Paper II Mathematics

91. If and , then is equal to
    (A) 2m + n
    (B) m + 2n
    (C) m – n
    (D) n – m
    (E) m + n
92. is equal to
    (A) 
    (B) 
    (C) 
    (D) 
    (E) 


93. is equal to
    (A) 
    (B) e² – 2e
    (C) 2(e² –e)
    (D) 2e^–2 – 2e
    (E) 0


94. The family of curves y = e^asinx, where a is an arbitrary constant, is represented by the differential equation
    (A) log y = tan x
    (B) y log y = tan x
    (C) y log y = sin x
    (D) log y = cos x
    (E) y log y = cos x


95. The integrating factor of is
    (A) x
    (B) 2x
    (C) e^xlogx
    (D) e^x
    (E) xe^x


96. The degree and order of the differential equation , where
    p = , are
    (A) 3,1
    (B) 1, 3
    (C) 1, 1
    (D) 3, 3
    (E) 3, 2


97. The solution of the differential equation is
    (A) x + e^x+y = C
    (B) x – e^x+y = C
    (C) x + e^–(x+y) = C
    (D) x – e^–(x+y) = C
    (E) xe^x+y + y = C


98. Let . The value of for which ƒ(a) = a, (a ≠ 0) is
    (A) 
    (B) 
    (C) 
    (D) 
    (E) 


99. For a, b ∈ R, define a*b = , where a+b≠0. If a*b = 5, then the value of b*a is
    (A) 5
    (B) –5
    (C) 4
    (D) –7
    (E) –4


100. Let A = {x, y, z} and B = {a, b, c, d}. Which one of the following is not a relation
     from A to B?
     (A) {(x, a), (x, c)}
     (B) {(y, c), (y, d)}
     (C) {(z, a), (z, d)}
     (D) {(z, b), (y, b), (a, d)}
     (E) {(x, c)}

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