Commerce (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

Find the square root of the following complex number:

 4i

Find the square root of the following complex number:

−i

Write the values of the square root of −i.

If x + iy =\[\sqrt{\frac{a + ib}{c + id}}\] then write the value of (x² + y²)².

If\[\sqrt{a + ib} = x + iy,\] then possible value of \[\sqrt{a - ib}\] is

If a = 1 + i, then a² equals

For all positive integers n, show that ²ⁿC_n + ²ⁿC_{n − 1} = `1/2` ^{2n + 2}C_n+1 

Evaluate

Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:

Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
n · _^n − 1C_{r − 1} = (n − r + 1) ⁿC_{r − 1}

Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:

Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:

 ⁿC_r + 2 · ⁿC_{r − 1} + ⁿC_{r − 2} = ^n + 2C_r.

There are 10 persons named\[P_1 , P_2 , P_3 , . . . . , P_{10}\]
Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P₁ must occur whereas P₄ and P₅ do not occur. Find the number of such possible arrangements.

How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if (i) 4 letters are used at a time 

How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if  all letters are used at a time 

How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if all letters are used but first letter is a vowel?