HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

Determine the order and degree of the following differential equation:

`(d^2y)/(dx^2) + x((dy)/(dx)) + y` = 2 sin x

Find the cartesian equation of the plane passing through the point A(–1, 2, 3), the direction ratios of whose normal are 0, 2, 5.

Find `(dy)/(dx)`, if x³ + x2y + xy² + y³ = 81

Find the equation of the tangents to the curve x² + y² – 2x – 4y + 1 = 0 which is parallel to the X-axis.

Write the joint equation of co-ordinate axes.

Find the general solution of sin θ + sin 3θ + sin 5θ = 0

Differentiate `tan^-1 (sqrt((3 - x)/(3 + x)))` w.r.t. x.

Find the combined equation of the pair of lines passing through the origin and perpendicular to the lines represented by 3x² + 2xy – y² = 0.

Find the probability of guessing correctly at least seven out of ten answers in a ‘true’ or ‘false’ objective test.

Prove that the general solution of cos θ = cos α is θ = 2nπ ± α, n ∈ Z.

If `x^2/a + y^2/b + (2xy)/h` = 0 represents a pair of lines and slope of one line is twice the other, then find the value of ab : h².

Find the vector equation of the line passing through the points A(2, 3, –1) and B(5, 1, 2).

If `cos((x^2 - y^2)/(x^2 + y^2))` = log a, show that `dy/dx = y/x`

Find the order and degree of the differential equation

`sqrt(1 + 1/(dy/dx)^2) = ((d^2y)/(dx^2))^(3/2)`

Diffierentiate: `tan^-1((a + b cos x)/(b - a cos x))` w.r.t.x.

The general solution to cos¹⁰⁰x – sin¹⁰⁰x = 1 is ______.

The coordinates of the point on the curve y = 2x – x², the tangent at which has slope 4 are ______.

Combined equation of the lines bisecting the angles between the coordinate axes, is ______.

If y = log (sec x + tan x), find `dy/dx`.

Show that the lines `(x - 1)/1 = (y - 2)/2 = (z + 1)/-1` and `x/2 = (y - 3)/2 = z/(-1)` do not intersect.