Chemistry
1. $$ \text { Match List-I with List-II and select the correct option: } $$
List-I (Molecule / ion)
List-II (Bond or 2. The electronic configuration of X and Y are given below:
$$ \begin{aligned} & X: 1 s^2 2 s^2 2 p^6 3 s^2 3 p^3 \\ & Y: 1 3. $$ \text { Match List-I with List-II } $$
List-I (Types of redox reactions)
List-II (Examples)
a. Combinatio 4. In the following pairs, the one in which both transition metal ions are colourless is 5. In the reaction between hydrogen sulphide and acidified permanganate solution, 6. A member of the Lanthanoid series which is well known to exhibit +4 oxidation state is 7. In which of the following pairs, both the elements do not have $(n-1) d^{10} n s^2$ configuration? 8. A ligand which has two different donor atoms and either of the two ligates with the central metal atom/ion in the comple 9. Which of the following statements are true about $\left[\mathrm{NiCl}_4\right]^{2-}$ ?
(a) The complex has tetrahedral g 10. $$ \text { Which formula and its name combination is incorrect? } $$ 11. $$ \text { In the complex ion }\left[\mathrm{Fe}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-} \text {, the co-ord 12. Match List-I with List-II for the following reaction pattern
Glucose $\xrightarrow{\text { Reagent }}$ Product $\longrig 13. The correct sequence of $\alpha$-amino acids, hormone, vitamin, carbohydrates respectively is 14. Which examples of carbohydrates exhibit $\alpha-$ link, ( $\alpha-$ glycosidic link) in their structure?
15. In the titration of potassium permanganate $\left(\mathrm{KMnO}_4\right)$ against Ferrous ammonium sulphate $(\mathrm{FA 16. The group reagent $\mathrm{NH}_4 \mathrm{Cl}(\mathrm{s})$ and aqueous $\mathrm{NH}_3$ will precipitate which of the foll 17. In the preparation of sodium fusion extract, the purpose of fusing organic compound with a piece of sodium metal is to 18. The sodium fusion extract is boiled with concentrated nitric acid while testing for halogens. By doing so, it 19. $$ \text { Which of the following is not an aromatic compound } $$ 20. The IUPAC name of the given organic compound is
$$ \mathrm{HC} \equiv \mathrm{C}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}=\ma 21. $$ \text { Among the following, identify the compound that is not an isomer of hexane } $$ 22. 23. Chlorobenzene reacts with bromine gas in the presence of Anhyd $\mathrm{AlBr}_3$ to yield p-Bromochlorobenzene. This rea 24. The organometallic compound $\left(\mathrm{CH}_3\right)_3 \mathrm{CMgBr}$ on reaction with $\mathrm{D}_2 \mathrm{O}$ pro 25. The major product formed when $1-$ Bromo $-3-$ Chlorocyclobutane reacts with metallic sodium in dry ether is 26. Ethyl alcohol is heated with concentrated sulphuric acid at 413 K . The major product
27. Phenol can be distinguished from propanol by using the reagent 28. $$ \text { Match the following with their } \mathrm{pKa} \text { values } $$
Acid
pKa
(I) Phenol
(a) 16
(II) p-Ni 29.
$$ A \text { and } B \text { respectively are } $$ 30. Oxidation of Toluene with chromyl chloride followed by hydrolysis gives Benzaldehyde. This reaction is known as ________ 31. Statement - I : Reduction of ester by DIABL-H followed by hydrolysis gives aldehyde.
Statement - II : Oxidation of benzy 32. Arrange the following compounds in their decreasing order of reactivity towards Nucleop addition reaction.
$$ \mathrm{CH 33. Which of the following has most acidic Hydrogen ?
34. Which of the following reagents are suitable to differentiate Aniline and N-methylaniline chemical 35. $$ \text { Which of the following reaction/s does not yield an amine? } $$
36. $$ \text { Match the compounds given in List - I with the items given in List - II. } $$
List - I
List - II
37. The number of orbitals associated with ' N ' shell of an atom is 38. According to the Heisenberg's Uncertainty principle, the value of $\Delta \mathrm{b} . \Delta \mathrm{x}$ for an object 39. Given below are two statements.
Statement-I : Adiabatic work done is positive when work is done on the system and intern 40. Which one of the following reactions has $\Delta \mathrm{H}=\Delta \mathrm{U}$ ? 41. Identify the incorrect statements among the following:
(a) All enthalpies of fusion are positive
(b) The magnitude of en 42. Which of the following statements is/are true about equilibrium?
