HSC Science (Electronics) 12th Standard Board Exam - Maharashtra State Board Important Questions

The volume of the spherical ball is increasing at the rate of 4π cc/sec. Find the rate at which the radius and the surface area are changing when the volume is 288 π cc.

Find the local maximum and local minimum value of  f(x) = x³ − 3x² − 24x + 5

A rectangular sheet of paper has it area 24 sq. Meters. The margin at the top and the bottom are 75 cm each and the sides 50 cm each. What are the dimensions of the paper if the area of the printed space is maximum?

The maximum value of the function f(x) = `logx/x` is ______.

Find the equation of tangent to the curve y = 2x³ – x² + 2 at `(1/2, 2)`.

Show that function f(x) = tan x is increasing in `(0, π/2)`.

Find the approximate value of sin (30° 30′). Give that 1° = 0.0175^c and cos 30° = 0.866

Verify Lagrange’s mean value theorem for the function f(x) = `sqrt(x + 4)` on the interval [0, 5].

Find the point on the curve y² = 4x, which is nearest to the point (2, 1).

Find the approximate value of tan⁻¹ (1.002).
[Given: π = 3.1416]

A box with a square base is to have an open top. The surface area of box is 147 sq. cm. What should be its dimensions in order that the volume is largest?

Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`

Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`

Integrate : sec³ x w. r. t. x.

If `int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx`, then the value of I is:

(A) 0

(B) π

(C) π/2

(D) π/4

Show that:  `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`

Evaluate :`intxlogxdx`

Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`

`int1/xlogxdx=...............`

(A)log(log x)+ c

(B) 1/2 (logx )²+c

(C) 2log x + c

(D) log x + c

Evaluate : `int x^2/((x^2+2)(2x^2+1))dx`