Chemistry
1. Match List-I with List-II and select the correct option (Based on mole concept):List-IList-II(a)$2$ moles of ethene(i)$1 2. From the given information, select the suitable law of chemical combination:Cupric Carbonate% of Cu% of C% of ONatural S 3. Which of the following is the CORRECT statement about $\Psi^2$? 4. Which of the following represents de Broglie equation? 5. Match List-I with List-II:List-I (Element-Atomic number)List-II (Position in periodic table)(a)Ra – 88(i)$4^{th}$ period 6. With respect to resonance structures of $\text{CO}_3^{2-}$ ion, which of the following statements are correct?(a) All $\ 7. In which of the following option/options, the order of arrangement does not agree with the variation of property indicat 8. The types of hybrid orbitals of nitrogen in $\text{NO}_2^+, \text{NO}_3^-$ and $\text{NH}_4^+$ respectively are 9. A gas can be taken from A to B via two different paths ACB and ADB.When path ACB is used, $60$ J of heat flows into the 10. Which of the following is a correct statement for a thermodynamic system? 11. A: Entropy of a perfect crystalline solid at absolute zero approaches zero.B: For spontaneity of a reaction, $T\Delta S 12. For the following gaseous reversible reaction:$3\text{A}_{(g)} + \text{B}_{(g)} \rightleftharpoons \text{A}_3\text{B}_{( 13. For the reversible reaction,$\text{N}_{2(g)} + 3\text{H}_{2(g)} \rightleftharpoons 2\text{NH}_{3(g)}$When the partial pr 14. A $0.15$ mole of pyridinium chloride has been added to $500\text{ cm}^3$ of $0.2$ M pyridine solution (a base). Assuming 15. $a\text{C}_2\text{O}_4^{2-} + b\text{MnO}_4^- + c\text{H}^+ \rightarrow x\text{Mn}^{2+} + y\text{H}_2\text{O} + z\text{C 16. Given below are two statements.Statement-I: In $\text{H}_2\text{O}_2$, each oxygen atom is assigned an oxidation number 17. Statement I: Staggered conformation of ethane is more stable than the eclipsed conformation.Statement II: The torsional 18. Carboxylic acids are more acidic than phenols because 19. The correct IUPAC name of is 20. $\text{C}-\text{Cl}$ bond in methyl chloride compared to $\text{C}-\text{Cl}$ bond in chlorobenzene is 21. The compound with molecular formula $\text{C}_{20}\text{H}_{42}$ is 22. The number of chain isomers possible for the hydrocarbon with molecular formula $\text{C}_5\text{H}_{12}$ is 23. Statement-I: Nitrogen in pyridine cannot be estimated by Kjeldahl's method.Statement-II: Nitrogen in pyridine changes to 24. The intermediates in heteropolar reactions are 25. The relative lowering of vapour pressure produced by dissolving $18$ g of urea (Molar mass $= 60\text{ g mol}^{-1}$) in 26. When $0.0106$ mole of acetic acid was dissolved in $1$ kg of water, the freezing point depression for this strength of a 27. Match List-I (Laws) with the List-II (Mathematical expressions):List-IList-II(a)Henry's law(i)$p_1 = p_1^0 x_1$(b)Raoult 28. Which of the following is CORRECT with respect to the property mentioned against it? 29. The conductivity of centimolar solution of KCl at $298$ K is $0.021\text{ Ohm}^{-1}\text{cm}^{-1}$ and the resistance of 30. Given below are the half-cell reactions:$\text{Mn}^{2+} + 2e^- \rightarrow \text{Mn} \quad (E^0 = -1.18\text{ V})$$2(\te 31. $\Lambda^0_{m(\text{NH}_4\text{OH})}$ is equal to ____ 32. During the electrolysis of acidified water, $16$ g of $\text{O}_2$ gas is formed at anode. The volume of $\text{H}_2$ ga 33. The activation energy for the reaction $X \rightarrow Y$ is $150\text{ kJ mol}^{-1}$. The change in enthalpy for the abo 34. For a 1st order change $R \rightarrow P$, the concentration of Reactant R changes from $0.1$ M to $0.025$ M in $40$ minu 35. For a reaction having three steps, the overall rate constant is $k = \dfrac{k_1 k_2}{k_3}$. The values of $E_{a_1}, E_{a 36. Which one of the following graph is not applicable for a 1st order reaction ($R \rightarrow P$)? 37. The calculated spin only magnetic moment of $\text{Cr}^{2+}$ ion is 38. The highest oxidation state of manganese in fluoride is $+4$ ($\text{MnF}_4$), but the highest oxidation state in oxides 39. Which of the following will not act as an oxidising agent? 