(a) Equilibrium is possible only in a closed system of 43. According to Le Chatelier's principle, in the reaction $\mathrm{CO}(\mathrm{g})+3 \mathrm{H}_2(\mathrm{~g}) \rightleftha 44. The equilibrium constant at 298 K for the reaction $\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D}$ is 1 45. Among the following 0.1 m aqueous solutions, which one will exhibit the lowest boiling point elevation, assuming complet 46. Variation of solubility with temperature t for a gas in liquid is shown by the following graphs. The correct representat 47. 180 g of glucose, $\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6$, is dissolved in 1 kg of water in a vessel. The temperatur 48. If $N_2$ gas is bubbled through water at 293 K , how many moles of $N_2$ gas would dissolve in 1 litre of water? Assume 49. The correct statement/s about Galvanic cell is/are
(a) Current flows from cathode to anode
(b) Anode is positive termina 50. The electronic conductance depends on 51. For a given half cell, $\mathrm{Al}^{3+}+3 \mathrm{e}^{-} \rightarrow \mathrm{Al}$ on increasing of aluminium ion, the e 52. Match the following select the correct option for the quantity of electricity, in $\mathrm{Cmol}^{-1}$ required to
depo 53. Catalysts are used to increase the rate of a chemical reaction. Because it
54. Half-life of a first order reaction is 20 seconds and initial concentration of reactant is 0.2 M . The concentration of 55. $$ \text { In the given graph, } \mathrm{E}_{\mathrm{a}} \text { for the reverse reaction will be } $$
56. For the reaction $2 \mathrm{~N}_2 \mathrm{O}_{5(\mathrm{~g})} \rightarrow 4 \mathrm{NO}_{2(\mathrm{~g})}+\mathrm{O}_{2(\ 57. Which of the following methods of expressing concentration are unitless?
58. Select the INCORRECT statement/s from the following:
(a) 22 books have infinite significant figures
(b) In the answer of 59. $$ \text { Given below and the atomic masses of the elements: } $$
$$ \begin{array}{|l|l|l|l|l|l|l|l|l|l|} \hline \text 60. The change in hybridization (if any) of the 'Al' atom in the following reaction is $\mathrm{AlCl}_3+\mathrm{Cl}^{-} \rig
Mathematics
1. If $\mathrm{A}=\left\{\mathrm{x}: \mathrm{x}\right.$ is an integer and $\left.\mathrm{x}^2-9=0\right\}$
$B=\{x: x$ is a 2. $A$ and $B$ are two sets having 3 and 6 elements respectively. Consider the following statements.
Statement (I): Minimum 3. Domain of the function $f$, given by $f(x)=\frac{1}{\sqrt{(x-2)(x-5)}}$ is 4. If $f(x)=\sin \left[\pi^2\right] x-\sin \left[-\pi^2\right] x$, where $[x]=$ greatest integer $\leq x$, then which of th 5. Which of the following is not correct?
6. If $\cos x+\cos ^2 x=1$, then the value of $\sin ^2 x+\sin ^4 x$ is
7. The mean deviation about the mean for the date $4,7,8,9,10,12,13,17$ is 8. A random experiment has five outcomes $\mathrm{w}_1, \mathrm{w}_2, \mathrm{w}_3, \mathrm{w}_4$ and $\mathrm{w}_5$. The p 9. A die has two face each with number ' 1 ', three faces each with number ' 2 ' and one face with number ' 3 '. If the die 10. $$ \text { Let } A=\{a, b, c\} \text {, then the number of equivalence relations on A containing }(b, c) \text { is } $$ 11. Let the functions " f " and " g " be $\mathrm{f}:\left[0, \frac{\pi}{2}\right] \rightarrow \mathrm{R}$ given by $\mathrm 12. $$ \sec ^2\left(\tan ^{-1} 2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right)= $$ 13. $2 \cos ^{-1} x=\sin ^{-1}\left(2 x \sqrt{1-x^2}\right)$ is valid for all values of ' $x$ ' satisfying 14. Consider the following statements:
Statement (I): In a LPP, the objective function is always linear.
Statement (II): Ina 15. The maximum value of $\mathrm{z}=3 \mathrm{x}+4 \mathrm{y}$, subject to the constraints $\mathrm{x}+\mathrm{y} \leq 40, 16. Consider the following statements.
Statement (I): If E and F are two independent events, then $E^{\prime}$ and $F^{\prim 17. If A and B are two non-mutually exclusive events such that $\mathrm{P}(\mathrm{A} \mid \mathrm{B})=\mathrm{P}(\mathrm{B} 18. If $A$ and $B$ are two events such that $A \subset B$ and $P(B) \neq 0$, then which of the following is correct?
