List of top Mathematics Questions asked in KSEAB Class XII

If $F$ is an event of a sample space $S$, then $P(S|F)=$
The probability of obtaining an even prime number on each die when a pair of dice is rolled is
If $A$ and $B$ are independent events with $P(A)=0.3$ and $P(B)=0.4$, then $P(A \cap B)$ is
The left hand derivative of $|x|$ with respect to $x$ at $x=0$ is
The point of inflection of the function $f(x)=x^3$ in the interval $[-1,1]$ is
If $m$ and $n$ are respectively the order and degree of the differential equation $2x^2\dfrac{d^2y}{dx^2}-3\dfrac{dy}{dx}+y=0$, then $m+n=$
The value of $\hat{i}\cdot\hat{i}+\hat{j}\cdot\hat{j}$ is
Statement I: The function $f(x)=x^2$ is decreasing in the interval $(0,\infty)$.
Statement II: Any function $y=f(x)$ is decreasing if $\dfrac{dy}{dx}& Lt;0$.
Which of the following is correct?
The antiderivative of $\dfrac{1}{x\sqrt{x^2-1}},\; x>1$ with respect to $x$ is
The value of \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin^{7}x \, dx \] is
If $\vec{a}$ is a nonzero vector of magnitude $a$ and $\lambda$ is a nonzero scalar, then $\lambda \vec{a}$ is a unit vector if
The position vector of the midpoint of the line joining the points $P(2,3,4)$ and $Q(4,1,-2)$ is
The direction ratios of the $x$-axis are
A matrix has 13 elements. The number of possible different orders it can have is
For the matrix $A=\begin{bmatrix}5 & 0 \\ 0 & 5\end{bmatrix}$, the value of $|\text{adj}\,A|$ is
The derivative of $\sin^{-1}x$ exists in the interval
If $x-y=\pi$, then $\dfrac{dy}{dx}$ is
The minimum value of $f(x)=|x|,\; x\in \mathbb{R}$ is
If a relation $R$ in the set $\{1,2,3\}$ be defined by $R=\{(1,1),(2,2)\}$, then $R$ is
The domain of $\tan^{-1}x$ is