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

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 ______ 

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`

`int sqrt(4^x(4^x + 4))  "d"x`

`int 1/(x(x^3 - 1)) "d"x`

If f'(x) = `x - 3/x^3`, f(1) = `11/2` find f(x)