Chemistry
1. Which among the following has highest $$\mathrm{pH}$$ ? 2. In which of the following compounds, an element exhibits two different oxidation states? 3. Which of the following hydrides is electron deficient? 4. Amphoteric oxide among the following 5. Which property of $$\mathrm{CO}_2$$ makes it biologically and geo-chemically important? 6. The IUPAC name for
7. 1 mole of $$\mathrm{HI}$$ is heated in a closed container of capacity of $$2 \mathrm{~L}$$. At equilibrium half a mole o 8. Vacant space in body centered cubic lattice unit cell is about 9. How many number of atoms are there in a cube based unit cell, having one atom on each corner and 2 atoms on each body di 10. Which of the following is not true about the amorphous solids? 11. Identify, A and B in the following reaction
12. Solubility of a gas in a liquid increases with 13. The rise in boiling point of a solution containing $$1.8 \mathrm{~g}$$ of glucose in $$100 \mathrm{~g}$$ of solvent is $ 14. If $$3 \mathrm{~g}$$ of glucose (molar mass $$=180 \mathrm{~g}$$) is dissolved in $$60 \mathrm{~g}$$ of water at $$15^{\ 15. Which of the following colligative properties can provide molar mass of proteins, polymers and colloids with greater pre 16. In fuel cells _______ are used as catalysts. 17. The molar conductivity is maximum for the solution of concentration 18. Alkali halides do not show dislocation defect because 19. For spontaneity of a cell, which is correct? 20. For $$n$$th order of reaction, half-life period is directly proportional to 21. Half-life of a reaction is found to be inversely proportional to the fifth power of its initial concentration, the order 22. A first order reaction is half completed in $$45 \mathrm{~min}$$. How long does it need $$99.9 \%$$ of the reaction to b 23. The rate of the reaction, $$\mathrm{CH}_3 \mathrm{COOC}_2 \mathrm{H}_5+\mathrm{NaOH} \longrightarrow \mathrm{CH}_3 \math 24. Colloidal solution commonly used in the treatment of skin disease is 25. Specific conductance of $$0.1 \mathrm{~M} \mathrm{~HNO}_3$$ is $$6.3 \times 10^{-2} \mathrm{~ohm}^{-1} \mathrm{~cm}^{-1} 26. The property of halogens which is not correctly matched is 27. Which noble gas has least tendency to form compounds? 28. $$\left(\mathrm{NH}_4\right)_2 \mathrm{Cr}_2 \mathrm{O}_7$$ on heating liberates a gas. The same gas will be obtained by 29. The strong reducing property of hypophosphorus acid is due to 30. A transition metal exists in its highest oxidation state. It is expected to behave as 31. What will be the value of $$x$$ in $$\mathrm{Fe}^{x+}$$, if the magnetic moment, $$\mu=\sqrt{24} \mathrm{~BM}$$ ? 32. Which can adsorb larger volume of hydrogen gas? 33. All Cu(II) halides are known, except the iodide, the reason for it is that 34. The correct IUPAC name of cis-platin is 35. Crystal field splitting energy (CFSE) for $$\left[\mathrm{CoCl}_6\right]^{4-}$$ is $$18000 \mathrm{~cm}^{-1}$$. The crys 36. The complex hexamineplatinum(IV)chloride will give _____ number of ions on ionisation. 37. In the following pairs of halogen compounds, which compound undergoes faster $$S_N 1$$ reaction?
