HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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)

Find the slope of tangent to the curve x = sin θ and y = cos 2θ at θ = `pi/6`

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

Find points on the curve given by y = x³ − 6x² + x + 3, where the tangents are parallel to the line y = x + 5.

Find the cartesian equation of the plane passing through A(1, 2, 3) and the direction ratios of whose normal are 3, 2, 5.

Find the vector equation of the line `x/1 = (y - 1)/2 = (z - 2)/3`