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Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration


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25 Questions MCQ Test JEE Main & Advanced Mock Test Series | Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration

Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration for JEE 2022 is part of JEE Main & Advanced Mock Test Series preparation. The Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration questions and answers have been prepared according to the JEE exam syllabus.The Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration MCQs are made for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration below.
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Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 1

If  n ≠ 3k and 1 ,ω,ω2 are the cube roots of unity then    has the value

Detailed Solution for Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - 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

Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 2

If , then its value is equal to

Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 3

x,y,z being +ive equals

Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 4
The roots of the equation  are

Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 5
If the three equations are consistent


, then a =
Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 6

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 Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 6

For infinitely many solutions the two equation become identical.

Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 7
If   and  , then   is 
Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 8

Let  . Then A is 

Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 9

IF B is a non-singular matrix and A is a square matrix, then  det (B-1 AB)

Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 10

 will be equal to 

Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 11
The sum of the series is 

Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 12
The sum of the series is 

Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 13
 is equal to
Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 14
 is equal to 
Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 15

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.

Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 16

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

Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 17

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

Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 18

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

Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 19

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

Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 20

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
Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 21

Value of  is


Detailed Solution for Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 21

Value of odd order skew symmetric determinant

*Answer can only contain numeric values
Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 22

If  then value of (a + b) = ?


Detailed Solution for Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 22

*Answer can only contain numeric values
Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 23

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 Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 23

P(boy and his sister both are selected)

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

*Answer can only contain numeric values
Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 24

The probability that the 13th day of a randomly chosen month is a Friday, is?


Detailed Solution for Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - 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
Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - Question 25

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 Mathematics Test 4 - Matrices And Determinants, Probability, Indefinite Integration - 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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