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 following5. 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 o8. Vacant space in body centered cubic lattice unit cell is about9. 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 di10. 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 with13. 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 $$15^{\15. Which of the following colligative properties can provide molar mass of proteins, polymers and colloids with greater pre16. In fuel cells _______ are used as catalysts.17. The molar conductivity is maximum for the solution of concentration18. Alkali halides do not show dislocation defect because19. For spontaneity of a cell, which is correct?20. For $$n$$th order of reaction, half-life period is directly proportional to21. Half-life of a reaction is found to be inversely proportional to the fifth power of its initial concentration, the order22. A first order reaction is half completed in $$45 \mathrm{~min}$$. How long does it need $$99.9 \%$$ of the reaction to b23. The rate of the reaction, $$\mathrm{CH}_3 \mathrm{COOC}_2 \mathrm{H}_5+\mathrm{NaOH} \longrightarrow \mathrm{CH}_3 \math24. Colloidal solution commonly used in the treatment of skin disease is25. Specific conductance of $$0.1 \mathrm{~M} \mathrm{~HNO}_3$$ is $$6.3 \times 10^{-2} \mathrm{~ohm}^{-1} \mathrm{~cm}^{-1}26. The property of halogens which is not correctly matched is27. Which noble gas has least tendency to form compounds?28. $$\left(\mathrm{NH}_4\right)_2 \mathrm{Cr}_2 \mathrm{O}_7$$ on heating liberates a gas. The same gas will be obtained by29. The strong reducing property of hypophosphorus acid is due to30. A transition metal exists in its highest oxidation state. It is expected to behave as31. What will be the value of $$x$$ in $$\mathrm{Fe}^{x+}$$, if the magnetic moment, $$\mu=\sqrt{24} \mathrm{~BM}$$ ?32. Which can adsorb larger volume of hydrogen gas?33. All Cu(II) halides are known, except the iodide, the reason for it is that34. The correct IUPAC name of cis-platin is35. Crystal field splitting energy (CFSE) for $$\left[\mathrm{CoCl}_6\right]^{4-}$$ is $$18000 \mathrm{~cm}^{-1}$$. The crys36. The complex hexamineplatinum(IV)chloride will give _____ number of ions on ionisation.37. In the following pairs of halogen compounds, which compound undergoes faster $$S_N 1$$ reaction?
38. The only lanthanoid which is radioactive39. Identify the products $$A$$ and $$B$$ in the reactions :
$$\begin{aligned}
& R-X+\mathrm{AgCN} \longrightarrow A+\mathrm40. An organic compound with molecular formula $$\mathrm{C}_7 \mathrm{H}_8 \mathrm{O}$$ dissolves in $$\mathrm{NaOH}$$ and g41. In Kolbe's reaction the reacting substances are42. 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}$$ are44. Which one of the following chlorohydrocarbon readily undergoes solvolysis?45. The general name of the compound formed by the reaction between aldehyde and alcohol is46. Reaction by which benzaldehyde cannot be prepared is47. The test to differentiate between pentan-2-one and pentan-3-one is48. In carbylamine test for primary amines the resulting foul smelling product is49. Ethanoic acid undergoes Hell-Volhard Zelinsky reaction but methanoic acid does not, because of50. Which of the following is correctly matched?51. Which institute has approved the emergency use of 2-deoxy-D-glucose as additive therapy for COVID-19 patients?52. A nucleic acid, whether DNA or RNA gives on complete hydrolysis, two purine bases, two pyrimidine bases, a pentose sugar53. A secondary amine is54. If wavelength of photon is $$2.2 \times 10^{-11} \mathrm{~m}$$ and $$h=6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s}$$, th55. Elements $$X, Y$$ and $$Z$$ have atomic numbers 19, 37 and 55 respectively. Which of the following statements is true ab56. In oxygen and carbon molecule the bonding is57. Which is most VISCOUS?58. The volume of $$2.8 \mathrm{~g}$$ of $$\mathrm{CO}$$ at $$27^{\circ} \mathrm{C}$$ and 0.821 atm pressure is
($$R=0.0821059. The work done when 2 moles of an ideal gas expands rèversibly and isothermally from a volume of $$1 \mathrm{~L}$$ to $$160. An aqueous solution of alcohol contains $$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}$$, then3. A pandemic has been spreading all over the world. The probabilities are 0.7 that there will be a lockdown, 0.8 that the 4. If $$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$$ and the number o6. The domain of the function $$f(x)=\frac{1}{\log _{10}(1-x)}+\sqrt{x+2}$$ is7. The trigonometric function $$y=\tan x$$ in the II quadrant8. The degree measure of $$\frac{\pi}{32}$$ is equal to9. The value of $$\sin \frac{5 \pi}{12} \sin \frac{\pi}{12}$$ is10. $$\sqrt{2+\sqrt{2+\sqrt{2+2 \cos 8 \theta}}}=$$11. If $$A=\{1,2,3, \ldots, 10\}$$, then number of subsets of $$A$$ containing only odd numbers is12. If all permutations of the letters of the word MASK are arranged in the order as in dictionary with or without meaning, 13. If $$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}$$ equ14. If the straight line $$2 x-3 y+17=0$$ is perpendicular to the line passing through the points $$(7,17)$$ and $$(15, \bet15. The octant in which the point (2, $$-$$4, $$-7$$) lies is16. 