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

Find the graphical solution for the system of linear inequation 2x + y ≤ 2, x − y ≤ 1

Find the feasible solution of linear inequation 2x + 3y ≤ 12, 2x + y ≤ 8, x ≥ 0, y ≥ 0 by graphically

Find the solution set of inequalities 0 ≤ x ≤ 5, 0 ≤ 2y ≤ 7

Examine whether the statement pattern

[p → (∼q ˅ r)] ↔ ∼[p → (q → r)] is a tautology, contradiction or contingency.

The equation of X axis is ______ 

If the planes 2x – my + z = 3 and 4x – y + 2z = 5 are parallel then m = ______ 

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

The coordinates of the foot of perpendicular drawn from the origin to the plane 2x + y − 2z = 18 are ______ 

If y = `tan^-1((2x)/(1 - x^2))`, x ∈ (−1, 1) then `("d"y)/("d"x)` = ______.

If g is the inverse of f and f'(x) = `1/(1 + x^4)` then g'(x) = ______

Find the derivative of the inverse of function y = 2x³ – 6x and calculate its value at x = −2

Let f(x) = x⁵ + 2x – 3 find (f⁻¹)'(-3)

Find the derivative of cos⁻¹x w.r. to `sqrt(1 - x^2)`

Differentiate `tan^-1[(sqrt(1 + x^2) - 1)/x]` w.r. to `tan^-1[(2x sqrt(1 - x^2))/(1 - 2x^2)]`

A ladder 5 m in length is resting against vertical wall. The bottom of the ladder is pulled along the ground, away from the wall at the rate of 1.5 m /sec. The length of the higher point of the when foot of the ladder is 4 m away from the wall decreases at the rate of ______

Find the direction ratios of the normal to the plane 2x + 3y + z = 7

Find direction cosines of the normal to the plane `bar"r"*(3hat"i" + 4hat"k")` = 5

If the normal to the plane has direction ratios 2, −1, 2 and it’s perpendicular distance from origin is 6, find its equation

Find the perpendicular distance of origin from the plane 6x − 2y + 3z - 7 = 0

Find the vector equation of a plane at a distance 6 units from the origin and to which vector `2hat"i" - hat"j" + 2hat"k"` is normal