List of top Mathematics Questions asked in CBSE CLASS XII

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: xy = log y+C : y'= \(\frac{y^2}{1-xy}\,(xy\neq 1)\)

Given an example of a relation. Which is
(i) Symmetric but neither reflexive nor transitive.
(ii) Transitive but neither reflexive nor symmetric.
(iii) Reflexive and symmetric but not transitive.
(iv) Reflexive and transitive but not symmetric.
(v) Symmetric and transitive but not reflexive.

\(\int \sqrt{x^2-8x+7}dx\) is equal to

Integrate the function: \(e^{2x} sinx\)

Integrate the function: \(cot \ x .log\ sin\ x\)

Find the integrals of the function: \(cos^4 2x\)

Integrate the function: \(\frac{x+2}{\sqrt {x^2+2x+3}}\)

Find \(\frac {dy}{dx}\): \(2x+3y=sin\ x\)

Find \(\frac {dy}{dx}\): \(xy+y^2=tan\ x+y\)

Find \(\frac {dy}{dx}\): \(x^2+xy+y^2=100\)

Find \(\frac {dy}{dx}\): \(x^3+x^2y+xy^2+y^3=81\)

Find \(\frac {dy}{dx}:\) \(y=cos^{-1}(\frac {1-x^2}{1+x^2}),\ \ 0<x<1\)

Find \(\frac {dy}{dx}:\) \(sin^2x+cos^2y=1\)

\(Find\ \frac {dy}{dx}:\) \(y=tan^{-1}( \frac {3x-x^3}{1-3x^2}),\ \ -\frac {1}{\sqrt 3}<x<\frac {1}{\sqrt 3}\)