List of top Questions asked in Bihar Board XII

For \(|x|\le1\), \(2\tan^{-1}x=\ \ ?\)
For \(x\in\mathbb R\), \(\cot^{-1}x=\ \ ?\)
\(\tan^{-1}\!\left(\dfrac{x+y}{1-xy}\right)=\ \ ?\)
\(\sin^{-1}\!\big(\sin \tfrac{2\pi}{3}\big)=\ \ ?\)
\(\displaystyle \int_{\pi/6}^{\pi/4}\tan\theta\,d\theta=\ \ ?\)
\(\displaystyle \int \sin^{3}\theta\ \csc^{2}\theta\,d\theta=\ \ ?\)
\(\displaystyle \int \big(\cos\theta\,\csc^{2}\theta-\cos\theta\,\cot^{2}\theta\big)\,d\theta=\ \ ?\)
\(\displaystyle \int (4\cos x-5\sin x)\,dx=\ \ ?\)
\(\displaystyle \int \frac{3\cos x-2\sin x}{2\cos x+3\sin x}\,dx=\ \ ?\)
\(\displaystyle \int \frac{3x^{2}+2}{x^{3}+2x}\,dx=\ \ ?\)
\(\displaystyle \int \frac{dx}{x^{2}+5}=\ \ ?\)

\(\displaystyle \int_{-1}^{1}\log\!\left(\frac{3+x}{\,3-x\,}\right)dx=\ \ ?\)

If \(A\) and \(B\) are independent events, \(P(A)=0.3\) and \(P(B)=0.4\), then \(P(A\cap B)=\) ?

The adjoint (adjugate) of the matrix \(\begin{bmatrix}1&2 \\ 3&4\end{bmatrix}\) is

If the direction cosines of a line are \(\dfrac{4}{\sqrt{77}},\ \dfrac{5}{\sqrt{77}},\ \dfrac{x}{\sqrt{77}}\), then the value of \(x\) is

If \(A=\begin{bmatrix}1&0 \\ 0&1\end{bmatrix}\), then the value of \(A^{25}\) is

If a binary operation is defined by \(a\ \mathrm{o}\ b=3a+b\), then \((2\ \mathrm{o}\ 3)\ \mathrm{o}\ 5=\) ?

If \(A=\{a,b\}\), \(B=\{1,2,3\}\) then the total number of one–one (injective) functions from \(A\) to \(B\) is
\(\vec i\cdot\vec i=\) ?
\(\vec j\times\vec i=\) ?

\(\sin\!\big(\sin^{-1}\tfrac12\big)=\) ?

\(\sin^{-1}x+\sin^{-1}y=\) (principal values)

For \(x\in[-1,1]\), evaluate \(\ \sin\!\big(2(\sin^{-1}x+\cos^{-1}x)\big)\).

For \(x\in\mathbb{R}\), compute \(\csc\!\big(\tan^{-1}x+\cot^{-1}x\big)\).

If \(|x|\ge1\), then \(\tan\!\left[\dfrac{2}{3}\big(\tan^{-1}x+\cot^{-1}x\big)\right]=\) ?