38. The only lanthanoid which is radioactive 39. Identify the products $$A$$ and $$B$$ in the reactions :
$$\begin{aligned}
& R-X+\mathrm{AgCN} \longrightarrow A+\mathrm 40. An organic compound with molecular formula $$\mathrm{C}_7 \mathrm{H}_8 \mathrm{O}$$ dissolves in $$\mathrm{NaOH}$$ and g 41. In Kolbe's reaction the reacting substances are 42. The major product obtained when ethanol is heated with excess of conc. $$\mathrm{H}_2 \mathrm{SO}_4$$ at $$443 \mathrm{~ 43. Among the following, the products formed by the reaction of anisole with $$\mathrm{HI}$$ are 44. Which one of the following chlorohydrocarbon readily undergoes solvolysis? 45. The general name of the compound formed by the reaction between aldehyde and alcohol is 46. Reaction by which benzaldehyde cannot be prepared is 47. The test to differentiate between pentan-2-one and pentan-3-one is 48. In carbylamine test for primary amines the resulting foul smelling product is 49. Ethanoic acid undergoes Hell-Volhard Zelinsky reaction but methanoic acid does not, because of 50. Which of the following is correctly matched? 51. Which institute has approved the emergency use of 2-deoxy-D-glucose as additive therapy for COVID-19 patients? 52. A nucleic acid, whether DNA or RNA gives on complete hydrolysis, two purine bases, two pyrimidine bases, a pentose sugar 53. A secondary amine is 54. If wavelength of photon is $$2.2 \times 10^{-11} \mathrm{~m}$$ and $$h=6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s}$$, th 55. Elements $$X, Y$$ and $$Z$$ have atomic numbers 19, 37 and 55 respectively. Which of the following statements is true ab 56. In oxygen and carbon molecule the bonding is 57. Which is most VISCOUS? 58. The volume of $$2.8 \mathrm{~g}$$ of $$\mathrm{CO}$$ at $$27^{\circ} \mathrm{C}$$ and 0.821 atm pressure is
($$R=0.08210 59. The work done when 2 moles of an ideal gas expands rèversibly and isothermally from a volume of $$1 \mathrm{~L}$$ to $$1 60. An aqueous solution of alcohol contains $$18 \mathrm{~g}$$ of water and $$414 \mathrm{~g}$$ of ethyl alcohol. The mole f
Mathematics
1. Find the mean number of heads in three tosses of a fair coin. 2. If $$A$$ and $$B$$ are two events such that $$P(A)=\frac{1}{2}, P(B)=\frac{1}{2}$$ and $$P(A \mid B)=\frac{1}{4}$$, then 3. A pandemic has been spreading all over the world. The probabilities are 0.7 that there will be a lockdown, 0.8 that the 4. If $$A$$ and $$B$$ are two independent events such that $$P(\bar{A})=0.75, P(A \cup B)=0.65$$ and $$P(B)=x$$, then find 5. Suppose that the number of elements in set $$A$$ is $$p$$, the number of elements in set $$B$$ is $$q$$ and the number o 6. The domain of the function $$f(x)=\frac{1}{\log _{10}(1-x)}+\sqrt{x+2}$$ is 7. The trigonometric function $$y=\tan x$$ in the II quadrant 8. The degree measure of $$\frac{\pi}{32}$$ is equal to 9. The value of $$\sin \frac{5 \pi}{12} \sin \frac{\pi}{12}$$ is 10. $$\sqrt{2+\sqrt{2+\sqrt{2+2 \cos 8 \theta}}}=$$ 11. If $$A=\{1,2,3, \ldots, 10\}$$, then number of subsets of $$A$$ containing only odd numbers is 12. If all permutations of the letters of the word MASK are arranged in the order as in dictionary with or without meaning, 13. If $$a_1, a_2, a_3, \ldots, a_{10}$$ is a geometric progression and $$\frac{a_3}{a_1}=25$$, then $$\frac{a_9}{a_5}$$ equ 14. If the straight line $$2 x-3 y+17=0$$ is perpendicular to the line passing through the points $$(7,17)$$ and $$(15, \bet 15. The octant in which the point (2, $$-$$4, $$-7$$) lies is 16. If $$f(x)=\left\{\begin{array}{cc}x^2-1, & 0
