HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Integrate the following with respect to the respective variable : `(cos 7x - cos8x)/(1 + 2 cos 5x)`

Integrate the following with respect to the respective variable : `cot^-1 ((1 + sinx)/cosx)`

Integrate the following w.r.t.x : `x^2/sqrt(1 - x^6)`

Integrate the following w.r.t.x : `(1)/((1 - cos4x)(3 - cot2x)`

Integrate the following w.r.t.x : `(1)/(2cosx + 3sinx)`

Integrate the following w.r.t.x:

`x^2/((x - 1)(3x - 1)(3x - 2)`

Integrate the following w.r.t.x : `(1)/(sinx + sin2x)`

Integrate the following w.r.t.x :  `sec^2x sqrt(7 + 2 tan x - tan^2 x)`

Integrate the following w.r.t.x: `(x + 5)/(x^3 + 3x^2 - x - 3)`

Integrate the following w.r.t.x : `sqrt(tanx)/(sinx*cosx)`

Find `"dy"/"dx" if, sqrt"x" + sqrt"y" = sqrt"a"`

Find `"dy"/"dx"` if, x³ + y³ + 4x³y = 0 

Find `"dy"/"dx"` if, x³ + x²y + xy² + y³ = 81

Find `"dy"/"dx"` if, ye^x + xe^y = 1 

Find `"dy"/"dx"` if, `"x"^"y" = "e"^("x - y")`

Find `"dy"/"dx"` if, xy = log (xy)

If `"x"^5 * "y"^7 = ("x + y")^12` then show that, `"dy"/"dx" = "y"/"x"`

If log (x + y) = log (xy) + a then show that, `"dy"/"dx" = (- "y"^2)/"x"^2`.

Solve the following:

If `"e"^"x" + "e"^"y" = "e"^((x + y))` then show that, `"dy"/"dx" = - "e"^"y - x"`.

Choose the correct alternative.

If y = 5^x . x⁵, then `"dy"/"dx" = ?`