List of top Questions asked in KCET- 2026

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

If $y = \sqrt{\tan x + y}$, then $\frac{dy}{dx} = $

If $f(x) = \begin{cases} ax + 7 & \text{if } x<1 \\ 2x - 3 & \text{if } x = 1 \\ \frac{x+b}{b} & \text{if } x>1 \end{cases}$ is continuous at $x = 1$, then

The second order derivative of $\sec^{-1}\left(\frac{1}{2x^2 - 1}\right)$ with respect to $\cos^{-1}(2x^2 - 1)$, where $0<x<\frac{1}{\sqrt{2}}$ is

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

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

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

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)

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

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

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

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

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

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

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

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

If $n(A) = 2$ and the number of relations from set A to set B is 1024, then $n(B)$ 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 maximum value of $\sin(x + \pi/6) + \cos(x + \pi/6)$ is attained at $x =$

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

The mean and standard deviation of 100 items are 50 and 4, respectively then the sum of all squares of the items is

Probability of occurrence of an event A is 1/2 and that of B is 3/10. If A and B are mutually exclusive, then the probability of occurrence of neither A nor B is

Let R be the relation in the set N given by $R = \{(a, b) : a = b - 2, b>6\}$. Which of the following is the correct answer?

$f(x) = (x + 1)^2$ for $x \ge 1$. $g(x)$ is a function whose graph is the reflection of the graph of $f(x)$ in the line $y = x$, then $g(x)$ is