HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Important Questions for Mathematics and Statistics

Minimize z = 2x + 4y is subjected to 2x + y ≥ 3, x + 2y ≥ 6, x ≥ 0, y ≥ 0 show that the minimum value of z occurs at more than two points

Maximize z = −x + 2y subjected to constraints x + y ≥ 5, x ≥ 3, x + 2y ≥ 6, y ≥ 0 is this LPP solvable? Justify your answer.

If y=e^ax ,show that  `xdy/dx=ylogy`

If x^py^q = (x + y)^p+q then Prove that `dy/dx = y/x`

Find dy/dx if x sin y + y sin x = 0.

if `y = tan^2(log x^3)`, find `(dy)/(dx)`

Differentiate tan^-1 (cot 2x) w.r.t.x.

Differentiate the following w.r.t.x:

tan[cos(sinx)]

Find the derivative of the function y = f(x) using the derivative of the inverse function x = f^–1(y) in the following:

y = `sqrt(x)`

Differentiate the following w.r.t. x: `x^(tan^(-1)x`

Differentiate the following w.r.t. x: x^e + x^x + e^x + e^e.

Find `dy/dx`, if `sqrt(x) + sqrt(y) = sqrt(a)`.

Find `dy/dx`, if `xsqrt(x) + ysqrt(y) = asqrt(a)`.

If `log_10((x^3 - y^3)/(x^3 + y^3))` = 2, show that `dy/dx = -(99x^2)/(101y^2)`.

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

Find the second order derivatives of the following : e^4x. cos 5x

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 y = sec (tan⁻¹x), then `dy/dx` at x = 1 is ______.

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