HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find the principal solutions of tan x = `-sqrt(3)`

If cos^–1x + cos^–1y – cos^–1z = 0, then show that x² + y² + z² – 2xyz = 1

Differentiate y = `sqrt(x^2 + 5)` w.r. to x

Differentiate y = e^tanx w.r. to x

If y = sin⁻¹ (2^x), find `("d"y)/(""d"x)` 

If f(x) is odd and differentiable, then f′(x) is

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

If y = `tan^-1[sqrt((1 + cos x)/(1 - cos x))]`, 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

Differentiate `tan^-1((8x)/(1 - 15x^2))` w.r. to x

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

If y = `sin^-1[("a"cosx - "b"sinx)/sqrt("a"^2 + "b"^2)]`, then find `("d"y)/("d"x)`

The slope of the tangent to the curve x = 2 sin³θ, y = 3 cos³θ at θ = `pi/4` is ______.

The slope of the normal to the curve y = x² + 2e^x + 2 at (0, 4) is ______.

If the line y = 4x – 5 touches the curve y² = ax³ + b at the point (2, 3) then a + b is

If the tangent at (1, 1) on y² = x(2 − x)² meets the curve again at P, then P is

Find the slope of tangent to the curve y = 2x³ – x² + 2 at `(1/2, 2)`

Find the slope of normal to the curve 3x² − y² = 8 at the point (2, 2)