19. Meera visits only one of the two temples A and B in her locality. Probability that she visits temple A is $\frac{2}{5}$. 20. If $Z_1$ and $Z_2$ are two non-zero complex numbers, then which of the following is not true? 21. Consider the following statements :
Statement(I) : The set of all solutions of the linear inequalities $3 \mathrm{x}+8
S 22. The number of four digit even number that can be formed using the digits $0,1,2$ and 3 without repetition is
23. $$ \text { The number of diagonals that can be drawn in an octagon is } $$ 24. If the number of terms in the binomial expansion of $(2 \mathrm{x}+3)^{3 \mathrm{n}}$ is 22 , then the value of n is 25. If $4^{\text {th }}, 10^{\text {th }}$ and $16^{\text {th }}$ terms of a G.P. are $x, y$ and $z$ respectively, then 26. If $A$ is a square matrix such that $A^2=A$, then $(I-A)^3$ is 27. If $A$ and $B$ are two matrices such that $A B$ is an identity matrix and the order of matrix $B$ is $3 \times 4$, then 28. Which of the following statements is not correct?
29. If a matrix $A=\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]$ satisfies $A^6=k A^{\prime}$, then the value of 30. If $A=\left[\begin{array}{ll}k & 2 \\ 2 & k\end{array}\right]$ and $\left|A^3\right|=125$, then the value of $k$ is 31. If $A$ is a square matrix satisfying the equation $A^2-5 A+7 I=0$, where $I$ is the $I$ dentity matrix and 0 is null mat 32. If $A$ is a square matrix of order $3 \times 3, \operatorname{det} A=3$, then the value of $\operatorname{det}\left(3 A^ 33. If $B=\left[\begin{array}{ll}1 & 3 \\ 1 & \alpha\end{array}\right]$ be the adjoint of a matrix $A$ and $|A|=2$, then the 34. The system of equations $4 x+6 y=5$ and $8 x+12 y=10$ has 35. If $\vec{a}=\hat{i}+2 \hat{j}+\hat{k}, \vec{b}=\hat{i}-\hat{j}+4 \hat{k}$ and $\vec{c}=\hat{i}+\hat{j}+\hat{k}$ are such 36. If $|\overrightarrow{\mathrm{a}}|=10,|\overrightarrow{\mathrm{~b}}|=2$ and $\overrightarrow{\mathrm{a}} \cdot \overright 37. Consider the following statements :
Statement (I) : If either $|\vec{a}|=0$ or $|\vec{b}|=0$, then $\vec{a} \cdot \vec{b 38. If a line makes angles $90^{\circ}, 60^{\circ}$ and $\theta$ with $\mathrm{x}, \mathrm{y}$ and z axes respectively, wher 39. The equation of the line through the point $(0,1,2)$ and perpendicular to the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z- 40. A line passes through $(-1,-3)$ and perpendicular to $x+6 y=5$. Its $x$ intercept is 41. The length of the latus rectum of $x^2+3 y^2=12$ is 42. $\lim _{x \rightarrow 1} \frac{x^4-\sqrt{x}}{\sqrt{x}-1}$ is
43. If $y=\frac{\cos x}{1+\sin x}$, then
(a) $\frac{d y}{d x}=\frac{-1}{1+\sin x}$
(b) $\frac{d y}{d x}=\frac{1}{1+\sin x}$
44. Match the following:
In the following, $[\mathrm{x}]$ denotes the greatest integer less than or equal to x .
