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This mock test of Maths Test 1 - Complex Number, Binomial Theorem, Permutation And Combination, Linear Inequality for JEE helps you for every JEE entrance exam.
This contains 30 Multiple Choice Questions for JEE Maths Test 1 - Complex Number, Binomial Theorem, Permutation And Combination, Linear Inequality (mcq) to study with solutions a complete question bank.
The solved questions answers in this Maths Test 1 - Complex Number, Binomial Theorem, Permutation And Combination, Linear Inequality quiz give you a good mix of easy questions and tough questions. JEE
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QUESTION: 1

is equal to

Solution:

QUESTION: 2

Which of the following is true ?

Solution:

QUESTION: 3

If α is a complex number such that α^{2}+α+1 = 0 then α^{31} is equal to

Solution:

QUESTION: 4

Polar form of a complex number is

Solution:

QUESTION: 5

is equal to

Solution:

QUESTION: 6

. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

Solution:

QUESTION: 7

Number of non-zero integral solution of the equation |1-i|^{x} = 2^{x } is

Solution:

QUESTION: 8

The number in the form z = a + bι where a, b ∈ R and i = √−1 is called a

Solution:

QUESTION: 9

In how many ways 7 men and 7 women can be seated around a round table such that no two women can sit together ?

Solution:

QUESTION: 10

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

Solution:

QUESTION: 11

In z = a + bι, if i is replaced by −ι, then another complex number obtained is said to b

Solution:

QUESTION: 12

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

Solution:

QUESTION: 13

How many different nine digit numbers can be formed from the number 223355888 be rearranging its digits so that odd digits occupy even positions ?

Solution:

QUESTION: 14

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

Solution:

QUESTION: 15

The straight lines are parallel and lie in the same plane. A total number of m points are taken on points on k points on The maximum number of triangles formed with vertices of these points are

Solution:

QUESTION: 16

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

Solution:

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

QUESTION: 17

If n is an integer between 0 and 21, then the minimum value of n!(21â€“n) ! is

Solution:

QUESTION: 18

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

Solution:

QUESTION: 19

The middle term in the expansion of is

Solution:

QUESTION: 20

The value of is

Solution:

^{14}C_{1} + ^{14}C_{3} + ^{14}C_{5} +.......^{14}C_{11}

For odd numbers : 2^{(n-1)}

2^{13} -14

QUESTION: 21

The coefficient of in the expansion of

Solution:

QUESTION: 22

If the 21st and 22nd term in the expansion of are equal, then x is equal to

Solution:

QUESTION: 23

The term independent of x in the expansion of is

Solution:

7_{(r+1) }= 10Cr ((√x/3)^{(10-r)}+ (√3)/2x^{r}))^{10}

= 10Cr[x^{(10-r)/2}]/3^{(10-r)/2} * (√3))^{r}/(2^{r}.x^{2r})

x^{(10-r)/2}−2r = x^{o}

⇒ (10−r)/2=2r

⇒10−r=4r

⇒10=5r⇒r=2

7_{3} = 10C2((√3))^{2}/(3^{4}.2^{2})

7_{3}= 10!/8!2! − 3/(3^{4} 2^{2})

7_{3}= (10×9)/(2×3×3×3×4)

7_{3} = 5/12

QUESTION: 24

The coefficient of the term independent of y in the expansion of

is
Solution:

QUESTION: 25

The coefficient of in the expansion of is

Solution:

QUESTION: 26

The middle term in the expansion of is

Solution:

QUESTION: 27

If in the expansion of , the coefficient of x and are 3 and â€“6 respectively, then *m* is

Solution:

QUESTION: 28

If the coefficients of rth and (r +1)th terms in the expansion of

are equal, then *r *equals:

Solution:

QUESTION: 29

The greatest integer less than or equal to (√3+1)^{6} is

Solution:

QUESTION: 30

The 14th term from the end in the expansion of is

Solution:

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