HSC Science (General) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

If A = {1, 2, 3, 4, 5, 6, 7, 8, 9}, determine the truth value of the following statement:

∃ x ∈ A, such that x + 7 ≥ 11.

If A = {1, 2, 3, 4, 5, 6, 7, 8, 9}, determine the truth value of the following statement:

∀ x ∈ A, 3x ≤ 25.

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)`

Find `"dy"/"dx"` if : x = t² + t + 1, y = `sin((pit)/2) + cos((pit)/2) "at"  t = 1`

Find `dy/dx` if : x = 2 cos t + cos 2t, y = 2 sin t – sin 2t at t = `pi/(4)`

Find `"dy"/"dx"` if : x = t + 2sin (πt), y = 3t – cos (πt) at t = `(1)/(2)`

If x = `(t + 1)/(t - 1), y = (t - 1)/(t + 1), "then show that"  y^2 + "dy"/"dx"` = 0.

DIfferentiate x sin x w.r.t. tan x.