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 to19. 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 $$R$$ is22. $$\lim _\limits{y \rightarrow 0} \frac{\sqrt{3+y^3}-\sqrt{3}}{y^3}=$$23. If $$A$$ is a matrix of order $$3 \times 3$$, then $$\left(A^2\right)^{-1}$$ is equal to24. If $$A=\left[\begin{array}{ll}2 & -1 \\ 3 & -2\end{array}\right]$$, then the inverse of the matrix $$A^3$$ is25. If $$A$$ is a skew symmetric matrix, then A$$^{2021}$$ is26. 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 m27. If $$A$$ is a $$3 \times 3$$ matrix such that $$|5 \cdot \operatorname{adj} A|=5$$, then $$|A|$$ is equal to28. 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)$$, then the area of the triangle is30. Domain $$\cos ^{-1}[x]$$ is, where [ ] denotes a greatest integer function31. If $$y=\left(1+x^2\right) \tan ^{-1} x-x$$, then $$\frac{d y}{d x}$$ is32. If $$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 $$x=\log _e 3$$ is34. If $$f(1)=1, f^{\prime}(l)=3$$, then the derivative of $$f(f(f(x)))+(f(x))^2$$ at $$x=1$$ is35. If $$y=x^{\sin x}+(\sin x)^x$$, then $$\frac{d y}{d x}$$ at $$x=\frac{\pi}{2}$$ is36. 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}$$ is increasing on38. The coordinates of the point on the $$\sqrt{x}+\sqrt{y}=6$$ at which the tangent is equally inclined to the axes is39. The function $$f(x)=4 \sin ^3 x-6 \sin ^2 x +12 \sin x+100$$ is strictly40. If $$[x]$$ is the greatest integer function not greater than $$x$$, then $$\int_\limits0^8[x] d x$$ is equal to41. $$\int_0^{\pi / 2} \sqrt{\sin \theta} \cos ^3 \theta d \theta$$ is equal to42. If $$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$$ is equal to43. $$\int \frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha} d x$$ is equal to44. $$\int_0^1 \frac{x e^x}{(2+x)^3} d x$$ is equal to45. If $$\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,$$ then46. Area of the region bounded by the curve $$y=\tan x$$, the $$X$$-axis and line $$x=\frac{\pi}{3}$$ is47. Evaluate $$\int_\limits2^3 x^2 d x$$ as the limit of a sum48. $$\int_0^{\pi / 2} \frac{\cos x \sin x}{1+\sin x} d x$$ is equal to49. If $$\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$$ is51. If $$y(x)$$ is the solution of differential equation $$x \log x \frac{d y}{d x}+y=2 x \log x, y(e)$$ is equal to52. If $$|\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}}$$, then expr55. The sum of the degree and order of the differential equation $$\left(l+y_1^2\right)^{2 / 3}=y_2$$ is56. The coordinates of foot of the perpendicular drawn from the origin to the plane $$2 x-3 y+4 z=29$$ are57. The angle between the pair of lines $$\frac{x+3}{3}=\frac{y-1}{5}=\frac{z+3}{4}$$ and $$\frac{x+1}{1}=\frac{y-4}{4}=\fra58. 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 value59. 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}$$ and is made of a material of refractive index 1.6, the radii of 4. A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the an5. A convex lens of focal length $$f$$ is placed somewhere in between an object and a screen. The distance between the obje6. A series resonant $$\mathrm{AC}$$ circuit contains a capacitance $$10^{-6} \mathrm{~F}$$ and an inductor of $$10^{-4} \m7. Focal length of a convex lens will be maximum for8. For light diverging from a finite point source,9. The fringe width for red colour as compared to that for violet colour is approximately10. In case of Fraunhoffer diffraction at a single slit, the diffraction pattern on the screen is correct for which of the f11. When a compact disc (CD) is illuminated by small source of white light coloured bands are observed. This is due to12. Consider a glass slab which is silvered at one side and the other side is transparent. Given the refractive index of the13. The kinetic energy of the photoelectrons increases by $$0.52 \mathrm{~eV}$$ when the wavelength of incident light is cha14. The de-Broglie wavelength of a particle of kinetic energy $$K$$ is $$\lambda$$, the wavelength of the particle, if its k15. 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 o17. If an electron is revolving in its Bohr orbit having Bohr radius of 0.529$$\mathop A\limits^o $$, then the radius of thi18. Binding energy of a nitrogen nucleus $$\left[{ }_7^{14} \mathrm{~N}\right]$$, given $$m\left[{ }_7^{14} \mathrm{~N}\righ19. In a photo electric experiment, if both the intensity and frequency of the incident light are doubled, then the saturati20. Which of the following radiations is deflected by electric field?21. The resistivity of a semiconductor at room temperature is in between22. The forbidden energy gap for Ge crystal at 0K is23. Which logic gate is represented by the following combination of logic gates?
