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

A car firm has 2 cars, which are hired out day by day. The number of cars hired on a day follows Poisson distribution with mean 1.5. Find the probability that (i) no car is used on a given day, (ii) some demand is refused on a given day, given e^−1.5 = 0.2231.

It is known that, in a certain area of a large city, the average number of rats per bungalow is five. Assuming that the number of rats follows Poisson distribution, find the probability that a randomly selected bungalow has exactly 5 rats inclusive. Given e^-5  = 0.0067.

It is known that, in a certain area of a large city, the average number of rats per bungalow is five. Assuming that the number of rats follows Poisson distribution, find the probability that a randomly selected bungalow has more than 5 rats inclusive. Given e^-5  = 0.0067.

It is known that, in a certain area of a large city, the average number of rats per bungalow is five. Assuming that the number of rats follows Poisson distribution, find the probability that a randomly selected bungalow has between 5 and 7 rats inclusive. Given e⁻⁵ = 0.0067.

If E(X) = m and Var(X) = m then X follows ______.

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