Determinants Test

Result

Determinants Test - 6

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Weekly Quiz Competition

Question 1
1 / -0.25

A
(x –y)(y –z)(z –x)

B
2(x –y)(y –z)(z –x)

C
(x –y)(y –z)(z –x)(x+y+z)

D
none of these

Solution

⇒(x-y)(y-z)[y² + yz+z² - x² - xy - y² ]
⇒(x-y)(y-z) (z-x) (x+y+z)
Question 2
1 / -0.25

If , then is equal to

A
3D

B
0

C
2D

D
6D

Solution

=1(-5) -2(10) + 3(11)
=-5-20+33 = 8
=1(-30) - 6(20) + 3(66)
= -30-120+198= 48
D = 8 ⇒6D = 48
Question 3
1 / -0.25

A
3 or 3/2

B
3 or 6

C
3

D
none of these

Solution

Apply, R₂ →R₂ - R₁ ,

Apply, R₃ →R₃ - 4R₁ ,

⇒(x-3) (6x -9) = 0 ⇒x =
Question 4
1 / -0.25

If the order of matrix A is m*p. And the order of B is p ×n. Then the order of matrix AB is ?

A
n * p

B
m * n

C
n * p

D
n * m
Question 5
1 / -0.25

If each element of a 3 × 3 matrix A is multiplied by 3 , then the determinant of the newly formed matrix is

A
(det detA)³

B
27 det . A

C
3 det A

D
9 det A
Question 6
1 / -0.25

One root of the equation

A
8

B
2/3

C
1/3

D
5/3

Solution

Apply , R₁ →R₁ +R₂ +R₃ ,

⇒either (3x -2) = 0
Question 7
1 / -0.25

A
x³ (x+10)

B
0

C
(x+10)x²

D
None of these

Solution

Apply , C₁ →C₁ +C₂ +C₃ +C₄

Apply, R1 →R₁ - R₂ ,

Apply, R₁ →R₁ - R₂
⇒ (10+ x) x³
Question 8
1 / -0.25

The determinant is equal to

A
0

B
1

C
–1

D
none of these

Solution

Apply, C₁ →C₁ + C₂ + C₃ ,
Question 9
1 / -0.25

A
a₁ +a₂ +a₃ +a₄

B
a₁ a₂ a₃ a₄

C
0

D
none of these

Solution

The determinant of a lower triangular (or an upper triangular matrix is equal to the product of the diagonal elements.
Question 10
1 / -0.25

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

A
|A|⁶

B
|A|³

C
|A|⁴

D
none of these

Solution

where n is order of matrix. Here n = 3.