Column - 45. The function $f(x)=\left\{\begin{array}{ll}e^x+a x & , x 46. $$ \text { A function } f(x)=\left\{\begin{array}{cl} \frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}, & \text { if } x \neq 47. If $\mathrm{y}=\mathrm{a} \sin ^3 \mathrm{t}, \mathrm{x}=\mathrm{a} \cos ^3 \mathrm{t}$, then $\frac{\mathrm{dy}}{\mathr 48. The derivative of $\sin \mathrm{x}$ with respect to $\log \mathrm{x}$ is 49. The minimum value of $1-\sin x$ is
50. The function $f(x)=\tan x-x$
51. The value of $\int \frac{\mathrm{dx}}{(\mathrm{x}+1)(\mathrm{x}+2)}$ is
52. The value of $\int_{-1}^1 \sin ^5 \mathrm{x} \cos ^4 \mathrm{xdx}$ is 53. $$ \text { The value of } \int_0^{2 \pi} \sqrt{1+\sin \left(\frac{x}{2}\right)} d x \text { is } $$ 54. $\int \frac{\mathrm{dx}}{\mathrm{x}^2\left(\mathrm{x}^4+1\right)^{3 / 4}}$ equals
55. $\int_0^1 \log \left(\frac{1}{x}-1\right) d x$ is 56. The area bounded by the curve $y=\sin \left(\frac{x}{3}\right)$, $x$ axis, the lines $x=0$ and $x=3 \pi$ is 57. The area of the region bounded by the curve $y=x^2$ and the line $y=16$ is
58. General solution of the differential equation $\frac{d y}{d x}+y \tan x=\sec x$ is
59. If ' $a$ ' and ' $b$ ' are the order and degree respectively of the differentiable equation. $\left(\frac{d^2 y}{d x^2}\ 60. The distance of the point $\mathrm{P}(-3,4,5)$ from yz plane is
Physics
1. A wooden block of mass M lies on a rough floor. Another wooden block of the same mass is hanging from the point O throug 2. A block of certain mass is placed on a rough floor. The coefficients of static and kinetic friction between the block an 3. A body of mass 0.25 kg travels along a straight line from $x=0$ to $x=2 \mathrm{~m}$ with a speed $v=k x^{3 / 2}$ where 4. During an elastic collision between two bodies, which of the following statements are correct?
I. The initial kinetic en 5. Three particles of mass $1 \mathrm{~kg}, 2 \mathrm{~kg}$ and 3 kg are placed at the vertices A, B and C respectively of 6. Two fly wheels are connected by a non-slipping belt as shown in the figure. $I_1=4 \mathrm{~kg} \mathrm{~m}^2, r_1=20 \m 7. If $r_p, v_p, L_p$ and $r_a, v_a, L_a$ are radii, velocities and angular momenta of a planet at perihelion and aphelion 8. The total energy of a satellite in a circular orbit at a distance $(R+h)$ from the centre of the Earth varies as [ $R$ i 9. Two wires A and B are made of same material. Their diameters are in the ratio of $1: 2$ and lengths are in the ratio of 10. A horizontal pipe carries water in a streamlined flow. At a point along the pipe, where the cross-sectional area is $10 11. Three metal rods of the same material and identical in all respects are joined as shown in the figure. The temperatures 12. A gas is taken from state A to state B along two different paths 1 and 2. The heat absorbed and work done by the system 13. At $27^{\circ} \mathrm{C}$ temperature, the mean kinetic energy of the atoms of an ideal gas is $\mathrm{E}_1$. If the t 14. The variations of kinetic energy $K(x)$, potential energy $U(x)$ and total energy as a function of displacement of a par 15. The angle between the particle velocity and wave velocity in a transverse wave is [except when the particle passes throu 16. A metallic sphere of radius $R$ carrying a charge $q$ is kept at certain distance from another metallic sphere of radius 17. You are given a dipole of charge $+q$ and $-q$ separated by a distance $2 R$. A sphere ' $A$ ' of radius ' $R$ ' passes 18. A potential at a point A is -3 V and that at another point B is 5 V . What is the work done in carrying a charge of 5 m 19. Charges are uniformly spread on the surface of a conducting sphere. The electric field from the centre of sphere to a po 20. Match Column-I with Column - II related to an electric dipole of dipole moment $\vec{p}$ that is placed in a uniform ele 21. Which of the following statements is not true? 22. Which of the following is a correct statement?
