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JEE Main Maths Test- 12 - JEE MCQ


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30 Questions MCQ Test - JEE Main Maths Test- 12

JEE Main Maths Test- 12 for JEE 2024 is part of JEE preparation. The JEE Main Maths Test- 12 questions and answers have been prepared according to the JEE exam syllabus.The JEE Main Maths Test- 12 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Main Maths Test- 12 below.
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JEE Main Maths Test- 12 - Question 1
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If z is any complex number such that then the value of is

Detailed Solution for JEE Main Maths Test- 12 - Question 1

JEE Main Maths Test- 12 - Question 2
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If z is any complex number satisfying |z–1|=1, then which of the following is correct ?

Detailed Solution for JEE Main Maths Test- 12 - Question 2

Clearly, |z−1|=1 represents a circle with centre at (1,0) and radius 1.
Let P(z) be any point on it.

Then, arg(z−1) =∠XCP = θ [say]
Therefore, arg(z) =∠XOP = θ/2
Hence, arg(z−1) = 2arg(z)

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JEE Main Maths Test- 12 - Question 3
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If z satisfies |z+1| < |z–2| , then w = 3z+2+i satisfies

JEE Main Maths Test- 12 - Question 4
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The triangle formed by the points 1, and i as vertices in the argand diagram is
JEE Main Maths Test- 12 - Question 5
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For any complex number z, the minimum value of |z|+|z–1| is
JEE Main Maths Test- 12 - Question 6
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If (a ib)(c id)(e if)(g ih) = A iB, then (a2+b2) x (c2+d2) (e2+f2)(g2+h2) is equal to
JEE Main Maths Test- 12 - Question 7
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In how many ways 7 men and 7 women can be seated around a round table such that no two women can sit together ?
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JEE Main Maths Test- 12 - Question 8
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A lady gives a dinner party to six guests. The number of ways in which they may be selected from among ten friends, if two of the friends will not attend the party together is
Detailed Solution for JEE Main Maths Test- 12 - Question 8

The lady has ten friends. Two of these friends will not agree to go to the party together. So, let us consider the following case: neither of the two friends will attend the party. So, the number of ways six guests can be invited in this case will be equal to the number of ways to choose 6 friends out of the remaining 8 friends. So, we have

Therefore, there are 28 ways to invite 6 friends when the two friends will not be going to the party.
Now, we will consider the next case, which is that one of the two friends decides to attend the party. So, if either of the two decide to attend the party, then the rest 5 guests will be chosen from the remaining 8 friends. Therefore, if one friend decides to attend the party, the number of ways to invite the other 5 guests is 8C5 . Similarly, if the other friend decides to attend the party, the number of ways to invite the other 5 guests is 8C5 . Therefore, the number of ways to invite the guests if either, if the two friends is going to the party, is the following,

Therefore, the total number of ways to invite six guests out of ten with the given conditions is 28+112 = 140.

JEE Main Maths Test- 12 - Question 9
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How many numbers less than 40,000 can be formed from the digits 1,2,3,4,5 where repetition is not allowed ?
JEE Main Maths Test- 12 - Question 10
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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
Detailed Solution for JEE Main Maths Test- 12 - Question 10

To solve this problem, we need to calculate the sum of the digits at the unit place of all numbers that can be formed using the digits 3, 4, 5, and 6, taken all at a time.

Step 1: Find the total number of numbers formed

Since we are arranging 4 digits (3, 4, 5, 6) in all possible ways, the total number of numbers formed is 4!4!4! (4 factorial), which equals:

4!=4×3×2×1=24

So, 24 numbers are formed.

Step 2: Consider the unit place

Each digit (3, 4, 5, 6) will appear at the unit place equally in all possible permutations. Since there are 24 numbers and 4 digits, each digit will appear 24/4=6 times in the unit place.

Step 3: Calculate the sum of digits at the unit place

Now, we calculate the sum of the digits appearing at the unit place:

(3+4+5+6)×6=18×6=108

Thus, the sum of the digits at the unit place of all the numbers formed is 108.

The correct answer is:

2. 108.

JEE Main Maths Test- 12 - Question 11
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If then n is equal to
JEE Main Maths Test- 12 - Question 12
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The letters of the word RANDOM are written in all possible orders and these words are written out as in dictionary. Then the rank of the word RANDOM is
JEE Main Maths Test- 12 - Question 13
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The straight lines are parallel and lie in the same plane. A total number of m points are taken on n points on ,k Points on The maximum number of triangles formed with vertices of these points are
JEE Main Maths Test- 12 - Question 14
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Number of divisors of the form 4n+2 of the integer 240 is
Detailed Solution for JEE Main Maths Test- 12 - Question 14

Hence there are four such numbers.

JEE Main Maths Test- 12 - Question 15
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Given 5 different green dyes, 4 different blue dyes and 3 different red dyes. The number of combinations of dyes which can be chosen taking at least one green and one blue dye is
JEE Main Maths Test- 12 - Question 16
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JEE Main Maths Test- 12 - Question 17
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JEE Main Maths Test- 12 - Question 18
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JEE Main Maths Test- 12 - Question 19
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JEE Main Maths Test- 12 - Question 20
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JEE Main Maths Test- 12 - Question 21
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Let x be an irrational, then equals
JEE Main Maths Test- 12 - Question 22
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If f(a) = 2, f`(a) = 1, g(a) = –1, g`(a) = 2,then value of is
JEE Main Maths Test- 12 - Question 23
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JEE Main Maths Test- 12 - Question 24
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If G(x) = ,th is
JEE Main Maths Test- 12 - Question 25
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JEE Main Maths Test- 12 - Question 26
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JEE Main Maths Test- 12 - Question 27
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If x = a b,y = aω + bω, z = aω2 + bω then xyz is equal to
JEE Main Maths Test- 12 - Question 28
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The value of the sum where i = ,equals
JEE Main Maths Test- 12 - Question 29
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The smallest positive number n for with (1 + i)2n = (1– i)2n is
JEE Main Maths Test- 12 - Question 30
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If z is a complex number such that z ≠ 0 and Re(z) =0, then
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