Determinants Test

Result

Determinants Test - 2

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Weekly Quiz Competition

Question 1
1 / -0.25

Order of a matrix [ 2 5 7 ] is:

A
3 x 3

B
1 x 1

C
3 x 1

D
1 x 3

Solution

The order of matrix is defined by (row × column). The follwing matrix has 1 row and 3 columns. So, the correct option is (d) i.e 1×3.
Question 2
1 / -0.25

A
-1

B
2

C
0

D
1

Solution

To find the determinant we have to cross mutliply the elements and then subtract it.
cos²θ - (-sin²θ) = 1
Question 3
1 / -0.25

A
2|A|

B
4|A|

C
±2|A|

D
|A|

Solution

Due to the rule if a square matrix is of order n x n then, |kA| = kⁿ |A|.
Question 4
1 / -0.25

A
(a-b)²

B
a²-b²

C
(a+b)²

D
a²

Solution

(a² + b²)×1 - (2a) × b
= a² +b² - 2ab
= (a - b)²
Question 5
1 / -0.25

A
-3/2

B
3/2

C
-1/2

D
1/2

Solution

As value of both determinants are equal
∴ (1×1) - (1×1) = 4x - 2
0 = 4x-2.
4x = 2.
x = 2/4 = 1/2
Question 6
1 / -0.25

A
(a)²

B
(a – b)²

C
1

D
(a+b)²

Solution

Determinant = [(a² + b²).1 - (-2ab)]
= (a+b)²
Question 7
1 / -0.25

A
0

B
±1

C
-1

D
1

Solution

As the value of both determinants are equal,
∴ 1 = x²
x = ±1
Question 8
1 / -0.25

A
-2

B
1

C
2

D
-1

Solution

8-6 = 4x-2x
⇒ x = 1
Question 9
1 / -0.25

A
43/2

B
44/7

C
47/2

D
48/7

Solution

Δ = 1/2 [2(1-8) -7(1-10) +1(8-10)]
= 47/2
Question 10
1 / -0.25

A
-10

B
11

C
12

D
-13

Solution

9(2x+5) - 3(5x+2) = 0
3x = -39
x = -13