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JEE Questions for Maths Matrices And Determinants Quiz 5 - MCQExams.com
JEE
Maths
Matrices And Determinants
Quiz 5
If A and B are square matrices of the same order and AB = 3I, then A
-1
is equal to
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3B
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(1/B
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3B-1
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(1/B-1
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AT = A
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AT = - A
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A2 = I
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AT = A-1
If A is square matrix all of whose entries are integers, Then, which one of the following is correct?
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If |A| = ± 1, then A-1 need not exist
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If |A| = ± 1, then A-1 exists but all its entries are not necessarily integers
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If |A| = ± 1, then A-1 exists and all its entries are non -integers
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If |A| = ± 1, then A-1exists and all its entries are integers
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A is orthogonal matris
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A' is orthogonal matrix
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Determinant A = 1
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A is not invertible
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0%
2)
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0%
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A (θ)
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A (θ/2)
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A (-θ)
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A (-θ/2)
If A
2
- A + I = 0, then the inverse of A is
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I - A
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A - I
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A
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A + I
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2
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0
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5
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4
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0%
2)
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0%
None of these
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A is zero matrix
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A = (-I, where I is a unit matrix
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A-1 does not exist
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A2 = I
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a = 1, b = 1
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a = sin 2θ, b = cos 2θ
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a = cos2θ , b = sin 2θ
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None of these
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A
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- A
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adj (A)
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- adj (A)
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1 , 1
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± 1 , 1
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1 , 0
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None of these
If A, B and C are n × n matrices. Then, which of the following is a correct statement ?
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If AB = AC, then B = C
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If A3 + 2A2 + 3A + 5I = 0, then A is invertible
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If A2 = 0, then a = o
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None of the above
If A is a matrix of order 3 and B = |A|
-1
. If |A| = - 5, then |B| is equal to
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1
0%
- 5
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- 1
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25
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- 125
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0%
2)
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0%
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0%
2)
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0%
For non – singular square matrices A, B and C of the same order (AB
-1
C)
-1
is equal to
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A-1 BC-1
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C-1 B-1 A-1
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CBA-1
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C-1 BA-1
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5
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25
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- 1
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1
0%
125
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[-4 1 ]
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[- 4 -1]
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[4 1]
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[4 - 1]
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0%
2)
0%
0%
None of these
The value of k such that the lines 2χ- 3y + k = 0, 3χ - 4y – 13 = 0 and 8χ - 11y – 33 = 0 are concurrent, is
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20
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- 7
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7
0%
- 20
The existence of the unique solution of the system of equations χ + y + z = β ; 5 χ - y + az = 10 and 2 χ + 3y - z = 6 depends on
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α only
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β only
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Both α and β
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Neither α and β
The number of values of k, for which the system of equations (K +χ + 8y = 4k and k χ + (K + 3)y = 3k - 1 has no solution, is
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infinite
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1
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2
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3
The system of linear equations χ - y - 2z = 6, -χ + y + z = μ and λχ + y + z = 3 has
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infinite number of solutions, for λ ≠ - 1 and all μ
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infinite number of solutions, λ = - 1 and μ = 3
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no solution, for λ ≠ - 1
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unique solution, for λ = - 1 and μ = 3
The number of 3 x 3 matrices A , whose entries are either 0 or 1 and for which the system
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0
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29 - 1
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168
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2
Consider the system of linear equations χ
1
+ 2χ
2
+ χ
3
= 3, 2χ
1
+ 3χ
2
+ χ
3
= 3, 3χ
1
+ 5χ
2
+ 2χ
3
= 1 and the system has
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infinite number of solutions
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exactly 3 solutions
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a unique solution
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no solution
The system of equations χ + y + z = 6, χ + 2y + 3z = 10 and χ + 2y + λz = μ has no solution, if
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λ = 3, μ = 10
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λ ≠ 3, μ = 10
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λ ≠ 3, μ ≠ 10
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λ = 3, μ ≠ 10
Consider the system of equations in χ, y and z as χsin 3θ - y + z = 0, χ cos 2θ + 4y + 3z = 0, 2χ + 7y + 7z = 0 and If the system has a non - trivial solution, then for integer n, values of θ are given by
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0%
2)
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0%
If the three linear equations χ + 4ay + az = 0, χ + 3by + bz = 0 and χ + 2cy + cz = 0 has a non - trivial solution, where a ≠ 0, b ≠ 0, and c ≠ 0 then ab + bc is equal to
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2ac
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- ac
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ac
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- 2ac
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a
If M is a 3 × 3 matrix satisfying
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9
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8
0%
10
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11
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0%
2)
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0%
If A is symmetric matrix and n ϵ N, then A
n
is
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symmetric matrix
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a diagonal matrix
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a skew - symmetric
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None of the above
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17
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25
0%
3
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12
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there exist more than one but number of B's such that AB = BA
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there exist exactly more B such that AB = BA
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there exists infinitely many B's such that AB = BA
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there cannot exist any B such that AB = BA
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2100A
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299A
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100A
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299A
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[20]
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20
0%
[-20]
0%
- 20
If A is skew - symmetric matrix of order n and C is a column matrix of order of n × 1, Then C
T
AC is
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an identity matrix of order n
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an identity matrix of order 1
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a zero matrix of order 1
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None of the above
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αβ
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1/ αβ
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1
0%
- 1
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1
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0
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2
0%
None of these
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0
0%
e
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e
0%
e
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0
0%
χ - (a + B + c)
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a + b + c
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9χ2 + a + b + c
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a4 – a1
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2)
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1
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0%
0
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1/4(abc)
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1/8 (abc)
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1/4
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1/8
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1/12
If three - digit numbers A28, 3B9 and 62C, ehere A, B and C are integers between 0 and 9, are divisible by a fixed integer k, then the determinant
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divisible by k
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divisible by k2
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divisible by 2k
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None of these
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sinα sinβ sinδ
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cosα cosβ cosδ
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1
0%
0
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2
0%
- 2
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1
0%
0
If ω ≠ 1 is a cube root of unity and S is the set of all non - singular matrices of the form
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2
0%
6
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4
0%
8
If A is a 2 × 2 matrix with non - zero entries let A
2
= I, where I is 2 × 2 identity matrix. Define tr (A) = Sum of diagonal element of A and |A| = Determinant of matrix A. Statement I tr (A) = 0 Statement Ii |A| = i
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Statement I is correct, Statement Ii is correct; Statement Ii is correct explanation for Statement I
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Statement I is correct, statement II is correct, Statement II is not correct explanation for Statement I
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Statement I is correct, Statement II is incorrect
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Statement I is incorrect, Statement II is correct
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1
0%
6
0%
log5 9
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log3 5 . log5 81
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Incorrect : 0
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