Test: Determinants - 1 - JEE MCQ

# Test: Determinants - 1 - JEE MCQ

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## 25 Questions MCQ Test - Test: Determinants - 1

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

### Let a =  , then Det. A is

Detailed Solution for Test: Determinants - 1 - Question 1

Apply C2 → C2 + C3,

Test: Determinants - 1 - Question 2
Detailed Solution for Test: Determinants - 1 - Question 2

because , the value of the determinant is zero only when , the two of its rows are identical., Which is possible only when Either x = 3 or x = 4 .

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Test: Determinants - 1 - Question 3
Detailed Solution for Test: Determinants - 1 - Question 3

Apply , R1 → R1+R2+R3,

Apply , C3→ C- C1, C2C2 - C1,

=(a+b+c)3

Test: Determinants - 1 - Question 4

If A and B matrices are of same order and A + B = B + A, this law is known as

Detailed Solution for Test: Determinants - 1 - Question 4

Commutative law, in mathematics, either of two laws relating to number operations of addition and multiplication, stated symbolically: a + b = b + a and ab = ba

Test: Determinants - 1 - Question 5

If A’ is the transpose of a square matrix A , then

Detailed Solution for Test: Determinants - 1 - Question 5

The determinant of a matrix A and its transpose always same.

Test: Determinants - 1 - Question 6

The value of the determinant  is

Detailed Solution for Test: Determinants - 1 - Question 6

, Apply , C2 → C2 + C3

= 0, (∵ C1 = C2)

Test: Determinants - 1 - Question 7

The roots of the equation det.   are

Detailed Solution for Test: Determinants - 1 - Question 7

⇒ (1-x)(2-x)(3-x) = 0 ⇒x = 1,2,3

Test: Determinants - 1 - Question 8

If A is a square matrix of order 2 , then det (adj A) = x

Detailed Solution for Test: Determinants - 1 - Question 8

Let A be a square matrix of order 2 . then ,|adj.A| = |A|

Test: Determinants - 1 - Question 9

If A is a symmetric matrix, then At =

Detailed Solution for Test: Determinants - 1 - Question 9

If A is a symmetric matrix then by definition AT=A
Option A is correct.

Test: Determinants - 1 - Question 10

Detailed Solution for Test: Determinants - 1 - Question 10

, because , row 1 and row 3 are identical.

Test: Determinants - 1 - Question 11

is equal to

Detailed Solution for Test: Determinants - 1 - Question 11

Apply , C1→C1 - C3, C2→C2-C3

= 10 - 12 = -2

Test: Determinants - 1 - Question 12

If A+B+C = π, then the value of

Detailed Solution for Test: Determinants - 1 - Question 12

Test: Determinants - 1 - Question 13

If A is a non singular matrix of order 3 , then |adj(A3)| =

Detailed Solution for Test: Determinants - 1 - Question 13

If A is anon singular matrix of order , then

Test: Determinants - 1 - Question 14

If A and B are any 2 × 2 matrices , then det. (A+B) = 0 implies

Detailed Solution for Test: Determinants - 1 - Question 14

Det.(A+B) ≠ Det.A + Det.B.

Test: Determinants - 1 - Question 15

Detailed Solution for Test: Determinants - 1 - Question 15

Correct option is D.

Test: Determinants - 1 - Question 16

If A B be two square matrices such that AB = O, then

Detailed Solution for Test: Determinants - 1 - Question 16

If A B be two square matrices such that AB = O, then,

Test: Determinants - 1 - Question 17

Detailed Solution for Test: Determinants - 1 - Question 17

Apply , C1 → C1 - C2, C2 → C2 - C3,

Because here row 1 and 2 are identical

Test: Determinants - 1 - Question 18

If   , then equals

Detailed Solution for Test: Determinants - 1 - Question 18

Because , the determinant of a skew symmetric matrix of odd order is always zero and of even order is a non zero perfect square.

Test: Determinants - 1 - Question 19

If I3 is the identity matrix of order 3 , then 13−1 is

Detailed Solution for Test: Determinants - 1 - Question 19

Because , the inverse of an identity matrix is an identity matrix.

Test: Determinants - 1 - Question 20

If A and B are square matrices of same order and A’ denotes the transpose of A , then

Detailed Solution for Test: Determinants - 1 - Question 20

By the property of transpose of a matrix ,(AB)’ = B’A’.

Test: Determinants - 1 - Question 21

A square matrix A is invertible iff det A is equal to

Detailed Solution for Test: Determinants - 1 - Question 21

Only non-singular matrices possess inverse.

Test: Determinants - 1 - Question 22

Detailed Solution for Test: Determinants - 1 - Question 22

Apply, C1→ C1+ C2+C3+C4,

Apply, R1 →R1 - R2,

Apply, R1 R- R2, R→ R- R3

=(x+3a) (a -x)3 (1) = (x+3a)(a-x)3

Test: Determinants - 1 - Question 23

If the entries in a 3 x 3 determinant are either 0 or 1 , then the greatest value of this determinant is :

Detailed Solution for Test: Determinants - 1 - Question 23

Greatest value = 2

Test: Determinants - 1 - Question 24

The roots of the equation  are

Detailed Solution for Test: Determinants - 1 - Question 24

Operate,

Apply R3→R3- R1, R2 R2 -R1,

⇒ -6(5x2 - 20) +15(2x-4) = 0

⇒ (x- 2)(x+1) = 0⇒x=2, -1

⇒-6(5x2 - 20) + 15(2x-4) = 0

⇒(x-2)(x+1) = 0 ⇒ x=2, -1

Test: Determinants - 1 - Question 25

In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has value

Detailed Solution for Test: Determinants - 1 - Question 25

N = 2 ×3 × 4 = 24.

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