MHT CET 2023 14th May Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Which from following molecules does NOT contain nitrogen in it? 2. Calculate the volume of unit cell if an element having molar mass $$56 \mathrm{~g} \mathrm{~mol}^{-1}$$ that forms bcc u 3. Find the number of orbitals and maximum electrons respectively present in $$\mathrm{M}$$-shell? 4. Which from following expressions is used to find the cell potential of $$\mathrm{Cd}_{(\mathrm{s})}\left|\mathrm{Cd}_{(\ 5. Which of the following is formed when propene is heated with bromine at high temperature? 6. Identify the product '$$B$$' in the following sequence of reactions. $$\mathrm{CH}_3 \mathrm{Br} \xrightarrow{\mathrm{KC 7. Identify '$$\mathrm{A}$$' in the following reaction. A+ Acetic anhydride $$\xrightarrow{\mathrm{H}^{+}}$$ Aspirin + Acet 8. What is the value of $$\angle \mathrm{S}-\mathrm{S}-\mathrm{S}$$ in puckered $$\mathrm{S}_8$$ rhombic sulfur? 9. Identify the reagent used in the following reaction. Benzoic acid $$\xrightarrow[\Delta]{\text { Reagent }}$$ Benzoyl ch 10. Which activity from following is exhibited by Lewis base according to definition? 11. Which of the following ion has greater coagulating power for negatively charged sol? 12. If enthalpy change for following reaction at $$300 \mathrm{~K}$$ is $$+7 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ find the entr 13. Identify the polymer obtained from 14. What is IUPAC name of the following compound? 15. Calculate the $$\mathrm{pH}$$ of $$0.01 \mathrm{~M}$$ strong dibasic acid. 16. Which among the following cations produces colourless aqueous solution in their respective oxidation state? 17. What is the number of moles of electrons gained by one mole oxidizing agent in following redox reaction? $$\mathrm{Zn_{( 18. Find the temperature in degree Celsius if volume and pressure of 2 mole ideal gas is $$20 \mathrm{~dm}^3$$ and $$4.926 \ 19. What is the geometry of $$\mathrm{PCl}_5$$ molecule as per VSEPR? 20. What is coordination number of central metal ion in $$\left[\mathrm{Fe}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{ 21. Which among the following is NOT a true statement for enantiomers? 22. Which from following formulae is of sodium hexanitrocobaltate(III)? 23. Which isomer among the following has the highest boiling point? 24. Which element from following exhibits the highest number of allotropes? 25. Which of the following is a pair of dihydric phenols? 26. Calculate $$\Delta \mathrm{H}$$ for following reaction, at $$25{ }^{\circ} \mathrm{C}$$. $$\mathrm{NH}_2 \mathrm{CN}_{(\ 27. What is number of atoms present in $$2.24 \mathrm{~dm}^3 \mathrm{~NH}_{3(\mathrm{~g})}$$ at STP? 28. What is the number of moles of tertiary carbon atoms in a molecule of isobutane? 29. According to carbinol system, name of isopropyl alcohol is 30. Calculate the relative lowering of vapour pressure if the vapour pressure of benzene and vapour pressure of solution of 31. Which from following is NOT true about voltaic cell? 32. Calculate the percent atom economy when a product of formula weight $$175 \mathrm{u}$$ is obtained in a chemical reactio 33. Identify false statement regarding isothermal process from following. 34. Calculate dissociation constant of $$0.001 \mathrm{M}$$ weak monoacidic base undergoing $$2 \%$$ dissociation. 35. Find the rate law for the reaction, $$\mathrm{CHCl}_{3(\mathrm{~g})}+\mathrm{Cl}_{2(\mathrm{~g})} \rightarrow \mathrm{CC 36. The rate for reaction $$2 \mathrm{~A}+\mathrm{B} \rightarrow$$ product is $$6 \times 10^{-4} \mathrm{~mol} \mathrm{~dm}^ 37. Calculate molar conductivity of $$\mathrm{NH}_4 \mathrm{OH}$$ at infinite dilution if molar conductivities of $$\mathrm{ 38. Calculate radius of third orbit of $$\mathrm{He}^{+}$$. 39. Calculate the depression in freezing point of solution when $$4 \mathrm{~g}$$ nonvolatile solute of molar mass $$126 \ma 40. In an ionic crystalline solid, atoms of element Y forms hcp structure. The atoms of element X occupy one third of tetrah 41. What is total number of crystal systems associated with 14 Bravais lattices? 42. Which from following catalyst is used in decomposition of $$\mathrm{KCl}_3$$ ? 43. Which from following polymers is used to obtain plastic dinner ware? 44. Identify non reducing sugar from following. 45. In which of the following carbohydrate, molecular mass increases by $$84 \mathrm{u}$$ after complete acetylation? 46. Which element from following exhibits common oxidation state +2 ? 47. Calculate half life of first order reaction if rate constant of reaction is $$2.772 \times 10^{-3} \mathrm{~s}^{-1}$$ 48. Which among the following is NOT colligative property? 49. Identify the reaction in which carbonyl group of aldehydes and ketones is reduced to methylene group on treatment with h 50. Identify the product '$$\mathrm{B}$$' in the following reaction. Toluene $$\xrightarrow[\mathrm{CS}_2]{\text { Chromylch

