List of top Mathematics Questions asked in CBSE CLASS XII

Prove cot\((\frac{\sqrt{1+sinx}+\sqrt{1-sinx}}{\sqrt{1+sinx}-\sqrt{1-sinx}}=\frac{x}{2},x∈[0,\frac{π}{4}]\)

By using the properties of definite integrals, evaluate the integral: \(\int_{0}^{4}|x-1|dx\)

Evaluate the integral: \(\int^1_0\frac{x}{x^2+1}dx\)

Evaluate the definite integral: \(∫_0^2\frac{6x+3}{x^2+4} dx\) 

Evaluate the definite integral: \(∫_0^\frac{π}{4}(2sec^2x+x^3+2)dx\)

Evaluate the definite integral: \(∫_0^1\frac{5x^2}{x2+4x+3}\)

Evaluate the definite integral as limit of sums: \(∫^1_0 xe^{x^2} dx\)

Evaluate the definite integral: \(∫^1_0 \frac{2x+3}{5x^2+1}dx\)

Evaluate the definite integral: \(∫_0^1 \frac{dx}{√1-x^2}\)

Evaluate the definite integral: \(∫_0^\frac{π}{2}cos2xdx\)

Integrate the function: \(tan^{-1}x\)

Find the integrals of the function: \(tan^4x\)

Find the integrals of the function: \(tan^3 2x\, sec 2x\)

Find the integrals of the function: \(\frac{cos x - sin x}{1+sin 2x}\)

Find the integrals of the function: \(\frac{cos2 x-cos2 α}{cos x - cos α}\)

Find the integrals of the function: \(\frac{sin2 x}{1+cos x}\)

Find an anti derivative (or integral) of the following function by the method of inspection: (ax + b)²

Find an anti derivative (or integral) of the following function by the method of inspection: \(e^{2x}\)

Find an anti derivative (or integral) of the following function by the method of inspection:Cos 3x

Find an anti derivative (or integral) of the following function by the method of inspection: sin 2x

Choose the correct answer.
If \(a,b,c\),are in A.P.,then the determinant
\(\begin{vmatrix}x+2& x+3& x+2a\\ x+3& x+4& x+2b\\ x+4& x+5& x+2c\end{vmatrix}\) is:

Write Minors and Cofactors of the elements of following determinants:
I. \(\begin{vmatrix}1&0&0\\0&1&0\\0&0&1\end{vmatrix}\)II. \(\begin{vmatrix}1&0&4\\3&5&-1\\0&1&2\end{vmatrix}\)

Prove: \(∫^1_0sin^{-1}x\,dx=\frac{π}{2}-1\)

Prove: \(∫^{\frac{π}{4}}_0 2tan^3xdx=1-log2\)