List of top Questions asked in CBSE CLASS XII

Integrate the function: \(\frac{1}{x-x^3}\)

By using the properties of definite integrals, evaluate the integral: \(\int_{o}^{a} \frac{\sqrt{x}}{\sqrt x+\sqrt{a-x} }dx\)

By using the properties of definite integrals, evaluate the integral: \(∫^\frac{π}{2}_0\frac{sinx-cosx}{1+sinx\,cosx\,}dx\)

By using the properties of definite integrals, evaluate the integral: \(∫^{2π}_0 cos^5 xdx\)

The value of e integral \(∫^1_\frac{1}{3}\frac{(x-x^3)}{x^4}^\frac{1}{3} dx\)  is.

By using the properties of definite integrals, evaluate the integral: \(∫_0^π\frac{xdx}{1+sinx}\)

By using the properties of definite integrals, evaluate the integral: \(∫^\frac{π}{2}_\frac{-π}{2}sin^2xdx\)

By using the properties of definite integrals, evaluate the integral: \(∫^\frac{π}{2}_0(2logsinx-logsin2x)dx\)

By using the properties of definite integrals, evaluate the integral: \(∫^2_0 x\sqrt{2-x}dx\)

By using the properties of definite integrals, evaluate the integral: \(∫_0^{\frac \pi4} log(1+tanx)dx\)

By using the properties of definite integrals, evaluate the integral: \(\int^1_0x(1-x)^n\,dx\)

By using the properties of definite integrals, evaluate the integral: \(\int_{2}^{8} |x-5| \,dx\)

By using the properties of definite integrals, evaluate the integral: \(\int_{-5}^{5} |x+2|\,dx\)

By using the properties of definite integrals, evaluate the integral: \(∫^{\frac{π}{2}}_0\frac{cos^5xdx}{sin^5x+cos^5x}\)

By using the properties of definite integrals, evaluate the integral: \(\int^{\frac{π}{2}}_0 \frac{sin^{\frac{3}{2}}xdx}{sin^{\frac{3}{2}}x+cos^{\frac{3}{2}}x}\)

By using the properties of definite integrals, evaluate the integral: \(∫_0^\frac{π}{2}\frac{\sqrt{sinx}}{\sqrt{sinx}+\sqrt{cosx}}dx\)

By using the properties of definite integrals, evaluate the integral: \(∫_0^{\frac \pi2}cos^2x\ dx\)

Evaluate the integral: \(∫_1^2(\frac 1x-\frac {1}{2x^2})e^{2x}\ dx\)

Evaluate the integral: \(∫_{-1}^1\frac {dx}{x^2+2x+5}\)

Evaluate the integral: \(\int_{0}^{2}\frac{dx}{x+4-x^2}\)

Evaluate the integral: \(∫_0^{\frac \pi2} \frac {sinx}{1+cos^2x}dx\)

Evaluate the integral: \(\int^2_0 x\sqrt{x+2}\)

Evaluate the integral: \(\int_{0}^{4} \sin^{-1} \frac{2x}{1+x^2}\,dx\)

Evaluate the integral: \(\int_{0}^{π/2} \sqrt{\sin \phi}\cos^5 \phi\, d\,\phi\)

Describe the following:

1. Acetylation
2. Cannizzaro reaction
3. Cross aldol condensation
4. Decarboxylation