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

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.

The p.m.f. of a r.v. X is given by P (X = x) =`("" ^5 C_x ) /2^5` , for x = 0, 1, 2, 3, 4, 5 and = 0, otherwise.

Then show that P (X ≤ 2) = P (X ≥ 3).

In the p.m.f. of r.v. X

Find a and obtain c.d.f. of X. 

Solve the following problem :

A player tosses two coins. He wins ₹ 10 if 2 heads appear, ₹ 5 if 1 head appears, and ₹ 2 if no head appears. Find the expected value and variance of winning amount.

Find the Cartesian equations of the line passing through A(3, 2, 1) and B(1, 3, 1).

`int sqrt(tan x)/(sin x cos x)` dx = _______________

The combined equation of the two lines passing through the origin, each making angle 45° and 135° with the positive X-axis is ______  

`int 1/(sqrtx + sqrt(x^3))` dx = ______.

The combined equation of the lines through origin and perpendicular to the pair of lines 3x² + 4xy − 5y² = 0 is ______

Show that the combined equation of pair of lines passing through the origin is a homogeneous equation of degree 2 in x and y. Hence find the combined equation of the lines 2x + 3y = 0 and x − 2y = 0