List of top Questions asked in KCET- 2024

If $f(x) = \begin{vmatrix} x - 3 & 2x^2 - 18 & 2x^3 - 81 \\ x - 5 & 2x^2 - 50 & 4x^2 - 500 \\ 1 & 2 & 3 \end{vmatrix}$, then $f(1) \cdot f(3) \cdot f(5) + f(5) \cdot f(1)$ is:

Let $f : \mathbb{R} \to \mathbb{R}$ be defined by $f(x) = x^2 + 1$. Then the pre-images of $17$ and $-3$ respectively are:

Let $A = \begin{pmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{pmatrix}$ is the adjoint of a $3 \times 3$ matrix $A$ and $|A| = 4$, then $\alpha$ is equal to:

Which one of the following observations is correct for the features of the logarithm function to any base $b > 1$?

If $A = \begin{bmatrix} x & 1 \\ 1 & x \end{bmatrix}$ and $B = \begin{bmatrix} x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x \end{bmatrix}$, then $\frac{dB}{dx}$ is:

If $\cos^{-1} x + \cos^{-1} y + \cos^{-1} z = 3\pi$, then $x(y + z) + y(z + x) + z(x + y)$ equals to:

If $2\sin^{-1} x - 3\cos^{-1} x = 4x$, $x \in [-1, 1]$, then $2\sin^{-1} x + 3\cos^{-1} x$ is equal to:

Two finite sets have m and a elements respectively. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and a respectively are:

If \(f(x) = \begin{bmatrix} \cos x & x &1 \\ 2 \sin x & x & 2x \\ \sin x & x & x \end{bmatrix}\). Then \(\lim_{x \to 0} \frac{f(x)}{x^2}\) is:

The negation of the statement “For every real number $x$, $x^2 + 5$ is positive” is:

For the function $f(x) = x^3 - 6x^2 + 12x - 3$, $x = 2$ is:}

If a random variable $X$ follows the binomial distribution with parameters $n = 5$, $p$, and $P(X = 2) = 9P(X = 3)$, then $p$ is equal to:

Corner points of the feasible region for an LPP are $(0, 2), (3, 0), (6, 0), (6, 8)$ and $(0, 5)$. Let $z = 4x + 6y$ be the objective function. The minimum value of $z$ occurs at:

The function $f(x) = |\cos x|$ is:

The value of $C$ in $(0, 2)$ satisfying the mean value theorem for the function $f(x) = x(x - 1)^2$, $x \in [0, 2]$ is equal to:}

The distance between the two planes $2x + 3y + 4z = 4$ and $4x + 6y + 8z = 12$ is:

If $y = 2x^{3x}$, then $\frac{dy}{dx}$ at $x = 1$ is:

Let $a$, $b$, $c$, and $d$ be the observations with mean $m$ and standard deviation $S$. The standard deviation of the observations $a + k, b + k, c + k, d + k$ is:

Let $f : \mathbb{R} \to \mathbb{R}$ be given by $f(x) = \tan x$. Then $f^{-1}(1)$ is:

$\int \frac{\sin x}{3 + 4\cos^2 x} \, dx =$

$\frac{d}{dx} \left[ \cos^2 \left( \cot^{-1} \sqrt{\frac{2 + x}{2 - x}} \right) \right]$ is:}

If lines $\frac{x - 1}{-3} = \frac{y - 2}{2k} = \frac{z - 3}{2}$ and $\frac{x - 1}{3k} = \frac{y - 5}{1} = \frac{z - 6}{-5}$ are mutually perpendicular, then $k$ is equal to:

If A.M. and G.M. of roots of a quadratic equation are $5$ and $4$ respectively, then the quadratic equation is:

Let the function satisfy the equation $f(x + y) = f(x)f(y)$ for all $x, y \in \mathbb{R}$, where $f(0) \neq 0$. If $f(5) = 3$ and $f'(0) = 2$, then $f'(5)$ is: