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

Find the vector equation of the plane passing through the point A(–1, 2, –5) and parallel to the vectors `4hati - hatj + 3hatk` and `hati + hatj - hatk`.

Evaluate: `int (dx)/(2 + cos x - sin x)`

Evaluate: `int (2x^2 - 3)/((x^2 - 5)(x^2 + 4))dx`

If the foot of the perpendicular drawn from the origin to the plane is (4, –2, 5), then the equation of the plane is ______.

ΔOAB is formed by lines x² – 4xy + y² = 0 and the line x + y – 2 = 0. Find the equation of the median of the triangle drawn from O.

Minimize z = x + 2y,

Subject to x + 2y ≥ 50, 2x – y ≤ 0, 2x + y ≤ 100, x ≥ 0, y ≥ 0.

Find the coordinates of the point of intersection of the pair of lines 6x² + 5xy – 4y² + 7x + 13y – 3 = 0.

Find the equation of the plane containing the lines `(x - 1)/2 = (y + 1)/-1 = z/3` and `x/2 = (y - 2)/-1 = (z + 1)/3`.

Find the point of intersection of the lines given by x² + 3xy + 2y² + x – y – 6 = 0

Find the values of p and q if the equation px² – 6xy + y² + 18x – qy + 8 = 0 represents a pair of parallel lines.

If Rolle's theorem holds for the function f(x) = x³ + bx² + ax + 5, x ∈ [1, 3] with c = `2 + 1/sqrt(3)`, find the values of a and b.

Reduce the equation `barr*(3hati - 4hatj + 12hatk)` = 3 to the normal form and hence find the length of perpendicular from the origin to the plane.

Draw the rough graph and shade the feasible region for the inequalities x + y ≥ 2, 2x + y ≤ 8, x ≥ 0, y ≥ 0.

Find the equation of plane which is at a distance of 4 units from the origin and which is normal to the vector `2hati - 2hatj + hatk`.

Find `dy/dx`, if y = `sec^-1((1 + x^2)/(1 - x^2))`.

If x – y ≥ 8, x ≥ 3, y ≥ 3, x ≥ 0, y ≥ 0 then find the coordinates of the corner points of the feasible region.

The coordinates of the foot of the perpendicular from the point P(1, 0, 0) in the line `(x - 1)/2 = (y + 1)/-3 = (z + 10)/8` are ______.

If y = `cos^-1 sqrt((1 + x^2)/2`, then `dy/dx` = ______.

If y = `sin^-1((2tanx)/(1 + tan^2x))`, find `dy/dx`.

Find the vector equation of the line passing through the point (–2, 1, 4) and perpendicular to the plane `barr*(4hati - 5hatj + 7hatk)` = 15