Arts (English Medium) इयत्ता ११ - CBSE Question Bank Solutions for Mathematics

The real value of α for which the expression `(1 - i sin alpha)/(1 + 2i sin alpha)` is purely real is ______.

The value of `(z + 3)(barz + 3)` is equivalent to ______.

If `((1 + i)/(1 - i))^x` = 1, then ______.

A real value of x satisfies the equation `((3 - 4ix)/(3 + 4ix))` = α − iβ (α, β ∈ R) if α² + β² = ______.

Which of the following is correct for any two complex numbers z₁ and z₂?

The point represented by the complex number 2 – i is rotated about origin through an angle `pi/2` in the clockwise direction, the new position of point is ______.

Let x, y ∈ R, then x + iy is a non-real complex number if ______.

If a + ib = c + id, then ______.

The complex number z which satisfies the condition `|(i + z)/(i - z)|` = 1 lies on ______.

If z is a complex number, then ______.

In how many ways can 5 children be arranged in a line such that two particular children of them are always together 

In how many ways can 5 children be arranged in a line such that two particular children of them are never together.

If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?

In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together.

Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`

Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated? Find also the number of ways of their seating if all the ladies sit together.

Find the number of permutations of n different things taken r at a time such that two specific things occur together.

Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.

The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.