Mathematics

1. The negation of the statement "The number is an odd number if and only if it is divisible by 3." 2. Two cards are drawn successively with replacement from well shuffled pack of 52 cards, then the probability distribution 3. For an initial screening of an entrance exam, a candidate is given fifty problems to solve. If the probability that the 4. General solution of the differential equation $$\cos x(1+\cos y) \mathrm{d} x-\sin y(1+\sin x) \mathrm{d} y=0$$ is 5. The variance of 20 observations is 5. If each observation is multiplied by 2, then variance of resulting observations is 6. The statement $$[(p \rightarrow q) \wedge \sim q] \rightarrow r$$ is tautology, when $$r$$ is equivalent to 7. The solution set of the inequalities $$4 x+3 y \leq 60, y \geq 2 x, x \geq 3, x, y \geq 0$$ is represented by region 8. If the line $$x-2 y=\mathrm{m}(\mathrm{m} \in \mathrm{Z})$$ intersects the circle $$x^2+y^2=2 x+4 y$$ at two distinct po 9. If $$\bar{a}, \bar{b}, \bar{c}$$ are three vectors such that $$|\bar{a}+\bar{b}+\bar{c}|=1, \overline{\mathrm{c}}=\lambd 10. The equation $$x^3+x-1=0$$ has 11. Let $$\bar{a}, \bar{b}, \bar{c}$$ be three vectors such that $$|\bar{a}|=\sqrt{3}, |\bar{b}|=5, \bar{b} \cdot \bar{c}=10 12. Let $$A=\left[\begin{array}{cc}2 & -1 \\ 0 & 2\end{array}\right].$$ If $$B=I-{ }^3 C_1(\operatorname{adj} A)+{ }^3 C_2(\ 13. If $$\triangle \mathrm{ABC}$$ is right angled at $$\mathrm{A}$$, where $$A \equiv(4,2, x), \mathrm{B} \equiv(3,1,8)$$ an 14. The angle between the lines, whose direction cosines $$l, \mathrm{~m}, \mathrm{n}$$ satisfy the equations $$l+\mathrm{m} 15. Let $$f: R \rightarrow R$$ be a function such that $$\mathrm{f}(x)=x^3+x^2 \mathrm{f}^{\prime}(1)+x \mathrm{f}^{\prime \ 16. If $$\sin (\theta-\alpha), \sin \theta$$ and $$\sin (\theta+\alpha)$$ are in H.P., then the value of $$\cos 2 \theta$$ i 17. $$\text { If } y=\left(\sin ^{-1} x\right)^2+\left(\cos ^{-1} x\right)^2, \text { then }\left(1-x^2\right) y_2-x y_1=$$ 18. If $$a>0$$ and $$z=\frac{(1+i)^2}{a-i}, i=\sqrt{-1}$$, has magnitude $$\frac{2}{\sqrt{5}}$$, then $$\bar{z}$$ is 19. In $$\triangle \mathrm{ABC}$$, with usual notations, $$2 \mathrm{ac} \sin \left(\frac{1}{2}(\mathrm{~A}-\mathrm{B}+\math 20. $$\int \frac{\sin 2 x\left(1-\frac{3}{2} \cos x\right)}{e^{\sin ^2 x+\cos ^3 x}} d x=$$ 21. If $$\mathrm{f}^{\prime}(x)=\tan ^{-1}(\sec x+\tan x),-\frac{\pi}{2} 22. If $$\int \frac{\cos \theta}{5+7 \sin \theta-2 \cos ^2 \theta} d \theta=A \log _e|f(\theta)|+c$$ (where $$c$$ is a const 23. If $$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$$ are unit vectors and $$\theta$$ is angle betw 24. The integral $$\int_\limits{\frac{\pi}{6}}^{\frac{\pi}{3}} \sec ^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x d 25. The principal solutions of the equation $$\sec x+\tan x=2 \cos x$$ are 26. If $$\bar{a}, \bar{b}, \bar{c}$$ are three vectors with magnitudes $$\sqrt{3}$$, 1, 2 respectively, such that $$\bar{a} 27. Let the curve be represented by $$x=2(\cos t+t \sin t), y=2(\sin t-t \cos t)$$. Then normal at any point '$$t$$' of the 28. Equation of the plane passing through $$(1,-1,2)$$ and perpendicular to the planes $$x+2 y-2 z=4$$ and $$3 x+2 y+z=6$$ i 29. If $$\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi$$, then the value of $$x^{2025}+x^{2026}+x^{2027}$$ is 30. $$\mathrm{p}$$ is the length of perpendicular from the origin to the line whose intercepts on the axes are a and $$\math 31. $$\text { If } f(x)= \begin{cases}3\left(1-2 x^2\right) & ; 0 32. $$\int \frac{\sin x+\sin ^3 x}{\cos 2 x} d x=A \cos x+B \log \mathrm{f}(x)+c$$ (where $$\mathrm{c}$$ is a constant of in 33. If $$y=[(x+1)(2 x+1)(3 x+1) \ldots \ldots(\mathrm{n} x+1)]^n$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x=0$$ i 34. Let $$\mathrm{B} \equiv(0,3)$$ and $$\mathrm{C} \equiv(4,0)$$. The point $$\mathrm{A}$$ is moving on the line $$y=2 x$$ 35. $$\lim _\limits{x \rightarrow \infty} x^3\left\{\sqrt{x^2+\sqrt{1+x^4}}-x \sqrt{2}\right\}=$$ 36. The money invested in a company is compounded continuously. If ₹ 200 invested today becomes ₹ 400 in 6 years, then at th 37. The range of the function $$\mathrm{f}(x)=\frac{x^2}{x^2+1}$$ is 38. The differential equation of $$y=\mathrm{e}^x(\mathrm{a} \cos x+\mathrm{b} \sin x)$$ is 39. If $$\int \frac{x^3 \mathrm{~d} x}{\sqrt{1+x^2}}=\mathrm{a}\left(1+x^2\right) \sqrt{1+x^2}+\mathrm{b} \sqrt{1+x^2}+\math 40. The perpendiculars are drawn to lines $$L_1$$ and $$L_2$$ from the origin making an angle $$\frac{\pi}{4}$$ and $$\frac{ 41. The function $$\mathrm{f}(x)=[x] \cdot \cos \left(\frac{2 x-1}{2}\right) \pi$$, where $$[\cdot]$$ denotes the greatest i 42. A line with positive direction cosines passes through the point $$\mathrm{P}(2,-1,2)$$ and makes equal angles with the c 43. If the shortest distance between the lines $$\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{\lambda}$$ and $$\frac{x-2}{1}=\frac 44. If the angles $$\mathrm{A}, \mathrm{B}$$, and $$\mathrm{C}$$ of a triangle are in an Arithmetic Progression and if $$\ma 45. A linguistic club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this group including the se 46. The maximum value of the function $$f(x)=3 x^3-18 x^2+27 x-40$$ on the set $$\mathrm{S}=\left\{x \in \mathrm{R} / x^2+30 47. Let $$f(x)=\int \frac{x^2-3 x+2}{x^4+1} \mathrm{~d} x$$, then function decreases in the interval 48. Three critics review a book. For the three critics the odds in favour of the book are $$2: 5, 3: 4$$ and $$4: 3$$ respec 49. Consider the lines $$\mathrm{L}_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{\mathrm{z}+1}{2}$$ $$\mathrm{L}_2: \frac{x-2}{1}=\f 50. The area bounded by the curves $$y=(x-1)^2, y=(x+1)^2$$ and $$y=\frac{1}{4}$$ is

