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

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 ______.

If `sin^-1  4/5 + cos^-1  12/13` = sin^–1α, then find the value of α.

Find the direction cosines of the line `(2x - 1)/3 = 3y = (4z + 3)/2`

If tan θ + sec θ = `sqrt(3)`, find the general value of θ.

In Δ ABC with the usual notations prove that `(a-b)^2 cos^2(C/2)+(a+b)^2sin^2(C/2)=c^2`

Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`

Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`

Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.

[~(~p ∧ ~q)] v q

In any ΔABC if  a² , b² , c² are in arithmetic progression, then prove that Cot A, Cot B, Cot C are in arithmetic progression.