40. Match List-I with List-IIList-I (Complex)List-II (Geometry)(a)$[\text{Co(NH}_3\text{)}_6]^{3+}$(i)Trigonal bipyramidal(b 41. Given below are two statements:Statement-I: The $\text{M}-\text{C}$ $\sigma$ bond is formed by the donation of lone pair 42. How many ions per molecule are produced from the complex $[\text{Co(NH}_3\text{)}_6]\text{Cl}_2$ in solution? 43. Which of the following is the most stable complex ion? 44. In $\text{S}_\text{N}1$ reaction, the alkyl halide that on hydrolysis produces racemic mixture is 45. The compound from which chlorobenzene cannot be prepared easily is 46. Organic compound 'D' is 47. Glycerol is a trihydric alcohol. It contains ____. 48. $R-\text{CH}_2\text{OH}$ is converted into $R-\text{CHO}$ by reacting with ________. 49. Match List-I with List-II and select the correct optionsList-I (Functional group)List-II (Functional group reagent)(a)(i 50. The compound that does not answer iodoform test is 51. The major product '$A$' in the given reaction isBenzaldehyde $\xrightarrow{\large{\text{Acetophenone, OH}^-/293\text{K}} 52. Match the reagents in List-I with products obtained from their carbonyl compounds in List-II.List-IList-II(a)$\text{NH}_ 53. $\text{C}_3\text{H}_6 \xrightarrow{\large{(i)\text{ BH}_3;\ (ii)\text{ H}_2\text{O}_2/\text{NaOH}}} P \xrightarrow{\larg 54. Basic strength of alkylamines in aqueous phase is not decided by ________. 55. Nitration of aniline in strong acidic medium gives significant amount of m-nitroaniline because 56. Incorrect statement about $\alpha$-amino acids of proteins among the following is 57. Consider the following statements:Statement-I: All monosaccharides are reducing sugars.Statement-II: Sucrose can reduce 58. Match List-I with List-IIList-I (Vitamins)List-II (Deficiency Diseases)(a)$\text{B}_1$(i)Convulsions(b)$\text{B}_2$(ii)R 59. Match the compounds of List-I with their effects in List-II:List-IList-II(a)Chloramphenicol(i)Malaria(b)Thyroxine(ii)Ana 60. When salt BA is treated with Conc. $\text{H}_2\text{SO}_4$ reddish brown gas is liberated. The aqueous solution of BA gi
Mathematics
1. The solution of $3(x - 1) \leq 2(x - 3)$ is 2. If $\alpha$ and $\beta$ are acute angles such that $\alpha - \beta$ and $\alpha + \beta$ satisfy the equation $\tan^2\th 3. $\sum\limits_{n=1}^{4} (-1)^{2n} \cdot i^{2n} = $ 4. How many ways can you arrange all the letters and numbers in "KCET 2025" which start with K and end with $5$? 5. $10$ distinct points are taken on a circle. Then using these pointsStatement I: The number of triangles that can be form 6. If we insert two numbers between $\sqrt{2}$ and $4$ so that the resulting sequence is in G.P, then the inserted numbers 7. The angles of a triangle are in A.P and the greatest angle is double the least angle, then sine of the third angle is 8. The value at $x = 2$ for $\dfrac{x^3 + 3x^2 + 3x + 1}{x^4 + 4x^3 + 6x^2 +4x + 1}$ 9. The maximum value of $\sin\left(x + \dfrac{\pi}{6}\right) + \cos\left(x + \dfrac{\pi}{6}\right)$ is attained at $x = $ 10. The line $L_2$ passing through $(3, -1)$ divides the line segment $L_1$ joining the points $(-1, 2)$ and $(3, 6)$ in the 11. The area of the triangle with vertices $(3, 8), (-4, 2)$ and $(5, 1)$ is $\dfrac{P}{4}$, then the value of $P$ is 12. In the figureStatement-I: When $\alpha > \beta \geq 0$, the section is hyperbolaStatement-II: When $\beta > 90^\ci 13. If $f(x) = \begin{cases} x^2 - 1 & \text{if } x \geq 2 \\ x + 1 & \text{if } x 14. If $\lim\limits_{x \to 3}\left(\dfrac{x^2 - ax - 3b}{x - 3}\right) = 5$, then $a + b = $ 15. The mean and standard deviation of $100$ items are $50$ and $4$, respectively then the sum of all squares of the items i 16. Let R be the relation in the set $\mathbb{N}$ given by $R = \{(a, b) : a = b - 2, b > 6\}$. Which of the following is th 17. If $n(A) = 2$ and the number of relations from set A to set B is $1024$, then $n(B)$ is 18. If $A = \{1, 2, 3, 4, \ldots, 10\}$, then the number of non-empty subsets of A containing only even number is 19. If $A = \{a, b, c, d, e, f\}$, then the number of subsets of A which contains at least $2$ elements is 20. If A and B are invertible matrices of same order, then which of the following is not correct? 