List of top Mathematics Questions asked in Bihar Board Class XII

Evaluate: \(\displaystyle \int_0^a \left( \sqrt{x} + \sqrt{a - x} \right) \sqrt{x} \, dx = \)
Evaluate: \(\displaystyle \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin^7 x \, dx = \)
The equation of the \( xy \)-plane is:
The distance between the points \( (4, 3, 7) \) and \( (1, -1, -5) \) is:
If \( P(A) = \frac{1}{3} \), \( P(B) = \frac{1}{4} \), and \( P(A \cap B) = \frac{1}{5} \), then \( P(B|A) \) is:
A coin is tossed 10 times. The probability of getting exactly six heads is:
If \( P(A) = \frac{6}{11} \), \( P(B) = \frac{5}{11} \), and \( P(A \cup B) = \frac{7}{11} \), then \( P(A \cap B) \) is:
The direction cosines of the \( z \)-axis are:
The probability of drawing a king from a pack of 52 cards is:
If events \( A \) and \( B \) are independent, then:
The slope of the tangent to the curve \( y = 2x^P + 3\sin x \) at \( x = 0 \) is:
The rate of change of the area of a circle with respect to its radius \( r \) (in cm\(^2\)/cm) at \( r = 6 \) cm is:
If the direction ratios of two parallel lines are \(a_1, b_1, c_1\) and \(a_2, b_2, c_2\) then \(\dfrac{a_1 c_2}{a_2}=\) ?
If the direction ratios of two parallel lines are \(x,\,5,\,3\) and \(20,\,10,\,6\) then the value of \(x\) is:
\(\left\lVert 3\vec i-4\vec j-5\vec k\right\rVert =\) ?
\([\,2a-7\ \ \ 1\,]=[\,a\ \ \ b-1\,]\Rightarrow (a,b)=\ ?\)
Evaluate \(\begin{vmatrix}1&1&5 \\ 4&9&17 \\ 5&10&22\end{vmatrix}\).

Evaluate \(\begin{vmatrix}1&2&-1 \\ 5&4&1 \\ 7&6&1\end{vmatrix}\).

Evaluate \(\begin{vmatrix}-\sin\theta&\cos\theta \\ \sec\theta&\csc\theta\end{vmatrix}\).

Compute \(\begin{bmatrix}1&0 \\ 0&1\end{bmatrix}\begin{bmatrix}2&-3 \\ 0&4\end{bmatrix}=\) ?
Compute \([\,6\ \ 5\,]\begin{bmatrix}1 \\ -1\end{bmatrix}=\) ?
\(\dfrac{d}{dx}\big(2\cos \tfrac{3x}{4}\big)=\) ?
\(\dfrac{d}{dx}\left(e^{-3x}\right)=\) ?
\(\dfrac{d}{dx}\left(11^x\right)=\) ?
\(\dfrac{d}{dx}\left(\dfrac{1}{3x-2}\right)=\) ?