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is equal to
Which of the following is true ?
If α is a complex number such that α^{2}+α+1 = 0 then α^{31} is equal to
Polar form of a complex number is
is equal to
. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Number of nonzero integral solution of the equation 1i^{x} = 2^{x } is
The number in the form z = a + bι where a, b ∈ R and i = √−1 is called a
In how many ways 7 men and 7 women can be seated around a round table such that no two women can sit together ?
There are (n + 1) white and (n + 1) black balls, each set numbered 1 to n + 1. The number of ways the balls can be arranged in a row so that adjacent balls are of different colors, is
In z = a + bι, if i is replaced by −ι, then another complex number obtained is said to b
The sum of the digits at the unit place of all the numbers formed with the help of 3,4,5,6 taken all at a time is
How many different nine digit numbers can be formed from the number 223355888 be rearranging its digits so that odd digits occupy even positions ?
Ten different letters of an alphabet are given. Words with 5 letters are formed from these given letters. Then the number of words which have at least one letters repeated is
Six ‘X’s have to be placed in the squares of the figure given below such that each row contains at least one ‘X’. The number of ways in which this can be done is
Number of ways of placed six X's in 8 squares
Here two squares of first and third row are empty
. ^{.}. Required arrangements = 28  2 = 26
If the ratio of the 7th term from the beginning to the 7th term from the end in the expansion of
is 1/6, then x is
The value of is
^{14}C_{1} + ^{14}C_{3} + ^{14}C_{5} +.......^{14}C_{11}
For odd numbers : 2^{(n1)}
2^{13} 14
By using 2, 4, 5, 7, 8, 9. How many three digit numbers are formed in form xyz when x < y and z < y (Repition not allowed) :
If sum of the coefficient of the first, second and third terms of the expansion of is 46, then the coefficient of the term that does not contain x is :
If area of triangle formed by z, ωz and z + ωz is 16√3 square units (where ω is complex cube root of unity) the z is equal to :
If z_{1} = 1, z_{2} = 2, z_{3} = 3 and 9z_{1} z_{2} + z_{2} z_{3} + 4z_{1} z_{3} = 12, then z_{1} + z_{2} + z_{3} = ?
Total number of rational terms in expansion of (5^{1/12} + 7^{1/18})^{360} is
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