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JEE Exam  >  JEE Tests  >  Properties of Determinants (May 1) - JEE MCQ

Properties of Determinants (May 1) - JEE MCQ


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10 Questions MCQ Test - Properties of Determinants (May 1)

Properties of Determinants (May 1) for JEE 2024 is part of JEE preparation. The Properties of Determinants (May 1) questions and answers have been prepared according to the JEE exam syllabus.The Properties of Determinants (May 1) MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Properties of Determinants (May 1) below.
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Properties of Determinants (May 1) - Question 1
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If the value of the determinant   , then the value of   is​

Detailed Solution for Properties of Determinants (May 1) - Question 1

Determinant = -2(-12 + 12) -2(-6 - 2) +1(-12 - 4)
= - 2(0) - 2(-8) + 1(16)
= 0 + 16 + 16
= 32

Properties of Determinants (May 1) - Question 2
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The value of x, if  = 0 , is​

Detailed Solution for Properties of Determinants (May 1) - Question 2

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Properties of Determinants (May 1) - Question 3
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If the value of   , then the value of

Detailed Solution for Properties of Determinants (May 1) - Question 3

If you interchange (switch) two rows (or columns) of a matrix A to get B, then det(B) = –det(A). Hence, the determinant is -(-7)

= 7

Properties of Determinants (May 1) - Question 4
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The operation that will simplify the Determinant

by taking (a+b+c) common from the first Row is​
Detailed Solution for Properties of Determinants (May 1) - Question 4

R1 ------> R1 + R2, taking (a+b+c) common from the first row, we get the resultant matrix.

Properties of Determinants (May 1) - Question 5
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The value of the determinant   is 
Detailed Solution for Properties of Determinants (May 1) - Question 5

|A|=3((4)-(4))-2((-4)-(2))-1((-8)-(-4))
|A|= -2(-6)-(-6)
|A|= -2(0)
=0

Properties of Determinants (May 1) - Question 6
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The value of the Δ  ​
Properties of Determinants (May 1) - Question 7
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If the value of the determinant  is equal to 14, then the value of the determinant  is equal to​
Detailed Solution for Properties of Determinants (May 1) - Question 7

Taking 3 common from the column I in second determinant, we get the 14 * 3 = 42

Properties of Determinants (May 1) - Question 8
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The value of   is 
Detailed Solution for Properties of Determinants (May 1) - Question 8

A = {(5x+2, 2x, 2x) (5x+2, x+2, 2x) (5x+2, 2x, x+2)}
= (5x+2) {(1, 2x, 2x) (1, x+2, 2x) (1, 2x, x+2)}
= (5x+2) [(1(x+2)^2 - 4x^2) - 2x(x+2 - 2x) + 2x(2x - x - 2)]
= (5x+2) [(x+2 - 2x)(x+2+2x)-2x(2 - x) + 2x(x-2)]
= (5x+2) [(2-x)(3x+2) -2x(2-x) -2x(2-x)]
= (5x+2) (2-x)[3x+2-2x-2x]
= (5x+2) (2-x)2

Properties of Determinants (May 1) - Question 9
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Given ​
Detailed Solution for Properties of Determinants (May 1) - Question 9

Properties of Determinants (May 1) - Question 10
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 + Δ. then Δ is 
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