the quadratic equation whose roots are $$\lim _\limits{x \rightarrow 2^{-}} 17. If $$3 x+i(4 x-y)=6-i$$ where $$x$$ and $$y$$ are real numbers, then the values of $$x$$ and $$y$$ are respectively, 18. If the standard deviation of the numbers $$-1, 0,1, k$$ is $$\sqrt{5}$$ where $$k>0$$, then $$k$$ is equal to 19. If the set $$x$$ contains 7 elements and set $$y$$ contains 8 elements, then the number of bijections from $$x$$ to $$y$ 20. If $$f: R \rightarrow R$$ be defined by
$$f(x)=\left\{\begin{array}{llc}
2 x: & x>3 \\
x^2: & 1
then $$f(-1)+f(2)+f(4)$$ 21. Let the relation $$R$$ is defined in $$N$$ by $$a R b$$, if $$3 a+2 b=27$$ then $$R$$ is 22. $$\lim _\limits{y \rightarrow 0} \frac{\sqrt{3+y^3}-\sqrt{3}}{y^3}=$$ 23. If $$A$$ is a matrix of order $$3 \times 3$$, then $$\left(A^2\right)^{-1}$$ is equal to 24. If $$A=\left[\begin{array}{ll}2 & -1 \\ 3 & -2\end{array}\right]$$, then the inverse of the matrix $$A^3$$ is 25. If $$A$$ is a skew symmetric matrix, then A$$^{2021}$$ is 26. If $$A=\left[\begin{array}{ll}0 & 1 \\ 0 & 0\end{array}\right]$$, then $$(a I+b A)^n$$ is (where $$I$$ is the identify m 27. If $$A$$ is a $$3 \times 3$$ matrix such that $$|5 \cdot \operatorname{adj} A|=5$$, then $$|A|$$ is equal to 28. If there are two values of '$$a$$' which makes determinant
$$\Delta=\left|\begin{array}{ccc}
1 & -2 & 5 \\
2 & a & -1 \\ 29. If the vertices of a triangle are $$(-2,6),(3,-6)$$ and $$(1,5)$$, then the area of the triangle is 30. Domain $$\cos ^{-1}[x]$$ is, where [ ] denotes a greatest integer function 31. If $$y=\left(1+x^2\right) \tan ^{-1} x-x$$, then $$\frac{d y}{d x}$$ is 32. If $$x=e^\theta \sin \theta, y=e^\theta \cos \theta$$ where $$\theta$$ is a parameter, then $$\frac{d y}{d x}$$ at $$(1, 33. If $$y=e^{\sqrt{x \sqrt{x} \sqrt{x}}...,} x >1$$, then $$\frac{d^2 y}{d x^2}$$ at $$x=\log _e 3$$ is 34. If $$f(1)=1, f^{\prime}(l)=3$$, then the derivative of $$f(f(f(x)))+(f(x))^2$$ at $$x=1$$ is 35. If $$y=x^{\sin x}+(\sin x)^x$$, then $$\frac{d y}{d x}$$ at $$x=\frac{\pi}{2}$$ is 36. If $$A_n=\left[\begin{array}{cc}1-n & n \\ n & 1-n\end{array}\right]$$, then
$$\left|A_1\right|+\left|A_2\right|+\ldots 37. The function $$f(x)=\log (1+x)-\frac{2 x}{2+x}$$ is increasing on 38. The coordinates of the point on the $$\sqrt{x}+\sqrt{y}=6$$ at which the tangent is equally inclined to the axes is 39. The function $$f(x)=4 \sin ^3 x-6 \sin ^2 x +12 \sin x+100$$ is strictly 40. If $$[x]$$ is the greatest integer function not greater than $$x$$, then $$\int_\limits0^8[x] d x$$ is equal to 41. $$\int_0^{\pi / 2} \sqrt{\sin \theta} \cos ^3 \theta d \theta$$ is equal to 42. If $$e^y+x y=e$$ the ordered pair $$\left(\frac{d y}{d x}, \frac{d^2 y}{d x^2}\right)$$ at $$x=0$$ is equal to 43. $$\int \frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha} d x$$ is equal to 44. $$\int_0^1 \frac{x e^x}{(2+x)^3} d x$$ is equal to 45. If $$\int \frac{d x}{(x+2)\left(x^2+1\right)}=a \log \left|1+x^2\right|+b \tan ^{-1} x +\frac{1}{5} \log |x+2|+c,$$ then 46. Area of the region bounded by the curve $$y=\tan x$$, the $$X$$-axis and line $$x=\frac{\pi}{3}$$ is 47. Evaluate $$\int_\limits2^3 x^2 d x$$ as the limit of a sum 48. $$\int_0^{\pi / 2} \frac{\cos x \sin x}{1+\sin x} d x$$ is equal to 49. If $$\frac{d y}{d x}+\frac{y}{x}=x^2$$, then $$2 y(2)-y(1)=$$ 50. The solution of the differential equation $$\frac{d y}{d x}=(x+y)^2$$ is 51. If $$y(x)$$ is the solution of differential equation $$x \log