21. Let X be a matrix of order $2 \times n$ and Z be a matrix of order $2 \times p$. If $n = p$, then the order of the matri 22. A row matrix has only 23. Consider the following statements:Statement I: If A is a non-singular matrix, then $A^{-1}$ exists.Statement II: If A an 24. Match List-I with List-IIList-IList-IIa)A matrix which is not a square matrixi)Symmetric matrixb)A square matrix $A = A' 25. The system of equations $x + 2y = 3$ and $2x + 3y = 3$ has 26. If A and B are invertible square matrices of order n, then which of the following is not correct? 27. Which of the following is correct? 28. The second order derivative of $\cos^{-1}(4x^3 - 3x)$ with respect to $\cos^{-1}(2x^2 - 1)$, where $\dfrac{1}{2} 29. $\tan^{-1}\left(\dfrac{1}{1 + 1 \cdot 2}\right) + \tan^{-1}\left(\dfrac{1}{1 + 2 \cdot 3}\right) + \ldots + \tan^{-1}\le 30. If $\sin^{-1} x + \sin^{-1} y = \dfrac{\pi}{2}$, then $x^2$ is equal to 31. $f(x) = (x-1)^2$ for $x \geq 1$, $g(x)$ is a function whose graph is the reflection of the graph of $f(x)$ in the line $ 32. The domain of the function $\sqrt{\dfrac{x-7}{9-x}}$ is 33. If $f(x) = \begin{cases} ax + 7 & \text{if } x 1 \end{cases}$ is continuous at $x = 1$, then 34. If $f(x) = \sin^{-1}\left(\dfrac{2x}{1 + x^2}\right)$, then $f'\left(\dfrac{1}{2}\right) = $ 35. If $y = \sqrt[3]{\tan x + y}$, then $\dfrac{dy}{dx} = $ 36. A YouTube short video is getting viral according to $f(t) = -2t^3 + 3t^2 + 5$. At what time does the video get maximum n 37. In a Mahakumbh, a drone camera is moving along $3y = x^3 - 3$. When $y$-coordinate changes $9$ times as fast as $x$-coor 38. $\int e^{-x \log 2} \cdot 2^x\,dx = $ 39. If '$n$' is a natural number, then $\int \dfrac{\sin^n x}{\cos^{n+2} x}\,dx = $ 40. $\int\limits_{a-6}^{b-6} f(x + 6)\,dx$ is equal to 41. One of the possible functions $f(x)$ which satisfies $\int\limits_{-2}^{2} f(x)\,dx = 0$ is 42. The area enclosed by the curve $x = \sqrt{3}\cos\theta, y = \sqrt{3}\sin\theta$ is 43. The area of the region bounded by the curve $y^2 = x^3$, the $y$-axis and the lines $y = 1$ and $y = 8$ is 44. Sum of the squares of the order and degree (if defined) of a differential equation $2 y^{\prime}+\left(y^{\prime \prime} 45. $\int xf(x)\,dx + \dfrac{f(x)}{2} = 0$, then $f(x)$ is equal to 46. If $\sqrt{x} \sqrt[3]{y} = (x + y)^n$ and $x\dfrac{dy}{dx} - y = 0$, then $n = $ 47. Integrating factor of the differential equation $(1 + x^2)\dfrac{dy}{dx} + xy = 1$ is 48. The value of $\lambda$ for which the vectors $\vec{a} = 2\hat{i} + \lambda\hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + 2\ 49. If $\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = \hat{j} - \hat{k}$ and $\vec{a} \times \vec{c} = \vec{b}, \vec{a} \ 50. If $\vec{a} = 2\hat{i} + 2\hat{j} - \hat{k}, \vec{b} = \alpha\hat{i} + \beta\hat{j} + 2\hat{k}$ and $|\vec{a} + \vec{b}| 51. The three points $A(2, 4, 3), B(4, a, 9)$ and $C(10, -1, 7)$ form a right-angled triangle with $\angle B = 90^\circ$, th 52. The measure of the angle between the lines $x = k + 1, y = 2k - 1, z = 2k + 3, k \in \mathbb{R}$ and $\dfrac{x - 1}{2} = 53. The angle between the lines whose direction ratios are $a, b, c$ and $b - c, c - a, a - b$ is 54. In Linear Programming Problem (LPP), the objective function $Z = ax + by$ has the same maximum value at two corner point 55. The corner points of the feasible region determined by the system of linear constraints are $(0, 10), (5, 5), (15, 15), 56. Recent studies suggest that $12\%$ of the world population is left handed. Depending on parents' hand usage, the chances 57. The probability that a man and his wife live after $20$ years are $\dfrac{1}{4}$ and $\dfrac{1}{3}$ respectively. The pr 58. Probability of obtaining an even prime number on each die when a pair of dice is rolled is 59. Probability of occurrence of an event A is $\dfrac{1}{2}$ and that of B is $\dfrac{3}{10}$. If A and B are mutually excl 60. Probability of at least one of the events A and B occur is $0.6$. If A and B occur simultaneously with probability $0.2$
