HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions

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`

`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1))  "d"x`

Select and write the correct alternative from the given option for the question

Solution of the equation `x  ("d"y)/("d"x)` = y log y is