HSC Science (Electronics) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

A ladder 10 meter long is leaning against a vertical wall. If the bottom of the ladder is pulled horizontally away from the wall at the rate of 1.2 meters per seconds, find how fast the top of the ladder is sliding down the wall when the bottom is 6 meters away from the wall

The volume of the spherical ball is increasing at the rate of 4π cc/sec. Find the rate at which the radius and the surface area are changing when the volume is 288 π cc.

A man of height 180 cm is moving away from a lamp post at the rate of 1.2 meters per second. If the height of the lamp post is 4.5 meters, find the rate at which
(i) his shadow is lengthening
(ii) the tip of the shadow is moving

If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______

`int  ("e"^x(x - 1))/(x^2)  "d"x` = ______ 

`int sqrt(1 + sin2x)  dx`

`int (sin4x)/(cos 2x) "d"x`

`int ("e"^(3x))/("e"^(3x) + 1)  "d"x`

`int logx/x  "d"x`

`int (2 + cot x - "cosec"^2x) "e"^x  "d"x`

`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`

`int ("e"^(2x) + "e"^(-2x))/("e"^x)  "d"x`

`int x^x (1 + logx)  "d"x`

`int 1/(xsin^2(logx))  "d"x`

`int sqrt(x)  sec(x)^(3/2) tan(x)^(3/2)"d"x`

`int (cos2x)/(sin^2x)  "d"x`

`int cot^2x  "d"x`

`int x/(x + 2)  "d"x`

`int cos^7 x  "d"x`

`int(log(logx))/x  "d"x`