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

Fill in the blank:

If f(x) = `7/"x" - 3`, x ∈ R x ≠ 0 then f ''(x) is ______

State whether the following statement is True or False:

The equation of tangent to the curve y = 4xe^x at `(-1, (- 4)/"e")` is ye + 4 = 0

State whether the following statement is True or False:

x + 10y + 21 = 0 is the equation of normal to the curve y = 3x² + 4x - 5 at (1, 2).

Find the equation of tangent and normal to the following curve.

xy = c² at `("ct", "c"/"t")` where t is parameter.

Find the equation of tangent and normal to the following curve.

y = x² + 4x at the point whose ordinate is -3.

Choose the correct alternative.

The differential equation of y = `k_1 + k_2/x` is

Find the equation of tangent and normal to the following curve.

x = `1/"t",  "y" = "t" - 1/"t"`,  at t = 2

The differential equation of `y = k_1e^x+ k_2 e^-x` is ______.

Find the equation of tangent and normal to the following curve.

y = x³ - x² - 1 at the point whose abscissa is -2.

Find the equation of normal to the curve y = `sqrt(x - 3)` which is perpendicular to the line 6x + 3y – 4 = 0.

The solution of `dy/ dx` = 1 is ______.

The solution of `dy/dx + x^2/y^2 = 0` is ______

Choose the correct alternative.

The solution of `x dy/dx = y` log y is

Choose the correct alternative.

Bacteria increases at the rate proportional to the number present. If the original number M doubles in 3 hours, then the number of bacteria will be 4M in

Choose the correct alternative.

The integrating factor of `dy/dx -  y = e^x `is e^x, then its solution is

A solution of a differential equation which can be obtained from the general solution by giving particular values to the arbitrary constants is called ___________ solution.

The integrating factor of the differential equation `dy/dx - y = x` is e^−x.

State whether the following is True or False:

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

Solve the differential equation:

`e^(dy/dx) = x`

Solve the differential equation:

dr = a r dθ − θ dr