List of top Questions asked in UP Board XII

One die is thrown two times. If the sum of the appeared numbers on their faces is 6, find the conditional probability of appearing number 4 at least one time in that.
Prove that \[ \begin{vmatrix} a+b+2c & a & b \\ c & b+c+2a & b \\ c & a & c+a+2b \end{vmatrix} = 2(a+b+c)^3 \]
The modulus function $f: \mathbb{R} \to \mathbb{R}^{+}$ given by $f(x) = |x|$ will be:
If $\sin^{-1}\left(\dfrac{1}{2}\right) = \tan^{-1}x$, find the value of $x$.
If $A = \begin{bmatrix} 2 & 4 \\ 3 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 \\ -2 & 5 \end{bmatrix}$, then find the value of $(A + B)$ and $(A - B)$.
Solve $\dfrac{dy}{dx} = \dfrac{x + e^x}{y}$.
If the vectors $2\hat{i} + \hat{j} - a\hat{k}$ and $\hat{i} + 4\hat{j} + \hat{k}$ are perpendicular, find the value of $a$.
Evaluate: $\int x^{2}\sin(x^{3})\,dx$
If $A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}$, then $BA$ will be:
The slope of the normal to the curve $y = 2x^{2} + 3\sin x$ at $x = 0$ will be:
The value of $\int_{1}^{\sqrt{3}} \dfrac{dx}{1+x^{2}}$ will be:
If $y = 4t$ and $x = \dfrac{4}{t}$, then the value of $\dfrac{dy}{dx}$ will be:
Who is Mr. Lamb? What type of garden does he have?