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

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.

If the line `(x - 1)/2 = (y + 1)/3 = z/4` lies in the plane 4x + 4y – kz = 0, then the value of k is ______.