Paper II Mathematics

61. The probability distribution of a random variable X is given by
    
    

    x	–5	–4	–3	–2	–1	0	1	2	3	4	5
    P(X=x)	p	2p	3p	4p	5p	7p	8p	9p	10p	11p	12p

    
    Then the value of P is
    (A) 
    (B) 
    (C) 
    (D) 
    (E) 
62. The mean and variance of n observations x₁, x₂, x₃, ... , x_n are 5 and 0 respectively. If , then the value of n is equal to
    (A) 80
    (B) 25
    (C) 20
    (D) 16
    (E)  4


63. If A and B are mutually exclusive events and if P(B) = , P(A ∪ B) = , then P(A) is equal to
    (A) 
    (B) 
    (C) 
    (D) 
    (E) 


64. If ƒ is a real valued function such that ƒ(x + y) = ƒ(x) + ƒ(y) and ƒ(1) = 5, then the value of ƒ(100) is
    (A) 200
    (B) 300
    (C) 350
    (D) 400
    (E) 500


65. Let ƒ(x) = for x ≠ 0, and ƒ(0) = 12. If ƒ is continuous at x = 0, then the value of a is equal to
    (A) 1
    (B) –1
    (C) 2
    (D) –2
    (E) 3


66. is equal to
    (A) 0
    (B) 1
    (C) 2
    (D) –1
    (E) –2


67. is equal to
    (A) 
    (B) 
    (C) 0
    (D) 
    (E) 


68. If x^y = e^2(x-y) , then is equal to
    (A) 
    (B) 
    (C) 
    (D) 
    (E) 


69. If y = sin^-1 , then is equal to
    (A) 
    (B) 
    (C) 
    (D) 
    (E) 


70. The derivative of sin^-1 with respect to sin^-1 (3x – 4x³) is
    (A) 
    (B) 
    (C) 
    (D) 1
    (E) 0

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