HSC Science (General) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Evaluate the following integrals as limit of a sum:

\[\int\limits_0^4 x^2 \cdot dx\]

Choose the correct option from the given alternatives:

The order and degree of the differential equation `sqrt(1 + ("dy"/"dx")^2) = (("d"^2"y")/"dx"^2)^(3/2)` are respectively.

Determine the order and degree of the following differential equation:

`("d"^2"y")/"dx"^2 + 5 "dy"/"dx" + "y" = "x"^3`

Determine the order and degree of the following differential equation:

`"dy"/"dx" = 3"y" + root(4)(1 + 5 ("dy"/"dx")^2)`

Determine the order and degree of the following differential equation:

`("d"^4"y")/"dx"^4 + sin ("dy"/"dx") = 0`

Determine the order and degree of the following differential equation:

`(("d"^3"y")/"dx"^3)^2 = root(5)(1 + "dy"/"dx")`

Suppose error involved in making a certain measurement is continuous r.v. X with p.d.f.

f (x) = k `(4 – x^2 )`, for –2 ≤ x ≤ 2 and = 0 otherwise.

P(x > 0)

Suppose error involved in making a certain measurement is continuous r.v. X with p.d.f.

`"f(x)" = {("k"(4 - x^2)      "for –2 ≤ x ≤ 2,"),(0                                 "otherwise".):}`

P(–1 < x < 1)

Suppose error involved in making a certain measurement is continuous r.v. X with p.d.f.

f (x) = k `(4 – x^2)`, for –2 ≤ x ≤ 2 and = 0 otherwise.

P (–0·5 < x or x > 0·5)

The following is the p.d.f. of continuous r.v.

f (x) = `x/8`, for 0 < x < 4 and = 0 otherwise.

Find expression for c.d.f. of X

The following is the p.d.f. of continuous r.v.

f (x) = `x/8` , for 0 < x < 4 and = 0 otherwise.

Find F(x) at x = 0·5 , 1.7 and 5

Given the p.d.f. of a continuous r.v. X , f (x) = `x^2/3` ,for –1 < x < 2 and = 0 otherwise

Determine c.d.f. of X hence find

P( x < 1) 

Given the p.d.f. of a continuous r.v. X ,

f (x) = `x^2 /3` , for –1 < x < 2 and = 0 otherwise

Determine c.d.f. of X hence find P( x < –2)

Given the p.d.f. of a continuous r.v. X ,

f (x) = `x^2/3` , for –1 < x < 2 and = 0 otherwise

Determine c.d.f. of X hence find P(1 < x < 2)

Given the p.d.f. of a continuous r.v. X ,

f (x) = `x^2/ 3` , for –1 < x < 2 and = 0 otherwise

Determine c.d.f. of X hence find P( X > 0)

Solve the following :

Find the area of the circle x² + y² = 9, using integration.

Solve the following :

Find the area of the ellipse `x^2/(25) + y^2/(16)` = 1 using integration

Choose the correct option from the given alternative:

If the a d.r.v. X has the following probability distribution:

k = 

Solve the following :

Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.

An economist is interested the number of unemployed graduate in the town of population 1 lakh.

Which of the following is not a statement?