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

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

Find the equation of the plane passing through the point (7, 8, 6) and parallel to the plane `bar"r"*(6hat"i" + 8hat"j" + 7hat"k")` = 0

Show that the lines `(x + 1)/(-10) = (y + 3)/(-1) = (z - 4)/(1)` and `(x + 10)/(-1) = (y + 1)/(-3) = (z - 1)/4` intersect each other.also find the coordinates of the point of intersection

Find the vector equation of the plane which bisects the segment joining A(2, 3, 6) and B(4, 3, −2) at right angles

Draw the graph of inequalities x ≤ 6, y −2 ≤ 0, x ≥ 0, y ≥ 0 and indicate the feasible region

`int (2x - 7)/sqrt(4x- 1) dx`

`int "e"^(3logx) (x^4 + 1)^(-1) "d"x`

`int x^7/(1 + x^4)^2  "d"x`

`int x^2sqrt("a"^2 - x^6)  "d"x`