HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

Find `dy/dx`, if y = (sin x)^{tan x} – x^{log x}.

If y = `log(x + sqrt(x^2 + 4))`, show that `dy/dx = 1/sqrt(x^2 + 4)`

Find the acute angle between the lines `(x - 1)/1 = (y - 2)/-1 = (z - 3)/2` and `barr = (hati + 2hatj + 3hatk) + λ(2hati + hatj + hatk)`.

If y = `9^(log_3x)`, find `dy/dx`.

Find the value of c for which the conclusion of the mean value theorem holds for the function f(x) = log x on the interval [1, 3]

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

Evaluate:

`int log x dx`

If y=e^ax ,show that  `xdy/dx=ylogy`

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

Show that the lines ` (x+1)/-3=(y-3)/2=(z+2)/1; ` are coplanar. Find the equation of the plane containing them.

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

Show that four points A, B, C and D whose position vectors are 

`4hati+5hatj+hatk,-hatj-hatk-hatk, 3hati+9hatj+4hatk and 4(-hati+hatj+hatk)` respectively are coplanar.

Find dy/dx if x sin y + y sin x = 0.

Test whether the function is increasing or decreasing. 

f(x) = `"x" -1/"x"`, x ∈ R, x ≠ 0, 

The function f (x) = x³ – 3x² + 3x – 100, x∈ R is _______.

(A) increasing

(B) decreasing

(C) increasing and decreasing

(D) neither increasing nor decreasing

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

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

If `sin^-1((x^5 - y^5)/(x^5 + y^5)) = pi/(6), "show that" "dy"/"dx" = x^4/(3y^4)`

If y = `sqrt(cosx + sqrt(cosx + sqrt(cosx + ... ∞)`, then show that `"dy"/"dx" = sinx/(1 - 2y)`.

Find `"dy"/"dx"` if x = at², y = 2at.