x \frac{d y}{d x}+y=2 x \log x, y(e)$$ is equal to 52. If $$|\mathbf{a}|=2$$ and $$|\mathbf{b}|=3$$ and the angle between $$\mathbf{a}$$ and $$\mathbf{b}$$ is $$120^{\circ}$$, 53. If $$|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=36$$ and $$|\mathbf{a}|=3$$, then $$|\mathbf{a}|$$ 54. If $$\alpha=\hat{\mathbf{i}}-3 \hat{\mathbf{j}}, \beta=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$, then expr 55. The sum of the degree and order of the differential equation $$\left(l+y_1^2\right)^{2 / 3}=y_2$$ is 56. The coordinates of foot of the perpendicular drawn from the origin to the plane $$2 x-3 y+4 z=29$$ are 57. The angle between the pair of lines $$\frac{x+3}{3}=\frac{y-1}{5}=\frac{z+3}{4}$$ and $$\frac{x+1}{1}=\frac{y-4}{4}=\fra 58. The corner points of the feasible region of an LPP are $$(0,2),(3,0),(6,0),(6,8)$$ and $$(0,5)$$, then the minimum value 59. A dietician has to develop a special diet using two foods $$X$$ and $$Y$$. Each packet (containing $$30 \mathrm{~g}$$ ) 60. The distance of the point whose position vector is $$(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}})$$ from the p
Physics
1. In a series $$L C R$$ circuit, $$R=300 \Omega, L=0.9 \mathrm{H}, C=2.0 \mu \mathrm{F}$$ and $$\omega=1000 \mathrm{~rad} 2. Which of the following radiations of electromagnetic waves has the highest wavelength ? 3. The power of a equi-concave lens is $$-4.5 \mathrm{D}$$ and is made of a material of refractive index 1.6, the radii of 4. A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the an 5. A convex lens of focal length $$f$$ is placed somewhere in between an object and a screen. The distance between the obje 6. A series resonant $$\mathrm{AC}$$ circuit contains a capacitance $$10^{-6} \mathrm{~F}$$ and an inductor of $$10^{-4} \m 7. Focal length of a convex lens will be maximum for 8. For light diverging from a finite point source, 9. The fringe width for red colour as compared to that for violet colour is approximately 10. In case of Fraunhoffer diffraction at a single slit, the diffraction pattern on the screen is correct for which of the f 11. When a compact disc (CD) is illuminated by small source of white light coloured bands are observed. This is due to 12. Consider a glass slab which is silvered at one side and the other side is transparent. Given the refractive index of the 13. The kinetic energy of the photoelectrons increases by $$0.52 \mathrm{~eV}$$ when the wavelength of incident light is cha 14. The de-Broglie wavelength of a particle of kinetic energy $$K$$ is $$\lambda$$, the wavelength of the particle, if its k 15. The radius of hydrogen atom in the ground state is 0.53$$\mathop A\limits^o $$. After collision with an electron, it is 16. In accordance with the Bohr's model, the quantum number that characterises the Earth's revolution around the Sun in an o 17. If an electron is revolving in its Bohr orbit having Bohr radius of 0.529$$\mathop A\limits^o $$, then the radius of thi 18. Binding energy of a nitrogen nucleus $$\left[{ }_7^{14} \mathrm{~N}\right]$$, given $$m\left[{ }_7^{14} \mathrm{~N}\righ 19. In a photo electric experiment, if both the intensity and frequency of the incident light are doubled, then the saturati 20. Which of the following radiations is deflected by electric field? 21. The resistivity of a semiconductor at room temperature is in between 22. The forbidden energy gap for Ge crystal at 0K is 23. Which logic gate is represented by the following combination of logic gates?
