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Determinants
- Online Test
Determinants
TEST : 1
# Determinants
# CBSE 12th Mathematics
Prepare / Learn
Q1.
Let A =
, then Det. A is
A.
none of these
B.
0
C.
1+ab+bc+ca
D.
ab +bc+ca
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
( since C
1
and C
2
are identical)
# Determinants
# CBSE 12th Mathematics
Prepare / Learn
Q2.
A.
2
B.
3e
C.
None of these
D.
0
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
because , row 1 and row 3 are identical.
# Determinants
# CBSE 12th Mathematics
Prepare / Learn
Q3.
If A, B be two square matrices such that |AB|=O, then
A.
Det. A=0 or Det. B =0 or both A and B =0
B.
Det.=A =0
C.
Det.B=0
D.
BA
View Solution
Add Work Space
Answer :
Option A
Explaination / Solution:
If A B be two square matrices such that AB=O, then, |AB|=O⇒|A||B|=O⇒either|A|=0,or|B|=0
# Determinants
# CBSE 12th Mathematics
Prepare / Learn
Q4.
A square matrix A is invertible iff det A is equal to
A.
-1
B.
1
C.
0
D.
non zero
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
Only non-singular matrices possess inverse.
# Determinants
# CBSE 12th Mathematics
Prepare / Learn
Q5.
If A and B are square matrices of order 3 , then
A.
none of these
B.
adj(AB) = adj A adj B
C.
|B| = 0AB = O ⇒|A| = 0
D.
AB = O⇒|A|=0 and |B|=0
View Solution
Add Work Space
Answer :
Option C
Explaination / Solution:
If A B be two square matrices of order 3 and if |B|=0, AB=0 then this is possible only if |A| may be zero
# Determinants
# CBSE 12th Mathematics
Prepare / Learn
Q6.
The value of the determinant
A.
2(x–y)(y–z)(z–x)
B.
none of these
C.
(x–y)(y–z)(z–x)
D.
(x–y)(y–z)(z–x)(x+y+z)
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
# Determinants
# CBSE 12th Mathematics
Prepare / Learn
Q7.
One root of the equation
A.
4/3
B.
8
C.
1/3
D.
2/3
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
# Determinants
# CBSE 12th Mathematics
Prepare / Learn
Q8.
is equal to
A.
1
B.
none of these
C.
0
D.
1
View Solution
Add Work Space
Answer :
Option C
Explaination / Solution:
# Determinants
# CBSE 12th Mathematics
Prepare / Learn
Q9.
If A ,B andC be the three square matrices such that A = B + C , then Det A is equal to
A.
det B
B.
det C
C.
none of these
D.
det B + detC
View Solution
Add Work Space
Answer :
Option C
Explaination / Solution:
Because , if A=B+C then |A|=|B+C|
# Determinants
# CBSE 12th Mathematics
Prepare / Learn
Q10.
If
ω
is non real cube root of unity , then
A.
1
B.
0
C.
None of these
D.
-1
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
expanding along R
3
=
1
(
2
ω
+
ω
2
)
+
1
(
2
+
ω
2
)
=
(
2
+
2
ω
+
2
ω
2
)
=
2
(
1
+
ω
+
ω
2
)
=
2
(
0
)
=
0
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