List of top Questions asked in KCET

If $\vec{a} = \hat{i} + \hat{j} + \hat{k}$, $\vec{b} = \hat{j} - \hat{k}$ and $\vec{a} \times \vec{c} = \vec{b}$, $\vec{a} \cdot \vec{c} = 3$, then $\vec{c}$ is

The value of $\lambda$ for which the vectors $\vec{a} = 2\hat{i} + \lambda\hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + 2\hat{j} + 3\hat{k}$ are orthogonal is

The angle between the lines whose direction ratios are $a, b, c$ and $b - c, c - a, a - b$ is

The measure of the angle between the lines $x = k - 1, y = 2k + 1, z = 2k + 3, k \in \mathbb{R}$ and $\frac{x+1}{2} = \frac{y-2}{1} = \frac{z-1}{2}$ is

The line $L_{1}$ joining the two points $(-1, 2)$ and $(3, 6)$ divides the line $L_{2}$ which passes through $(3, -1)$ in the ratio $1 : 3$ internally, then the equation of $L_{2}$ is

In the figure
Statement I : When $\alpha>\beta \ge 0$, the section is hyperbola
Statement II : When $\beta = 90^\circ$, the section is ellipse
Which of the following is correct?

The three points $A(2, 4, 3)$, $B(4, a, 9)$ and $C(10, -1, 7)$ form a right-angled triangle with $\angle B = 90^\circ$, then the value of 'a' is

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

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