24. A metallic rod of mass per unit length $$0.5 \mathrm{~kg} \mathrm{~m}^{-1}$$ is lying horizontally on a smooth inclined 25. A nuclear reactor delivers a power of $$10^9 \mathrm{~W}$$, the amount of fuel consumed by the reactor in one hour is 26. The displacement $$x$$ (in $$\mathrm{m}$$) of a particle of mass $$m$$ (in $$\mathrm{kg}$$) moving in one dimension unde 27. Two objects are projected at an angle $$\theta^{\circ}$$ and $$\left(90-\theta^{\circ}\right)$$, to the horizontal with 28. A car is moving in a circular horizontal track of radius $$10 \mathrm{~m}$$ with a constant speed of $$10 \mathrm{~ms}^{ 29. Two masses of $$5 \mathrm{~kg}$$ and $$3 \mathrm{~kg}$$ are suspended with the help of massless inextensible strings as 30. The Vernier scale of a travelling microscope has 50 divisions which coincides with 49 main scale divisions. If each main 31. The angular speed of a motor wheel is increased from $$1200 \mathrm{~rpm}$$ to $$3120 \mathrm{~rpm}$$ in $$16 \mathrm{~s 32. The centre of mass of an extended body on the surface of the earth and its centre of gravity 33. A metallic rod breaks when strain produced is $$0.2 \%$$. The Young's modulus of the material of the $$\operatorname{rod 34. A tiny spherical oil drop carrying a net charge $$q$$ is balanced in still air, with a vertical uniform electric field o 35. "Heat cannot be flow itself from a body at lower temperature to a body at higher temperature". This statement correspond 36. A smooth chain of length $$2 \mathrm{~m}$$ is kept on a table such that its length of $$60 \mathrm{~cm}$$ hangs freely f 37. Electrical as well as gravitational affects can be thought to be caused by fields. Which of the following is true for an 38. Four charges $$+q_1+2 q_1+q$$ and $$-2 q$$ are placed at the corners of a square $$A B C D$$ respectively. The force on 39. An electric dipole with dipole moment $$4 \times 10^{-9} \mathrm{C}-\mathrm{m}$$ is aligned at $$30^{\circ}$$ with the d 40. A charged particle of mass $$m$$ and charge $$q$$ is released from rest in an uniform electric field E. Neglecting the e 41. The electric field and the potential of an electric dipole vary with distance $$r$$ as 42. The displacement of a particle executing SHM is given by $$x=3 \sin \left[2 \pi t+\frac{\pi}{4}\right]$$, where $$x$$ is 43. A parallel place capacitor is charged by connecting a $$2 \mathrm{~V}$$ battery across it. It is then disconnected from 44. A charged particle is moving in an electric field of $$3 \times 10^{-10} \mathrm{Vm}^{-1}$$ with mobility $$2.5 \times 1 45. Wire bound resistors are made by winding the wires of an alloy of 46. 10 identical cells each potential $$E$$ and internal resistance $$r$$ are connected in series to form a closed circuit.