Physics
1. Match the physical quantities given in List-I with dimensions expressed in terms of mass (M), length (L), time (T) and e 2. The velocity of a particle moving along $x$-axis is given as $V = x^2 - 5x + 4$ (in m/s) where $x$ denotes the $x$-coord 3. A car covers the first half of the distance between two places at $40$ km/h and another half at $50$ km/h. The average s 4. Two bodies are projected with the same velocity. If one is projected at an angle of $30^\circ$ and the other at $45^\cir 5. A horizontal force of $5$ N is applied on a stationary body of mass $5$ kg, which is initially at rest on a frictionless 6. A mass M is hung with a light inextensible string as shown in figure. Find the tension of the horizontal string. 7. A man weighs $80$ kg. He stands on a weighing scale in a lift which is moving upwards with a uniform acceleration of $6 8. Two bodies with kinetic energies in the ratio of $3:1$ are moving with equal linear momentum. The ratio of their masses 9. If the earth were to suddenly contract to half of its present radius, what would be the duration of the day? 10. The angular momentum of a moving body remains constant, if 11. Suppose the acceleration due to gravity at the earth's surface is $g \text{ m/s}^2$ and at the surface of moon it is $g' 12. Imagine a new planet having the same density as that of the earth, but it is two times bigger than the earth in size. If 13. There are two wires of same material and same length while the diameter of second wire is two times the diameter of the 14. A 30 cm long capillary tube is dipped in water, water rises upto a height of $10$ cm due to capillarity. If this experim 15. Instrument fitted in the carburetor of the automobile to provide the correct mixture of air and fuel necessary for combu 16. Following are statements of a few processes taking place in nature.I. Free expansion of a gasII. The combustion of a mix 17. In thermodynamic processes, which of the following statements is not true? 18. The graph of pressure P and volume V of $1$ mole of an ideal gas at constant temperature is 19. A mass of $1$ kg is executing SHM. Its displacement is given by $x = 6.0\cos(100t + \pi/4)$ cm. What is the maximum kine 20. A source of frequency $\nu$ gives $6$ beats/second when sounded with a source of frequency $200$ Hz. The second Harmonic 21. A $200$ J of work is done in moving a charge $5$ C from a point A where the potential is $-20$ V to another point B wher 22. An electric dipole of dipole moment $\vec{P}$ is placed in the uniform electric field $\vec{E}$. Then which of the follo 23. Consider three point charges $-2Q, Q$ and $-Q$ and three surfaces $S_1, S_2$ and $S_3$ as shown in the figure. Match the 24. What will be the total electric flux through the faces of the cube as given in the figure with side of length '$a$' if a 25. An electron falls through a distance $1.5$ cm in $2.0 \times 10^4$ N/C from rest. The time taken to cover this distance 26. A point charge is placed in a moving train. A passenger A sitting in the train and person B on the ground observe the fi 27. In the circuit shown in the figure, the potential difference across the $4 \mu\text{F}$ capacitor is 28. A parallel plate capacitor has a uniform electric field '$E$' in the space between the plates. If the distance between t 29. In the figure, the values of currents $I_1, I_2$ and $I_3$ respectively are 30. Which of the following circuits is correct for verification of Ohm's law? 31. In a conducting region, $10^{19}$ electrons and $10^{19}$ protons move to the left, while $10^{19}$ $\alpha$-particles m 32. Current flowing through a wire decreases linearly from $10$ A to zero in $4$ s as shown in the graph. Find the total cha 33. Given below are two statements:Statement-I: The resistivity of a conductor is independent of its temperature.Statement-I 34. The number of electrons moving per second through the filament of a lamp of $60$ W operating at $120$ V is nearly $(e = 35. Pick out the WRONG statements about magnetic substances.