period 'T'. Kinetic en 7. Two positive ions, each carrying a charge 'q' are separated by a distance 'd'. If 'F' is the force of repulsion between 8. Two circular loops P and Q are made from a uniform wire. The radii of P and Q are R$$_1$$ and R$$_2$$ respectively. The 9. A metre scale is supported on a wedge at its centre of gravity. A body of weight 'w'. is suspended from the $$20 \mathrm 10. A circuit containing resistance R$$_1$$, inductance L$$_1$$ and capacitance C$$_1$$ connected in series resonates at the 11. An object executes SHM along $$x$$-axis with amplitude $$0.06 \mathrm{~m}$$. At certain distance '$$\mathrm{x}$$' metre 12. Three charges $$-\mathrm{q}, \mathrm{Q}$$ and $$-\mathrm{q}$$ are placed at equal distances on a straight line. If the t 13. In photoelectric effect, the photo current 14. If the potential difference across a capacitor is increased from $$5 \mathrm{~V}$$ to $$15 \mathrm{~V}$$, then the ratio 15. A body of mass 'm' and radius of gyration 'K' has an angular momentum 'L'. Then its angular velocity is 16. In Young's double slit experiment, the intensity at a point where path difference is $$\frac{\lambda}{6}$$ ($$\lambda$$ 17. In Young's double slit experiment, the distance of $$\mathrm{n}^{\text {th }}$$ dark band from the central bright band i 18. A uniform rope of length $$12 \mathrm{~m}$$ and mass $$6 \mathrm{~kg}$$ hangs vertically from the rigid support. A block 19. For an ideal gas, $$R=\frac{2}{3} C_v$$. This suggests that the gas consists of molecules, which are [$$\mathrm{R}=$$ un 20. For a two input AND gate, the four entries are shown in the truth table. Identify the correct ones out of these $$(\math 21. A projectile is thrown with an initial velocity $$(a \hat{i}+b \hat{j}) \mathrm{m} / \mathrm{s}$$, where $$\hat{i}$$ and 22. To determine the internal resistance of a cell by using a potentiometer, the null point is at $$1 \mathrm{~m}$$ when shu 23. The rms speed of a gas molecule is '$$\mathrm{V}$$' at pressure '$$\mathrm{P}$$'. If the pressure is increased by two ti 24. A body executes SHM under the action of force '$$\mathrm{F}_1$$' with time period '$$\mathrm{T}_1$$'. If the force is ch 25. A long solenoid carrying current $$\mathrm{I}_1$$ produces magnetic field $$\mathrm{B}_1$$ along its axis. If the curren 26. A conducting loop of resistance 'R' is moved to magnetic field, the total induced charge depends upon 27. Equal volumes of two gases, having their densíties in the ratio of $$1: 16$$ exert equal pressures on the walls of two c 28. The self inductance of solenoid of length $$31.4 \mathrm{~cm}$$, area of cross section $$10^{-3} \mathrm{~m}^2$$ having 29. The charge on each capacitor when a voltage source os 15 V is connected in the circuit as shown, is 30. According to de-Broglie hypothesis if an electron of mass '$$m$$' is accelerated by potential difference '$$V$$', the as 31. What is the effect of pressure on the speed of sound in a medium, if pressure is doubled at constant temperature? 32. Two sound waves having wavelengths $$5.0 \mathrm{~m}$$ and $$5.5 \mathrm{~m}$$ propagates in a gas with velocity 300 $$\ 33. In biprism experiment, $$6^{\text {th }}$$ bright band with wavelength '$$\lambda_1$$' coincides with $$7^{\text {th }}$ 34. The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite will satellite 35. In the given circuit, the current in 8$$\Omega$$ resistance is 1.5 A. The total current (I) flowing in the circuit is 36. 'Circle of least confusion' refers to which one of the following defects occurring in images formed by mirrors or lenses 37. An ice cube of edge $$1 \mathrm{~cm}$$ melts in a gravity free container. The approximate surface area of water formed i 38. A plano-convex lens of refractive index ($$\mu_1^{\prime}$$ fits exactly into a plano-concave lens of refractive index $ 39. A cylindrical rod has temperatures '$$T_1$$' and '$$T_2$$' at its ends. The rate of flow of heat is '$$Q_1$$' cal $$\mat 40. Energy of electron in the second orbit of hydrogen atom is $$\mathrm{E}$$. The energy of electron '$$\mathrm{E}_3$$' in 41. A series L-C-R circuit containing a resistance of $$120 ~\Omega$$ has angular frequency $$4 \times 10^5 \mathrm{~rad} \m 42. A body of mass 'M' and radius 'R', situated on the surface of the earth becomes weightless at its equator when the rotat 43. A circuit has self-inductance 'L' H and carries a current 'I' A. To prevent sparking when the circuit is switched off, a 44. A straight wire of diameter $$0.4 \mathrm{~mm}$$ carrying a current of $$2 \mathrm{~A}$$ is replaced by another wire of 45. In a CE transistor, a change of $$8.0 \mathrm{~mA}$$ in the emitter current produces a change of $$7.8 \mathrm{~mA}$$ in 46. Water rises upto a height of $$4 \mathrm{~cm}$$ in a capillary tube. The lower end of the capillary tube is at a depth o 47. The initial pressure and volume of a gas is '$$\mathrm{P}$$' and '$$\mathrm{V}$$' respectively. First by isothermal proc 48. A particle is performing U.C.M. along the circumference of a circle of diameter $$50 \mathrm{~cm}$$ with frequency $$2 \ 49. The frequency of a tuning fork is $$220 \mathrm{~Hz}$$ and the velocity of sound in air is $$330 \mathrm{~m} / \mathrm{s 50. Two point charges $$+3 \mu \mathrm{C}$$ and $$+8 \mu \mathrm{C}$$ repel each other with a force of $$40 \mathrm{~N}$$. I

MHT CET 2021 23rd September Evening Shift

MCQ (Single Correct Answer)

-0

If the slopes of the lines given by the equation $$a x^2+2 h x y+b y^2=0$$ are in the ratio $$5: 3$$, then the ratio $$h^2: a b=$$

$$15: 16$$

$$5: 3$$

$$3: 5$$

$$16: 15$$

MHT CET 2021 23rd September Evening Shift

MCQ (Single Correct Answer)

-0

For all real $$x$$, the minimum value of the function $$f(x)=\frac{1-x+x^2}{1+x+x^2}$$ is

$$\frac{1}{3}$$

MHT CET 2021 23rd September Evening Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{d x}{\cos x \sqrt{\cos 2 x}}=$$

$$\sin ^{-1}(\tan x)+c$$

$$\frac{1}{2} \log \left|\tan \left(\frac{\pi}{4}+x\right)\right|+c$$

$$2 \log \left|\frac{1+\tan x}{1-\tan x}\right|+c$$

$$\frac{1}{2} \log \left|\frac{1-\tan x}{1+\tan x}\right|+c$$

MHT CET 2021 23rd September Evening Shift

MCQ (Single Correct Answer)

-0

If the function defined by $$f(x)=K(x-x^2)$$ if $$0 < x < 1=0$$, otherwise is the p.d.f. of a r.v.X, then the value of $$P\left(X<\frac{1}{2}\right)$$ is

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

$$ \frac{1}{3} $$

$$ \frac{1}{4} $$

$$ \frac{2}{3} $$

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