24. A metallic rod of mass per unit length $$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}$$, the amount of fuel consumed by the reactor in one hour is26. The displacement $$x$$ (in $$\mathrm{m}$$) of a particle of mass $$m$$ (in $$\mathrm{kg}$$) moving in one dimension unde27. Two objects are projected at an angle $$\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 main31. The angular speed of a motor wheel is increased from $$1200 \mathrm{~rpm}$$ to $$3120 \mathrm{~rpm}$$ in $$16 \mathrm{~s32. The centre of mass of an extended body on the surface of the earth and its centre of gravity33. A metallic rod breaks when strain produced is $$0.2 \%$$. The Young's modulus of the material of the $$\operatorname{rod34. A tiny spherical oil drop carrying a net charge $$q$$ is balanced in still air, with a vertical uniform electric field o35. "Heat cannot be flow itself from a body at lower temperature to a body at higher temperature". This statement correspond36. A smooth chain of length $$2 \mathrm{~m}$$ is kept on a table such that its length of $$60 \mathrm{~cm}$$ hangs freely f37. Electrical as well as gravitational affects can be thought to be caused by fields. Which of the following is true for an38. 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 d40. A charged particle of mass $$m$$ and charge $$q$$ is released from rest in an uniform electric field E. Neglecting the e41. The electric field and the potential of an electric dipole vary with distance $$r$$ as42. The displacement of a particle executing SHM is given by $$x=3 \sin \left[2 \pi t+\frac{\pi}{4}\right]$$, where $$x$$ is43. 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 $$2.5 \times 145. Wire bound resistors are made by winding the wires of an alloy of46. 10 identical cells each potential $$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 1048. When a metal conductor connected to left gap of a meter bridge is heated, the balancing point49. Two tiny spheres carrying charges $$1.8 \mu \mathrm{C}$$ and $$2.8 \mu \mathrm{C}$$ are located at $$40 \mathrm{~cm}$$ a50. A wire of a certain material is stretched slowly by $$10 \%$$. Its new resistance and specific resistance becomes respec51. A proton moves with a velocity of $$5 \times 10^6 \hat{\mathbf{\widehat j} m \mathrm{~m}^{-1}}$$ through the uniform ele52. A solenoid of length $$50 \mathrm{~cm}$$ having 100 turns carries a current of $$2.5 \mathrm{~A}$$. The magnetic field a53. A galvanometer of resistance $$50 \Omega$$ is connected to a battery $$3 \mathrm{~V}$$ along with a resistance $$2950 \O54. A circular coil of wire of radius $$r$$ has $$n$$ turns and carries a current $$I$$. The magnetic induction $$B$$ at a p55. If voltage across a bulb rated $$220 \mathrm{~V}, 100 \mathrm{~W}$$ drops by $$2.5 \%$$ of its rated value, then the per56. A long solenoid has 500 turns, when a current of $$2 \mathrm{~A}$$ is passed through it, the resulting magnetic flux lin57. A fully charged capacitor $$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 by60. Which of the following statements proves that Earth has a magnetic field ?
1
KCET 2022
MCQ (Single Correct Answer)
+1
-0
If $$A=\left[\begin{array}{ll}2 & -1 \\ 3 & -2\end{array}\right]$$, then the inverse of the matrix $$A^3$$ is
A
A
B
$$-1$$
C
1
D
$$-A$$
2
KCET 2022
MCQ (Single Correct Answer)
+1
-0
If $$A$$ is a skew symmetric matrix, then A$$^{2021}$$ is
A
Row matrix
B
Column matrix
C
Symmetric matrix
D
Skew symmetric matrix
3
KCET 2022
MCQ (Single Correct Answer)
+1
-0
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 matrix of order 2)
A
$$a^2 I+a^{n-1} b \cdot A$$
B
$$a^n I+n \cdot a^{n-1} b \cdot A$$
C
$$a^n I+n a^n b A$$
D
$$a^n I+b^n A$$
4
KCET 2022
MCQ (Single Correct Answer)
+1
-0
If $$A$$ is a $$3 \times 3$$ matrix such that $$|5 \cdot \operatorname{adj} A|=5$$, then $$|A|$$ is equal to
A
$$\pm 1$$
B
$$\pm 1 / 25$$
C
$$\pm 1 / 5$$
D
$$\pm 5$$