HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Solve the following problem :

If X follows Poisson distribution such that P(X = 1) = 0.4 and P(X = 2) = 0.2, find variance of X.

Solve the following problem :

If X follows Poisson distribution with parameter m such that
`("P"("X" = x + 1))/("P"("X" = x)) = (2)/(x + 1)`
Find mean and variance of X.

Solve the differential equation `("d"y)/("d"x) + y` = e^−x 

Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`

Solve the differential equation (x² – yx²)dy + (y² + xy²)dx = 0

Solve: `("d"y)/("d"x) + 2/xy` = x² 

For the differential equation, find the particular solution (x – y²x) dx – (y + x²y) dy = 0 when x = 2, y = 0

Solve the following differential equation

`yx ("d"y)/("d"x)` = x² + 2y² 

For the differential equation, find the particular solution

`("d"y)/("d"x)` = (4x +y + 1), when y = 1, x = 0

Solve the following differential equation y²dx + (xy + x²) dy = 0

The slope of the tangent to the curve y = x³ – x² – 1 at the point whose abscissa is – 2, is ______.

Choose the correct alternative:

Slope of the normal to the curve 2x² + 3y² = 5 at the point (1, 1) on it is 

The slope of the tangent to the curve x = `1/"t"`, y = `"t" - 1/"t"`, at t = 2 is ______

State whether the following statement is True or False:

The equation of tangent to the curve y = x² + 4x + 1 at (– 1, – 2) is 2x – y = 0 

Find the equations of tangent and normal to the curve y = 3x² – x + 1 at the point (1, 3) on it

Find the equation of tangent to the curve x² + y² = 5, where the tangent is parallel to the line 2x – y + 1 = 0

Find the equation of tangent to the curve y = x² + 4x at the point whose ordinate is – 3

Choose the correct alternative:

The value of `int ("d"x)/sqrt(1 - x)` is

Choose the correct alternative:

`int(("e"^(2x) + "e"^(-2x))/"e"^x) "d"x` =

`int 5^(6x + 9) "d"x` = ______ + c