Paper II Mathematics

11. If A is a non-singular matrix of order 3, then adj (adjA) is equal t0
    (A) 
    (B) 
    (C) 
    (D) 
    (E) 
12. If , then the values of x, y and z are respectively
    (A) 5, 2, 2
    (B) 1, –2, 3
    (C) 0, –3, 3
    (D) 11, 8, 3
    (E) 4, 1, 3


13. Which one of the following is true always for any two non-singular matrices A and B of same order?
    (A) AB = BA
    (B) (AB)^t = A^tB^t
    (C) (A + B) (A – B) = A² – B²
    (D) (AB)^-1 = B^-1A^-1
    (E) AB = –BA


14. The solution set of the inequation is
    (A) (–∞, –11) ∪ (3, ∞)
    (B) (–∞, –10) ∪ (2, ∞)
    (C) (–100, –11) ∪ (1, ∞)
    (D) (0, 5) ∪ (–1, 0)
    (E) (–5, 0) ∪ (3, 7)


15. If 3 ≤ 3t – 18 ≤ 18, then which one of the following is true?
    (A) 15 ≤ 2t + 1 ≤ 20
    (B) 8 ≤ t < 12
    (C) 8 ≤ t + 1 ≤ 13
    (D) 21 ≤ 3t ≤ 24
    (E) t ≤ 7 or t ≥ 12


16. Let p : 7 is not greater than 4 and
          q : Paris is in France
    be two statements.
    Then ∼(p ∨ q) is the statement
    (A) 7 is greater than 4 or Paris is not in France
    (B) 7 is not greater than 4 and Paris is not in France
    (C) 7 is greater than 4 or Paris is in France
    (D) 7 is not greater than 4 or Paris is not in France
    (E) 7 is greater than 4 and Paris is not in France


17. If S(p, q, r) = (∼p) ∨ [∼(q ∨r)] is a compound statement, then S(∼p, ∼q, ∼r) is
    (A) ∼S(p, q, r)
    (B) S(p, q, r)
    (C) p∨(q ∧ r)
    (D) p ∨ (q ∨ r)
    (E) S(p, q, ∼r)


18. For any two statements p and q, ∼ (p ∨ q) ∨ (∼p ∧ q) is logically equivalent to
    (A) p
    (B) ∼p
    (C) q
    (D) ∼q
    (E) p ∨ q
    


19. If tan , a > b > 0 and if , then is equal to
    (A) 
    (B) 
    (C) 
    (D) 
    (E) 


20. If tan^-1 (x + 2) + tan^-1 (x – 2) – tan^_1 = 0, then one of the values of x is equal to
    (A) –1
    (B) 5
    (C) 
    (D) 1
    (E) 

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