Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle α is one-third that of the cone and the greatest volume of cylinder is `4/27 pih^3` tan²α.

A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of ______.

Integrate the functions:

`(2x)/(1 + x^2)`

Integrate the functions:

`(log x)^2/x`

Integrate the functions:

`1/(x + x log x)`

Integrate the functions:

sin x ⋅ sin (cos x)

Integrate the functions:

sin (ax + b) cos (ax + b)

Integrate the functions:

`sqrt(ax + b)`

Integrate the functions:

`xsqrt(x + 2)`

Integrate the functions:

`xsqrt(1+ 2x^2)`

Integrate the functions:

(4x + 2) `sqrt(x^2 + x +1)`

Integrate the functions:

`1/(x-sqrtx)`

Integrate the functions:

`x/(sqrt(x+ 4))`, x > 0 

Integrate the functions:

`(x^3 - 1)^(1/3) x^5`

Integrate the functions:

`x^2/(2+ 3x^3)^3`

Integrate the functions:

`1/(x(log x)^m),  x > 0, m ne 1`

Integrate the functions:

`x/(9 - 4x^2)`

Integrate the functions:

`e^(2x+3)`

Integrate the functions:

`x/(e^(x^2))`

Integrate the functions:

`e^(tan^(-1)x)/(1+x^2)`