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

Find the Cartesian equations of the line passing through A(3, 2, 1) and B(1, 3, 1).

`int sqrt(tan x)/(sin x cos x)` dx = _______________

The combined equation of the two lines passing through the origin, each making angle 45° and 135° with the positive X-axis is ______  

`int 1/(sqrtx + sqrt(x^3))` dx = ______.

The combined equation of the lines through origin and perpendicular to the pair of lines 3x² + 4xy − 5y² = 0 is ______

Show that the combined equation of pair of lines passing through the origin is a homogeneous equation of degree 2 in x and y. Hence find the combined equation of the lines 2x + 3y = 0 and x − 2y = 0

The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______

Find the principal solutions of cosec x = 2

Find the principal solutions of sin x − 1 = 0

Find the principal solutions of cos 2𝑥 = 1

Find the principal solutions of sin x = `-1/2`

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