HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

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.

Find `"dy"/"dx"` if x = a cot θ, y = b cosec θ

Find `"dy"/"dx"`, if : x = `sqrt(a^2 + m^2), y = log(a^2 + m^2)`

Find `"dy"/"dx"`, if : x = sinθ, y = tanθ

Find `"dy"/"dx"`, if : x = a(1 – cosθ), y = b(θ – sinθ)

Find `"dy"/"dx"`, if : x = `(t + 1/t)^a, y = a^(t+1/t)`, where a > 0, a ≠ 1, t ≠ 0.

Find `"dy"/"dx"`, if : `x = cos^-1((2t)/(1 + t^2)), y = sec^-1(sqrt(1 + t^2))`

Find `"dy"/"dx"`, if : `x = cos^-1(4t^3 - 3t), y = tan^-1(sqrt(1 - t^2)/t)`.

Find `"dy"/"dx"` if : x = cosec²θ, y = cot³θ at θ= `pi/(6)`

Find `"dy"/"dx"` if : x = a cos³θ, y = a sin³θ at θ = `pi/(3)`