KCET 2026

Statement-I: Nitrogen in pyridine cannot be estimated by Kjeldahl's method.Statement-II: Nitrogen in pyridine changes to ammonium sulphate when heated with conc. $\text{H}_2\text{SO}_4$ in Kjeldahl's method.Read the above given statements a...

Match List-I with List-II and select the correct optionsList-I (Functional group)List-II (Functional group reagent)(a)(i)Neutral ferric chloride test(b)$\text{C}_6\text{H}_5\text{NH}_2$(ii)Azo dye test(c)$\text{CH}_3\text{CH}_2\text{CHO}$(i...

$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{CO}_2$$a$ and $x$ respectively are

Given below are two statements.Statement-I: In $\text{H}_2\text{O}_2$, each oxygen atom is assigned an oxidation number of $-1$, in $\text{RbO}_2$ each oxygen atom is assigned an oxidation number of $-\dfrac{1}{2}$.Statement-II: Representat...

When salt BA is treated with Conc. $\text{H}_2\text{SO}_4$ reddish brown gas is liberated. The aqueous solution of BA gives pale yellow precipitate with $\text{AgNO}_3$ solution. Which of the following anion ($\text{A}^-$) is present in the...

Match List-I with List-II and select the correct option (Based on mole concept):List-IList-II(a)$2$ moles of ethene(i)$11.2$ L volume at STP(b)Mass is equal to $66$ g(ii)$56$ g(c)$1$ g of $\text{H}_2$(iii)$12.04 \times 10^{23}$ Molecules(d)...

From the given information, select the suitable law of chemical combination:Cupric Carbonate% of Cu% of C% of ONatural Sample51.359.7438.91Synthetic Sample51.359.7438.91

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 system and $30$ J of work is done by the system. If path ADB is used, work done by the system is $10$ J.The heat flow in...

Which of the following is a correct statement for a thermodynamic system?

A: Entropy of a perfect crystalline solid at absolute zero approaches zero.B: For spontaneity of a reaction, $T\Delta S > \Delta H$.Among the two statements given above, identify the correct answer from the options given below.

A YouTube short video is getting viral according to $f(t) = -2t^3 + 3t^2 + 5$. At what time does the video get maximum number of shares? ($t$ is in hours)

In a Mahakumbh, a drone camera is moving along $3y = x^3 - 3$. When $y$-coordinate changes $9$ times as fast as $x$-coordinate, it captures good quality pictures. Then one of the precise positions of the drone at that instant is

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

The value at $x = 2$ for $\dfrac{x^3 + 3x^2 + 3x + 1}{x^4 + 4x^3 + 6x^2 +4x + 1}$

The area enclosed by the curve $x = \sqrt{3}\cos\theta, y = \sqrt{3}\sin\theta$ is

$\sum\limits_{n=1}^{4} (-1)^{2n} \cdot i^{2n} = $

$\int\limits_{a-6}^{b-6} f(x + 6)\,dx$ is equal to

One of the possible functions $f(x)$ which satisfies $\int\limits_{-2}^{2} f(x)\,dx = 0$ is

Sum of the squares of the order and degree (if defined) of a differential equation $2 y^{\prime}+\left(y^{\prime \prime}\right)^2=\sqrt{y^{\prime \prime}-3}$ is

$\int xf(x)\,dx + \dfrac{f(x)}{2} = 0$, then $f(x)$ is equal to

Integrating factor of the differential equation $(1 + x^2)\dfrac{dy}{dx} + xy = 1$ is

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

If $f(x) = \sin^{-1}\left(\dfrac{2x}{1 + x^2}\right)$, then $f'\left(\dfrac{1}{2}\right) = $

If $y = \sqrt[3]{\tan x + y}$, then $\dfrac{dy}{dx} = $

If $\sqrt{x} \sqrt[3]{y} = (x + y)^n$ and $x\dfrac{dy}{dx} - y = 0$, then $n = $

$f(x) = (x-1)^2$ 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

The domain of the function $\sqrt{\dfrac{x-7}{9-x}}$ is

In the figureStatement-I: When $\alpha > \beta \geq 0$, the section is hyperbolaStatement-II: When $\beta > 90^\circ$, the section is ellipseWhich of the following is correct?

$\int e^{-x \log 2} \cdot 2^x\,dx = $

If '$n$' is a natural number, then $\int \dfrac{\sin^n x}{\cos^{n+2} x}\,dx = $

$\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) = $

If $\sin^{-1} x + \sin^{-1} y = \dfrac{\pi}{2}$, then $x^2$ is equal to

If $f(x) = \begin{cases} x^2 - 1 & \text{if } x \geq 2 \\ x + 1 & \text{if } x < 2 \end{cases}$, then $\lim\limits_{x \to 1} f(x) + \lim\limits_{x \to 2} f(x) = $

If $\lim\limits_{x \to 3}\left(\dfrac{x^2 - ax - 3b}{x - 3}\right) = 5$, then $a + b = $

If $f(x) = \begin{cases} ax + 7 & \text{if } x < 1 \\ 3x - 1 & \text{if } x = 1 \\ \dfrac{b}{x + 3} & \text{if } x > 1 \end{cases}$ is continuous at $x = 1$, then

In Linear Programming Problem (LPP), the objective function $Z = ax + by$ has the same maximum value at two corner points. The number of points at which $Z_{max}$ occurs is

The corner points of the feasible region determined by the system of linear constraints are $(0, 10), (5, 5), (15, 15), (0, 20)$. Let $z = px + qy$ where $p, q > 0$. The relation between $p$ and $q$, so that the maximum $z$ occurs at both p...

The solution of $3(x - 1) \leq 2(x - 3)$ is

The area of the triangle with vertices $(3, 8), (-4, 2)$ and $(5, 1)$ is $\dfrac{P}{4}$, then the value of $P$ is

If A and B are invertible matrices of same order, then which of the following is not correct?

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 matrix $8X - 9Z$ is:

A row matrix has only

Consider the following statements:Statement I: If A is a non-singular matrix, then $A^{-1}$ exists.Statement II: If A and B are symmetric matrices of same order, then $(AB - BA)$ is a skew symmetric matrix.Choose the correct option.

Match List-I with List-IIList-IList-IIa)A matrix which is not a square matrixi)Symmetric matrixb)A square matrix $A = A'$ii)Null matrixc)The diagonal elements of a diagonal matrix are sameiii)Rectangular matrixd)A matrix which is both symme...

The system of equations $x + 2y = 3$ and $2x + 3y = 3$ has

If A and B are invertible square matrices of order n, then which of the following is not correct?

Which of the following is correct?

How many ways can you arrange all the letters and numbers in "KCET 2025" which start with K and end with $5$?

$10$ distinct points are taken on a circle. Then using these pointsStatement I: The number of triangles that can be formed is $100$Statement II: The number of chords that can be formed is $45$Which of the following is correct?

Recent studies suggest that $12\%$ of the world population is left handed. Depending on parents' hand usage, the chances of having left handed children are as follows:A: Both parents are left handed, chances of having left handed children $...