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

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

Evaluate the following.

`int x^3/(sqrt(1 + x^4))dx`

Evaluate `int1/(x(x - 1))dx`

Solve the following Evaluate.

`int(5x^2 - 6x + 3)/(2x - 3)dx`

If f ′(x) = 4x³ − 3x² + 2x + k, f(0) = 1 and f(1) = 4, find f(x)

Evaluate the following.

`int 1/(x^2 + 4x - 5)dx`

Solve the following problems by graphical method:

Maximize z = 4x + 2y subject to 3x + y ≥ 27, x + y ≥ 21, x ≥ 0 y ≥ 0

`int dx/((x+2)(x^2 + 1))`    ...(given)

`1/(x^2 +1) dx = tan ^-1 + c`

Write the following statement in symbolic form.

It is not true that `sqrt(2)` is a rational number.

Write the following statement in symbolic form.

4 is an odd number if 3 is not a prime factor of 6.

Cost of Living Index Numbers for the years 2000 and 2005 are 120 and 220, respectively. If a person has monthly earnings of ₹10,800 in year 2000, what should be his monthly earnings in year 2005 in order to maintain same standard of living?

Evaluate the following.

`int x sqrt(1 + x^2)  dx`

Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x²

The statement ∼(p ↔ ∼q) is ______.

Solve the following LPP by graphical method:

Maximize: z = 3x + 5y Subject to:  x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0

I.F. of dx = y (x + y ) dy is a function of ______.

The I.F. of differential equation `dy/dx+y/x=x^2-3  "is" log x.`

Solve the following LPP:

Maximize z = 7x + 11y, subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0.

`int x^3 e^(x^2) dx`

Evaluate `int (1)/(x(x - 1))dx`