HSC Arts (English Medium) इयत्ता १२ वी - Maharashtra State Board Important Questions

If y = `log(x + sqrt(x^2 + a^2))^m`, show that `(x^2 + a^2)(d^2y)/(dx^2) + x "d"/"dx"` = 0.

If y is a function of x and log (x + y) = 2xy, then the value of y'(0) = ______.

If f(x) = log_x (log x) then f'(e) is ______

If y = `"e"^(1 + logx)` then find `("d"y)/("d"x)` 

If y = log [cos(x⁵)] then find `("d"y)/("d"x)`

Differentiate sin² (sin⁻¹(x²)) w.r. to x

Differentiate `cot^-1((cos x)/(1 + sinx))` w.r. to x

Differentiate `sin^-1((2cosx + 3sinx)/sqrt(13))` w.r. to x

If log₅ `((x^4 + "y"^4)/(x^4 - "y"^4))` = 2, show that `("dy")/("d"x) = (12x^3)/(13"y"^2)`

If y = `sqrt(cos x + sqrt(cos x + sqrt(cos x + ...... ∞)`, show that `("d"y)/("d"x) = (sin x)/(1 - 2y)`

Solve `x + y (dy)/(dx) = sec(x^2 + y^2)`

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

If y = sin^–1x, then show that `(1 - x^2) (d^2y)/(dx^2) - x * dy/dx` = 0

Find `dy/dx`, if y = (log x)^x.

Evaluate:

`int log x dx`

Price P for demand D is given as P = 183 +120D - 3D² Find D for which the price is increasing

If `f'(x)=k(cosx-sinx), f'(0)=3 " and " f(pi/2)=15`, find f(x).

Find the approximate value of cos (89°, 30'). [Given is: 1° = 0.0175°C]

Find the approximate value of ` sqrt8.95 `

An open box is to be made out of a piece of a square card board of sides 18 cms by cutting off equal squares from the comers and turning up the sides. Find the maximum volume of the box.