KCET 2026

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 $...

The probability that a man and his wife live after $20$ years are $\dfrac{1}{4}$ and $\dfrac{1}{3}$ respectively. The probability that neither the man nor his wife live after $20$ years is

Probability of obtaining an even prime number on each die when a pair of dice is rolled is

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 exclusive, then the probability of occurrence of neither A nor B is

Probability of at least one of the events A and B occur is $0.6$. If A and B occur simultaneously with probability $0.2$, then $P(\bar{A}) + P(\bar{B})$ is

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

If we insert two numbers between $\sqrt{2}$ and $4$ so that the resulting sequence is in G.P, then the inserted numbers in the order are

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 the correct answer?

If $n(A) = 2$ and the number of relations from set A to set B is $1024$, then $n(B)$ is

If $A = \{1, 2, 3, 4, \ldots, 10\}$, then the number of non-empty subsets of A containing only even number is

If $A = \{a, b, c, d, e, f\}$, then the number of subsets of A which contains at least $2$ elements is