for all χ other than 2 and - 2

JEE Questions for Maths Matrices And Determinants Quiz 3

Maths-Matrices and Determinants-38407.png

0%
unitary
0%
orthogonal
0%
nilpotent
0%
involutary

Maths-Matrices and Determinants-38409.png

0%
0
0%
- 4
0%
4 but not 1
0%
1 or 4

If A is matrix that A² = A + I, where I is unit matrix then A⁵ is equal to

0%
5A + I
0%
5A + 2I
0%
5A + 3I
0%
5A + 4I

Maths-Matrices and Determinants-38412.png

0%
0%
2)
0%
0%

Maths-Matrices and Determinants-38418.png

0%
0%
2)
0%
0%

Maths-Matrices and Determinants-38424.png

0%
1 , – 1
0%
2 , –3
0%
– 1, 1
0%
3, - 2

If the area of the triangle on the complex plane formed by the points z , z + iz is 200, then the value of 3|z| be equal to

0%
20
0%
40
0%
60
0%
80

Maths-Matrices and Determinants-38427.png

0%
0
0%
2abc
0%
a2b2c2
0%
None of these

Maths-Matrices and Determinants-38429.png

0%
4
0%
6
0%
7
0%
8

Consider the following statements
I. If any two rows or columns of a determinant are identical, then the value of the determinant is zero.
II. If the corresponding rows and columns of a determinant are interchanged, then the value of determinant does not change.
III. If any two rows (or columns) of a determinant are interchanged, then the value of the determinant in sign.
Which of these correct ?

0%
I and II
0%
II and III
0%
I, II and III
0%
I and III

If I denotes the 3 × 3 identity matrix and P is a matrix obtained by rearranging the columns of I. Then,

0%
there are six distinct choices for P and det(P) = 1
0%
there are six distinct choices for P and det(p) = ± 1
0%
there are more than one choices for P and some of them are not invertible
0%
there are more than choices for P and P-1 = I in each choice

If a, b and c are non- zero and different from 1, then the value of
Maths-Matrices and Determinants-38432.png

0%
0
0%
1 + loga(a + b + c)
0%
loga(a + b + c)
0%
1

Maths-Matrices and Determinants-38434.png

0%
χyz = –1
0%
χyz = –1
0%
χyz = – 2
0%
χyz = 2

If K > 1 and the determinant of the matrix A², where
Maths-Matrices and Determinants-38436.png

0%
1/K2
0%
k
0%
K2
0%
1/k

Maths-Matrices and Determinants-38438.png

0%
x – y
0%
x2 – y2 + χy
0%
x2 + xy + y2
0%
x2 – xy + y2

Maths-Matrices and Determinants-38440.png

0%
11π/24
0%
17π/24
0%
5π/24
0%
π/24

Let P = [a_ij] bc a 3 × 3 matrix and Q = [b_ij], where b_ij = 2^i+j for 1 ≤ i, j ≤ 3, if the determinant of P is 2, then the determinant of the matrix Q is

0%
210
0%
211
0%
212
0%
213

Maths-Matrices and Determinants-38443.png

0%
(a + b + c)2
0%
a2 + b2 + c2
0%
a2 + b2 + c2 + 1
0%
1

If P, Q and R are angles of ΔPQR, then the value of
Maths-Matrices and Determinants-38445.png

0%
– 1
0%
0
0%
1/2
0%
1

Let P and Q be 3 × 3 matrices, P ≠ Q If P³ = Q³ and P²Q = Q²P, then determinant of (P² + Q²) is equal to

0%
–2
0%
1
0%
0
0%
– 1

Statement I . Determine of a skew- symmetric matrix of order 3 is zero
Statement II. For any matrix A , det (A^T) = det (A) and det (-A) = - det (A) . Where, det (B) denotes the determinant of matrix B. Then,