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Test: Properties Of Determinants - JEE MCQ


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10 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Properties Of Determinants

Test: Properties Of Determinants for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Properties Of Determinants questions and answers have been prepared according to the JEE exam syllabus.The Test: Properties Of Determinants MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Properties Of Determinants below.
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Test: Properties Of Determinants - Question 1

If the value of the determinant   , then the value of   is​

Detailed Solution for Test: Properties Of Determinants - Question 1

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

Test: Properties Of Determinants - Question 2

The value of x, if  = 0 , is​

Detailed Solution for Test: Properties Of Determinants - Question 2

Test: Properties Of Determinants - Question 3

If the value of   , then the value of

Detailed Solution for Test: Properties Of Determinants - Question 3

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

= 7
# Rule 
If any two rows( or columns) of a determinant are interchanged, then the value of determinant is changed in sign only

Test: Properties Of Determinants - Question 4

The operation that will simplify the Determinant

by taking (a+b+c) common from the first Row is​

Detailed Solution for Test: Properties Of Determinants - Question 4

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

Test: Properties Of Determinants - Question 5

The value of the determinant   is 

Detailed Solution for Test: Properties Of Determinants - Question 5

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

Test: Properties Of Determinants - Question 6

The maximum value of the determinant among all 2 × 2 real symmetric matrices with trace 24 is _______.

Detailed Solution for Test: Properties Of Determinants - Question 6

Let the symmetric matrix be

∴ |X| = bc – a2

Since the given matrix is real, to get maximum determinant value of a should be equal to 0.

b + c = 24

c = 24 – b

∴ |X| = b × (24 – b)

|X| = 24 b – b2

Differentiating with respect to b

|X|’ = 24 – 2b = 0

∴ b = 12

|X|’’ = - 2 < 0

At b = 12 it will have maximum value

c = 24 – 12 =12

Maximum value = 12 × 12 – 0 = 144

Test: Properties Of Determinants - Question 7

If the value of the determinant  is equal to 14, then the value of the determinant  is equal to​

Detailed Solution for Test: Properties Of Determinants - Question 7

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

Test: Properties Of Determinants - Question 8

The value of   is 

Detailed Solution for Test: Properties Of Determinants - 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

Test: Properties Of Determinants - Question 9

Given ​

Detailed Solution for Test: Properties Of Determinants - Question 9

Test: Properties Of Determinants - Question 10

 

 + Δ. then Δ is 

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