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

Solve the following:

A water tank in the farm of an inverted cone is being emptied at the rate of 2 cubic feet per second. The height of the cone is 8 feet and the radius is 4 feet. Find the rate of change of the water level when the depth is 6 feet.

Solve the following : Find all points on the ellipse 9x² + 16y² = 400, at which the y-coordinate is decreasing and the coordinate is increasing at the same rate.

Solve the following : The position of a particle is given by the function s (t) = 2t² + 3t – 4. Find the time t = c in the interval 0 ≤ t ≤ 4 when the instantaneous velocity of the particle equal to its average velocity in this interval.

Integrate the following w.r.t. x : x³ + x2 – x + 1

Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`

Integrate the following w.r.t. x:

`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`

Integrate the following w.r.t. x:

`2x^3 - 5x + 3/x + 4/x^5`

Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`

Evaluate the following integrals : tan²x dx

Evaluate the following integrals : `int (sin2x)/(cosx)dx`

Evaluate the following integrals : `int sin x/cos^2x dx`

Evaluate the following integrals:

`int (cos2x)/sin^2x dx` 

Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`

Evaluate the following integrals : `int sinx/(1 + sinx)dx`

Evaluate the following integrals : `int tanx/(sec x + tan x)dx`

Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`

Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`

Evaluate the following integrals: `int sin 4x cos 3x dx`

Evaluate the following integrals:

`int x/(x + 2).dx`

Evaluate the following integral: 

`int(4x + 3)/(2x + 1).dx`