List of top Mathematics Questions asked in KCET

The function $x^x$, $x > 0$ is strictly increasing at:

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

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

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:

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

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

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

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:

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:

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:

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 $A = \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix}$, then $A^{10}$ is equal to:

If $A$ is a square matrix such that $A^2 = A$, then $(I + A)^3$ is equal 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:

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

Let $A = \{2, 3, 4, 5, \ldots, 16, 17, 18\}$. Let $R$ be the relation on the set $A$ of ordered pairs of positive integers defined by $(a, b) R (c, d)$ if and only if $ad = bc$ for all $(a, b), (c, d) \in A \times A$. Then the number of ordered pairs of the equivalence class of $(3, 2)$ is:

Let $(g \circ f)(x) = \sin x$ and $(f \circ g)(x) = \left(\sin \sqrt{x}\right)^2$. Then:

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

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

$\lim_{x \to \frac{\pi}{4}} \frac{\sqrt{2}\cos x - 1}{\cot x - 1}$ is equal to:

The equation of the parabola whose focus is $(6, 0)$ and directrix is $x = -6$ is:

The angle between the line $x + y = 3$ and the line joining the points $(1, 1)$ and $(-3, 4)$ is: