HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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 ______.

lf p, q are true statements and r, s are false statements, then find the truth value of ∼ (p ∧ ∼r) ∨ (∼q ∨ s).

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

Using truth table prove that:

`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`

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 ______.

The general solution of cot 4x = –1 is ______.

Find the order and degree of the differential equation `(d^2y)/(dx^2) = root(3)(1 - (dy/dx)^4`

If `2sin^-1  3/7` = cos^–1β, then find the value of β.

Find the joint equation of the pair of lines through the origin and perpendicular to the lines given by 2x² + 7xy + 3y² = 0

Find the vector equation of a line passing through the point `hati + 2hatj + 3hatk` and perpendicular to the vectors `hati + hatj + hatk` and `2hati - hatj + hatk`.

Find the combined equation of y-axis and the line through the origin having slope 3.

Find the order and degree of the differential equation `(1 + 3 dy/dx)^(2/3) = 4((d^3y)/(dx^3))`.