23. $$ \text { In the following circuit, the terminal voltage across the cell is } $$
24. Two cells of emfs $E_1$ and $E_2$ and internal resistances $r_1$ and $r_2\left(E_2>E_1\right.$ and $\left.r_2>r_1\ 25. The variations of resistivity $\rho$ with absolute temperature T for three different materials $\mathrm{X}, \mathrm{Y}$ 26. Given, a current carrying wire of non-uniform cross-section, which of the following is constant throughout the length of 27. The graph between variation of resistance of a metal wire as a function of its diameter keeping other parameters like le 28. Two thin long parallel wires separated by a distance ' $r$ ' from each other in vacuum carry a current of I ampere in op 29. A solenoid is 1 m long and 4 cm in diameter. It has five layers of windings of 1000 turns each and carries a current of 30. Two similar galvanometers are covered into an ammeter and a milliammeter. The shunt resistance of ammeter as compared to 31. Which of the following statements is true in respect of diamagnetic susbtances? 32. Identify the correct statement
33. Which of the following graphs represents the variation of magnetic field $B$ with perpendicular distance ' $r$ ' from an 34. If we consider an electron and a photon of same de-Broglie wavelength, then they will have same
35. The anode voltage of a photocell is kept fixed. The frequency of the light falling on the cathode is gradually increased 36. When a bar magnet is pushed towards the coil, along its axis, as shown in the figure, the galvanometer pointer deflects 37. A square loop of side 2 m lies in the Y-Z plane in a region having a magnetic field $\overrightarrow{\mathrm{B}}=(5 \hat 38. In domestic electric mains supply, the voltage and the current are 39. A sinusoidal voltage produced by an AC generator at any instant t is given by an equation $\mathrm{V}=311 \sin 314$ t. T 40. A series LCR circuit containing an AC source of 100 V has an inductor and a capacitor of reactances $24 \Omega$ and $16 41. $$ \text { Match the following types of waves with their wavelength ranges } $$
$$
\begin{array}{|l|l|}
\hline \text { W 42. A ray of light passes from vaccum into a medium of refractive index $n$. If the angle of incidence is twice the angle of 43. A convex lens has power P. It is cut into two halves along its principal axis. Further one piece (out of two halves) is 44. The image formed by an objective lens of a compound microscope is
45. If $r$ and $r^1$ denotes the angles inside the prism having angle of prism $50^{\circ}$ considering that during interval 46. $$ \text { If } \mathrm{AB} \text { is incident plane wave front then refracted wave front in }\left(\mathrm{n}_2>\ma 47. The total energy carried by the light wave when it travels from a rarer to a non-reflecting and nonabsorbing medium 48. If the radius of first Bohr orbit is $r$, then the radius of the second Bohr orbit will be 49. $$ \text { Match the following types of nuclei with examples shown } $$
$$ \begin{array}{|l|l|} \hline \text { Column-I 50. Which of the following statements is incorrect with reference of 'Nuclear force'? 51. The range of electrical conductivity $(\sigma)$ and resistivity $(\rho)$ for metals, among the following, is 52. Which of the following statements is correct for an n-type semiconductor?
53. The circuit shown in figure contains two ideal diodes $D_1$ and $D_2$. If a cell of emf $3 V$ and negligible internal re 54. In determining the refractive index of a glass slab using a travelling microscope, the following readings are tabulated
55. In an experiment to determine the figure of merit of a galvanometer by half deflection method, a student constructed the 56. While determining the coefficient of viscosity of the given liquid, a spherical steel ball sinks by a distance $\mathrm{ 57. Which of the following expression can be deduced on the basis of dimensional analysis? (All symbols have their usual mea 58. Two stones begin to fall from rest from the same height, with the second stone starting to fall ' $\Delta \mathrm{t}$ ' 59. In the projectile motion of a particle on a level ground, which of the following remains constant with reference to time 60. A particle is in uniform circular motion. The equation of its trajectory is given by $(x-2)^2+y^2=25$, where x and y are
1
KCET 2025
MCQ (Single Correct Answer)
+1
-0
The function $f(x)=\left\{\begin{array}{ll}e^x+a x & , x<0 \\ b(x-1)^2 & , x \geq 0\end{array}\right.$ is differentiable at $x=0$. Then
A
$a=1, b=1$
B
$a=3, b=1$
C
$a=-3, b=1$
D
$a=3, b=-1$
2
KCET 2025
MCQ (Single Correct Answer)
+1
-0
$$ \text { A function } f(x)=\left\{\begin{array}{cl} \frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}, & \text { if } x \neq 0 \\ 0, & \text { if } x=0 \end{array}\right. $$
A
continuous at $\mathrm{x}=0$
B
not continuous at $x=0$
C
differentiable at $x=0$
D
differentiable at $\mathrm{x}=0$, but not continuous at $\mathrm{x}=0$
3
KCET 2025
MCQ (Single Correct Answer)
+1
-0
If $\mathrm{y}=\mathrm{a} \sin ^3 \mathrm{t}, \mathrm{x}=\mathrm{a} \cos ^3 \mathrm{t}$, then $\frac{\mathrm{dy}}{\mathrm{dx}}$ at $\mathrm{t}=\frac{3 \pi}{4}$ is
A
-1
B
$\frac{1}{\sqrt{3}}$
C
$-\sqrt{3}$
D
1
4
KCET 2025
MCQ (Single Correct Answer)
+1
-0
The derivative of $\sin \mathrm{x}$ with respect to $\log \mathrm{x}$ is
A
$\cos x$
B
$x \cos x$
C
$\frac{\cos x}{\log x}$
D
$\frac{\cos x}{x}$