($\chi$ = magnetic susceptibility)($\mu_r$ = relative permeabili 36. If a paramagnetic bar is brought near a bar magnet, then it is 37. Two identical circular current loops carrying equal currents are placed with their axes inclined at $45^\circ$ to each o 38. Biot-Savart law indicates that an electron moving with a velocity $\vec{V}$ produces a magnetic field $\vec{B}$ around i 39. A proton, an electron and an $\alpha$-particle enter at right angles to a uniform magnetic field with the same velocity. 40. In the figure shown, the conductor PQ of length $l$ is moved from $x = 0$ to $x = b$ and then up to $x = 2b$ with a cons 41. In Faraday-Henry's experiment, a coil is connected to a galvanometer. For the deflection of pointer in the galvanometer, 42. A small town with a demand of $900\text{ kW}$ of electric power at $220\text{ V}$ is situated $20\text{ km}$ away from a 43. A light bulb rated $100$ W is connected to an AC source of $220$ V, $50$ Hz. The rms current through the bulb is 44. In a circuit containing a pure resistor connected to an AC source, 45. What range of electromagnetic spectrum is considered as light? 46. Match the following Maxwell's equations:(The symbols used here have their usual meanings)List-IList-II(a)Gauss' law for 47. From the graph of angle of deviation versus angle of incidence for an equilateral prism, the refractive index of materia 48. The critical angle for a monochromatic light going from medium A to medium B is $\theta$. If the speed of light in mediu 49. The incorrect statement about refractive index for a pair of media is 50. The direction of a ray of light incident on a concave mirror is shown by PQ, while direction in which the ray would trav 51. With reference to the figure shown below, match the following:List-IList-II(a)Angle of reflection(i)$60^\circ$(b)Value o 52. In Young's double slit experiment, how many maxima can be seen on a screen (including central maxima) if $d = \dfrac{5\l 53. Variation of photoelectric current with anode potential is shown below. Choose the correct option ($V_0$ = stopping pote 54. Work function of the metal is 55. An electron transition takes place from excited state to ground state in hydrogen atom, then 56. Bohr's second postulate implies quantisation of 57. The radius of first orbit in hydrogen atom is $5.3 \times 10^{-11}$ m. The kinetic energy $E_K$, potential energy $E_P$ 58. A wafer of pure germanium crystal has two parts X and Y. The end X is obtained by doping with arsenic and Y with indium. 59. In which of the following figures, diode is reverse biased? 60. An n-type and p-type semiconductor can be obtained by respectively doping pure silicon with
1
KCET 2026
MCQ (Single Correct Answer)
+1
-0
The second order derivative of $\cos^{-1}(4x^3 - 3x)$ with respect to $\cos^{-1}(2x^2 - 1)$, where $\dfrac{1}{2} < x < 1$ is
A
$0$
B
$-\dfrac{1}{\sqrt{1 - x^2}}$
C
$\dfrac{3}{2}$
D
$-\dfrac{3}{2}$
2
KCET 2026
MCQ (Single Correct Answer)
+1
-0
$\tan^{-1}\left(\dfrac{1}{1 + 1 \cdot 2}\right) + \tan^{-1}\left(\dfrac{1}{1 + 2 \cdot 3}\right) + \ldots + \tan^{-1}\left(\dfrac{1}{1 + n(n+1)}\right) = $
A
$\tan^{-1}\left(\dfrac{n}{n+2}\right)$
B
$\tan^{-1}\left(\dfrac{n+1}{n}\right)$
C
$\tan^{-1}\left(\dfrac{n}{n+1}\right)$
D
$\tan^{-1}\left(\dfrac{n+2}{n}\right)$
3
KCET 2026
MCQ (Single Correct Answer)
+1
-0
If $\sin^{-1} x + \sin^{-1} y = \dfrac{\pi}{2}$, then $x^2$ is equal to
A
$1 - y^2$
B
$\sqrt{1 - y^2}$
C
$-\sqrt{1 - y^2}$
D
$1 + y^2$
4
KCET 2026
MCQ (Single Correct Answer)
+1
-0
$f(x) = (x-1)^2$ for $x \geq 1$, $g(x)$ is a function whose graph is the reflection of the graph of $f(x)$ in the line $y = x$, then $g(x)$ is
A
$-\sqrt{x} + 1$
B
$\sqrt{x} - 1$
C
$\sqrt{x} + 1$
D
$\sqrt{x - 1}$