Physics

1. A sphere and a cube, both of copper have equal volumes and are black. They are allowed to cool at same temperature and i 2. An alternating voltage is applied to a series LCR circuit. If the current leads the voltage by $$45^{\circ}$$, then $$\l 3. A horizontal wire of mass '$$m$$', length '$$l$$' and resistance '$$R$$' is sliding on the vertical rails on which unifo 4. Frequency of the series limit of Balmer series of hydrogen atom in terms of Rydberg's constant (R) and velocity of light 5. A string is stretched between two rigid supports separated by $$75 \mathrm{~cm}$$. There are no resonant frequencies bet 6. A straight wire carrying a current (I) is turned into a circular loop. If the magnitude of the magnetic moment associate 7. The diffraction fringes obtained by a single slit are of 8. A particle moves around a circular path of radius '$$r$$' with uniform speed '$$V$$'. After moving half the circle, the 9. On dry road, the maximum speed of a vehicle along a circular path is '$$V$$'. When the road becomes wet, maximum speed b 10. A wire of length $$3 \mathrm{~m}$$ connected in the left gap of a meter-bridge balances $$8 \Omega$$ resistance in the r 11. By adding soluble impurity in a liquid, angle of contact 12. For a common emitter configuration, if '$$\alpha$$' and '$$\beta$$' have their usual meanings, the incorrect relation be 13. A simple pendulum of length '$$l$$' and a bob of mass '$$\mathrm{m}$$' is executing S.H.M. of small amplitude '$$A$$'. T 14. Which of the following combination of 7 identical capacitors each of $$2 \mu \mathrm{F}$$ gives a capacitance of $$\frac 15. The potential energy of a molecule on the surface of a liquid compared to the molecules inside the liquid is 16. A progressive wave is given by, $$\mathrm{Y}=12 \sin (5 \mathrm{t}-4 \mathrm{x})$$. On this wave, how far away are the t 17. The de-Broglie wavelength $$(\lambda)$$ of a particle is related to its kinetic energy (E) as 18. For a purely inductive or a purely capacitive circuit, the power factor is 19. The electric field intensity on the surface of a solid charged sphere of radius '$$r$$' and volume charge density '$$\rh 20. A body is said to be opaque to the radiation if (a, r and t are coefficient of absorption, reflection and transmission r 21. In a thermodynamic system, $$\Delta U$$ represents the increases in its internal energy and dW is the work done by the s 22. A combination of two thin lenses in contact have power $$+10 \mathrm{D}$$. The power reduces to $$+6 \mathrm{D}$$ when t 23. The reciprocal of the total effective resistance of LCR a.c. circuit is called 24. If the radius of the first Bohr orbit is '$$r$$' then the de-Broglie wavelength of the electron in the $$4^{\text {th }} 25. A string of length '$$L$$' fixed at one end carries a body of mass '$$\mathrm{m}$$' at the other end. The mass is revolv 26. The temperature of a gas is $$-68^{\circ} \mathrm{C}$$. To what temperature should it be heated, so that the r.m.s. velo 27. The displacement of a particle executing S.H.M. is $$x=\mathrm{a} \sin (\omega t-\phi)$$. Velocity of the particle at ti 28. A uniformly charged semicircular arc of radius '$$r$$' has linear charge density '$$\lambda$$'. The electric field at it 29. A sphere, a cube and a thin circular plate all made of same material and having the same mass are heated to same tempera 30. For emission of light, a light emitting diode (LED) is 31. A solenoid of length $$0.4 \mathrm{~m}$$ and having 500 turns of wire carries a current $$3 \mathrm{~A}$$. A thin coil h 32. In semiconductors at room temperature, 33. Considering earth to be a sphere of radius '$$R$$' having uniform density '$$\rho$$', then value of acceleration due to 34. The equation of the wave is $$\mathrm{Y}=10 \sin \left(\frac{2 \pi \mathrm{t}}{30}+\alpha\right)$$ If the displacement i 35. The bob of simple pendulum of length '$$L$$' is released from a position of small angular displacement $$\theta$$. Its l 36. The value of acceleration due to gravity at a depth '$$d$$' from the surface of earth and at an altitude '$$h$$' from th 37. A magnetic field of $$2 \times 10^{-2} \mathrm{~T}$$ acts at right angles to a coil of area $$100 \mathrm{~cm}^2$$ with 38. In Young's double slit experiment, $$8^{\text {th }}$$ maximum with wavelength '$$\lambda_1$$' is at a distance '$$d_1$$ 39. The alternating e.m.f. induced in the secondary coil of a transformer is mainly due to 40. The efficiency of a heat engine is '$$\eta$$' and the coefficient of performance of a refrigerator is '$$\beta$$'. Then 41. A conducting sphere of radius $$0.1 \mathrm{~m}$$ has uniform charge density $$1.8 \mu \mathrm{C} / \mathrm{m}^2$$ on it 42. If $$\mathrm{I}_0$$ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be 43. Two circular coils made from same wire but radius of $$1^{\text {st }}$$ coil is twice that of $$2^{\text {nd }}$$ coil. 44. Five current carrying conductors meet at point $$\mathrm{P}$$. What is the magnitude and direction of the current in con 45. Water rises in a capillary tube of radius '$$r$$' upto a height '$$h$$'. The mass of water in a capillary is '$$m$$'. Th 46. A person with machine gun can fire 50 g bullets with a velocity of $$240 \mathrm{~m} / \mathrm{s}$$. A $$60 \mathrm{~kg} 47. If '$$l$$' is the length of the open pipe, '$$r$$' is the internal radius of the pipe and '$V$ ' is the velocity of soun 48. The angle of deviation produced by a thin prism when placed in air is '$$\delta_1$$' and that when immersed in water is 49. A thin uniform rod of mass '$$m$$' and length '$$P$$' is suspended from one end which can oscillate in a vertical plane 50. Magnetic field at the centre of the hydrogen atom due to motion of electron in $$\mathrm{n}^{\text {th }}$$ orbit is pro

