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

Choose the correct alternative.

The order and degree of `(dy/dx)^3 - (d^3y)/dx^3 + ye^x = 0` are respectively.

Choose the correct alternative.

The order and degree of `[ 1+ (dy/dx)^3]^(2/3) = 8 (d^3y)/dx^3` are respectively.

Show that function f(x) =`("x - 2")/("x + 1")`, x ≠ -1 is increasing.

Show that function f(x) =`3/"x" + 10`, x ≠ 0 is decreasing.

Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx

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

Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx

Evaluate `int (3"x"^2 - 5)^2` dx

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

If f'(x) = x² + 5 and f(0) = −1, then find the value of f(x).

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

If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).

Evaluate the following.

`int "x" sqrt(1 + "x"^2)` dx

Evaluate the following.

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

Evaluate the following.

`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx

Evaluate the following.

`int (1 + "x")/("x" + "e"^"-x")` dx

Fill in the blank:

The order of highest derivative occurring in the differential equation is called ___________ of the differential equation.

Evaluate the following.

∫ (x + 1)(x + 2)⁷ (x + 3)dx

Fill in the blank:

The power of the highest ordered derivative when all the derivatives are made free from negative and / or fractional indices if any is called __________ of the differential equation.

Evaluate the following.

`int 1/("x" log "x")`dx