Page 54 - ISC-12

Comprehension Type Jai Baba Ki7
2
(A) (p − 1) . (B) 2(p − 1).
2
(C) (p − 1) + 1. (D) 2p − 1.

30. The number of A in T p such that the trace of A is not divisible by p but det (A) is divisible by p is
[Note: The trace of a matrix is the sum of its diagonal entries.]

2
2
3
(A) (p − 1)(p − p + 1). (B) p − (p − 1) .
2
2
(C) (p − 1) . (D) (p − 1)(p − 2).
31. The number of A in T p such that det (A) is not divisible by p is
2
3
(A) 2p . (B) p − 5p.
3
3
2
(C) p − 3p. (D) p − p .
[JEE 2010]

Paragraph for Question Nos. 32 to 34

Let A be the set of all 3×3 symmetric matrices, all of whose entries are either 0 or 1. Five of these entries
are 1 and four of them are 0.

32. The number of matrices in A is

(A) 12. (B) 6.

(C) 9. (D) 3.

33. The number of matrices A in A for which the system of linear equations
   
x 1
   
A y = 0
z 0
has a unique solution, is

(A) less than 4. (B) at least 4 but less than 7.
(C) at least 7 but less than 10. (D) at least 10.

34. The number of matrices A in A for which the system of linear equations
   
x 1
   
A y = 0
z 0

is inconsistent, is
(A) 0. (B) more than 2.

2
(C) 9x 2. (D) 1.
[JEE 2009]