MHT CET 2023 14th May Morning Shift

MCQ (Single Correct Answer)

-0

If $$\int \frac{\cos \theta}{5+7 \sin \theta-2 \cos ^2 \theta} d \theta=A \log _e|f(\theta)|+c$$ (where $$c$$ is a constant of integration), then $$\frac{f(\theta)}{A}$$ can be

$$\frac{2 \sin \theta+1}{\sin \theta+3}$$

$$\frac{2 \sin \theta+1}{5(\sin \theta+3)}$$

$$\frac{5(\sin \theta+3)}{2 \sin \theta+1}$$

$$\frac{5(2 \sin \theta+1)}{\sin \theta+3}$$

MHT CET 2023 14th May Morning Shift

MCQ (Single Correct Answer)

-0

If $$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$$ are unit vectors and $$\theta$$ is angle between $$\overline{\mathrm{a}}$$ and $$\bar{c}$$ and $$\bar{a}+2 \bar{b}+2 \bar{c}=\overline{0}$$, then $$|\bar{a} \times \bar{c}|=$$

$$\frac{\sqrt{15}}{2}$$

$$\frac{\sqrt{15}}{4}$$

$$\sqrt{15}$$

$$\frac{\sqrt{15}}{3}$$

MHT CET 2023 14th May Morning Shift

MCQ (Single Correct Answer)

-0

The integral $$\int_\limits{\frac{\pi}{6}}^{\frac{\pi}{3}} \sec ^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x d x$$ is equal to

$$3^{\frac{5}{6}}-3^{\frac{2}{3}}$$

$$3^{\frac{7}{6}}-3^{\frac{5}{6}}$$

$$3^{\frac{5}{3}}-3^{\frac{1}{3}}$$

$$3^{\frac{4}{3}}-3^{\frac{1}{3}}$$