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

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))`.

Find k, if one of the lines given by kx² – 5xy – 3y² = 0 is perpendicular to the line x – 2y + 3 = 0

Find the points on the curve y = x³ – 9x² + 15x + 3 at which the tangents are parallel to y-axis.

If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.

If the line 2x – y + 7 = 0 touches the curve y = ax² + bx + 5 at (1, 9) then the values of ‘a’ and ‘b’ are ______.