47. In an atom electrons revolve around the nucleus along a path of radius $$0.72\mathop A\limits^o$$ making $$9.4 \times 10 48. When a metal conductor connected to left gap of a meter bridge is heated, the balancing point 49. Two tiny spheres carrying charges $$1.8 \mu \mathrm{C}$$ and $$2.8 \mu \mathrm{C}$$ are located at $$40 \mathrm{~cm}$$ a 50. A wire of a certain material is stretched slowly by $$10 \%$$. Its new resistance and specific resistance becomes respec 51. A proton moves with a velocity of $$5 \times 10^6 \hat{\mathbf{\widehat j} m \mathrm{~m}^{-1}}$$ through the uniform ele 52. A solenoid of length $$50 \mathrm{~cm}$$ having 100 turns carries a current of $$2.5 \mathrm{~A}$$. The magnetic field a 53. A galvanometer of resistance $$50 \Omega$$ is connected to a battery $$3 \mathrm{~V}$$ along with a resistance $$2950 \O 54. A circular coil of wire of radius $$r$$ has $$n$$ turns and carries a current $$I$$. The magnetic induction $$B$$ at a p 55. If voltage across a bulb rated $$220 \mathrm{~V}, 100 \mathrm{~W}$$ drops by $$2.5 \%$$ of its rated value, then the per 56. A long solenoid has 500 turns, when a current of $$2 \mathrm{~A}$$ is passed through it, the resulting magnetic flux lin 57. A fully charged capacitor $$C$$ with initial charge $$q_0$$ is connected to a coil of self inductance $$L$$ at $$t=0$$. 58. A magnetic field of flux densiity $$1.0 \mathrm{~Wb} \mathrm{~m}^{-2}$$ acts normal to a 80 turn coil of $$0.01 \mathrm{ 59. An alternating current is given by $$i=i_1 \sin \omega t+i_2 \cos \omega t$$. The rms current is given by 60. Which of the following statements proves that Earth has a magnetic field ?
1
KCET 2022
MCQ (Single Correct Answer)
+1
-0
If $$e^y+x y=e$$ the ordered pair $$\left(\frac{d y}{d x}, \frac{d^2 y}{d x^2}\right)$$ at $$x=0$$ is equal to
A
$$\left(\frac{1}{e}, \frac{1}{e^2}\right)$$
B
$$\left(\frac{-1}{e}, \frac{-1}{e^2}\right)$$
C
$$\left(\frac{1}{e}, \frac{-1}{e^2}\right)$$
D
$$\left(\frac{-1}{e}, \frac{1}{e^2}\right)$$
2
KCET 2022
MCQ (Single Correct Answer)
+1
-0
$$\int \frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha} d x$$ is equal to
A
$$2(\sin x-x \cos \alpha)+c$$
B
$$2(\sin x+x \cos \alpha)+c$$
C
$$2(\sin x-2 x \cos \alpha)+c$$
D
$$2(\sin x+2 x \cos \alpha)+c$$
3
KCET 2022
MCQ (Single Correct Answer)
+1
-0
$$\int_0^1 \frac{x e^x}{(2+x)^3} d x$$ is equal to
A
$$\frac{1}{27} \cdot e-\frac{1}{8}$$
B
$$\frac{1}{27} \cdot e+\frac{1}{8}$$
C
$$\frac{1}{9} \cdot e+\frac{1}{4}$$
D
$$\frac{1}{9} \cdot e-\frac{1}{4}$$
4
KCET 2022
MCQ (Single Correct Answer)
+1
-0
If $$\int \frac{d x}{(x+2)\left(x^2+1\right)}=a \log \left|1+x^2\right|+b \tan ^{-1} x +\frac{1}{5} \log |x+2|+c,$$ then
A
$$a=\frac{-1}{10}, b=\frac{2}{5}$$
B
$$a=\frac{1}{10}, b=\frac{2}{5}$$
C
$$a=\frac{-1}{10}, b=\frac{-2}{5}$$
D
$$a=\frac{1}{10}, b=\frac{-2}{5}$$