HSC Science (General) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Write the degree of the differential equation (y''')² + 3(y") + 3xy' + 5y = 0

Find the principal solutions of cot θ = 0

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

If 2 tan^–1(cos x) = tan^–1(2 cosec x). then find the value of x.

Solve `x + y (dy)/(dx) = sec(x^2 + y^2)`

The order and degree of the differential equation `[1 + ((dy)/(dx))^3]^(2/3) = 8((d^3y)/(dx^3))` are respectively ______.

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)`