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JEE Main Maths Test- 4 - JEE MCQ


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25 Questions MCQ Test - JEE Main Maths Test- 4

JEE Main Maths Test- 4 for JEE 2024 is part of JEE preparation. The JEE Main Maths Test- 4 questions and answers have been prepared according to the JEE exam syllabus.The JEE Main Maths Test- 4 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Main Maths Test- 4 below.
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JEE Main Maths Test- 4 - Question 1
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If  n ≠ 3k and 1 ,ω,ω2 are the cube roots of unity then    has the value

Detailed Solution for JEE Main Maths Test- 4 - Question 1

Del=(1-w^3n)+w^n(0)+w^2n(w^4n-w^n) =1-(w^3)^n+(w^6)^n-(w^3)^n =1-1+1-1 =0

JEE Main Maths Test- 4 - Question 2
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If , then its value is equal to

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JEE Main Maths Test- 4 - Question 3
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x,y,z being +ive equals

JEE Main Maths Test- 4 - Question 4
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The roots of the equation  are
JEE Main Maths Test- 4 - Question 5
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If the three equations are consistent


, then a =
JEE Main Maths Test- 4 - Question 6
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The number of values of k for which the system of equations ( k+1)x + 8y = 4k, kx + (k+3)y = 3k - 1 has inifinitely many solutions is
Detailed Solution for JEE Main Maths Test- 4 - Question 6

For infinitely many solutions the two equation become identical.

JEE Main Maths Test- 4 - Question 7
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If   and  , then   is 
JEE Main Maths Test- 4 - Question 8
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Let  . Then A is 
JEE Main Maths Test- 4 - Question 9
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IF B is a non-singular matrix and A is a square matrix, then  det (B-1 AB)
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JEE Main Maths Test- 4 - Question 10
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 will be equal to 
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JEE Main Maths Test- 4 - Question 11
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The sum of the series is 
JEE Main Maths Test- 4 - Question 12
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The sum of the series is 
JEE Main Maths Test- 4 - Question 13
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 is equal to
JEE Main Maths Test- 4 - Question 14
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 is equal to 
JEE Main Maths Test- 4 - Question 15
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Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.
JEE Main Maths Test- 4 - Question 16
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Seven chits are numbered 1 to 7. Three are drawn one by one with replacements. The probability that the least number on any selected chit is 5, is
JEE Main Maths Test- 4 - Question 17
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A student appear for tests I,II and III. The student is successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I,II and III are p,q and 1/2 respectively. If the probability that the student is successful is 1/2, then
JEE Main Maths Test- 4 - Question 18
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Words from the letters of the word PROBABILITY are formed by talking all at a time.The probability that both B’s are together & both I’s are together is
JEE Main Maths Test- 4 - Question 19
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The probability that a person will hit a target in a shooting practice is 0.3. If the shoots 10 times, the probability that he hit the target is
JEE Main Maths Test- 4 - Question 20
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The probability that Krishna will be alive 10 years hence is 7/15 and that Hari will be alive is 7/10. What is the probability that both Krishna and Hari will be dead 10 years hence
*Answer can only contain numeric values
JEE Main Maths Test- 4 - Question 21
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Value of  is

Detailed Solution for JEE Main Maths Test- 4 - Question 21

Value of odd order skew symmetric determinant

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JEE Main Maths Test- 4 - Question 22
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If  then value of (a + b) = ?

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JEE Main Maths Test- 4 - Question 23
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Three children are selected at random from a group of 6 boys and 4 girls. It is known that in this group exactly one girl and one boy belong to same parents. The probability that the selected group of children have no blood relations, is equal to?

Detailed Solution for JEE Main Maths Test- 4 - Question 23

P(boy and his sister both are selected)

∴  Required probability
= 1 – 1/15 = 14/15 = 0.93

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JEE Main Maths Test- 4 - Question 24
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The probability that the 13th day of a randomly chosen month is a Friday, is?

Detailed Solution for JEE Main Maths Test- 4 - Question 24

Probability of selecting a month = 1/12.
13th day of a randomly selected month is Friday if its first day is Sunday.
Probability of this event = 1/7.
Hence required probability  = 0.01

*Answer can only contain numeric values
JEE Main Maths Test- 4 - Question 25
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If two integers m and n are chosen at random from 1 to 100 then the probability that a number of the form 7m + 7n is divisible by 5 equals:

Detailed Solution for JEE Main Maths Test- 4 - Question 25

Since m and n are selected between 1 and 100, hence sample space = 100 × 100
Also, 71 = 7,  72 = 49, 73 = 343, 74 = 2401,
75 = 16807 etc. Hence 1, 3, 7 and 9 will be the last digits in the powers of 7.
n, m →
↓
1,1       1,2       1,3 ...........       1, 100
2,1       2,2       2,3 ...........       2, 100
...........................................
100, 1  100,2   100, 3.........     100, 100
For m = 1 ; n = 3, 7, 11, ...... 97
∴ Favourable cases =  25
For m = 2, n = 4, 8, 12, ......., 100
∴  Favourable cases =  25
Similarly for every m, favourable n are 25.
∴  Total favourable cases  = 100 × 25
Hence required probability = 

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