HSC Science (General) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

The odds in favour of A winning a game of chess against B are 3:2. If three games are to be played, what are the odds in favour of A's winning at least two games out of the three?

Select the correct option from the given alternatives :

A fair is tossed twice. What are the odds in favour of getting 4, 5 or 6 on the first toss and 1, 2, 3 or 4 on the second die?

Solve the following:

The odds against A solving a certain problem are 4 to 3 and the odds in favor of solving the same problem are 7 to 5 find the probability that the problem will be solved

Find n if ⁶P₂ = n ⁶C₂

Find x if ⁿP_r = x ⁿC_r 

Select the correct answer from the given alternative

There are 10 persons among whom two are brothers. The total number of ways in which these persons can be seated around a round table so that exactly one person sits between the brothers is equal to:

Answer the following:

Find the value of r if ⁵⁶P_r+6 : ⁵⁴P_r+3 = 30800 : 1

Answer the following:

Capital English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X, and Y. How many symmetric three letter passwords can be formed using these letters?

If A =  `([cos alpha, sin alpha],[-sinalpha, cos alpha])` , find α satisfying 0 < α < `pi/r`when `A+A^T=sqrt2I_2` where A^T is transpose of A.

Find the value of ¹⁵C₄ 

Find the value of ⁸⁰C₂

Find the value of ¹⁵C₄ + ¹⁵C₅ 

Find the value of ²⁰C₁₆ – ¹⁹C₁₆ 

Answer the following:

A question paper has 6 questions. How many ways does a student have to answer if he wants to solve at least one question?

Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 15

Find the Cartesian co-ordinates of points whose polar coordinates are :

(3, 90°)

Find the Cartesian co-ordinates of points whose polar coordinates are :

(1,180°)

Find the polar coordinates of points whose cartesian coordinates are:

(5, 5)

Find the polar coordinates of points whose cartesian coordinates are:

`(1, sqrt(3))`

Find the polar co-ordinates of points whose Cartesian co-ordinates are:

(–1, –1)