IIT-JEE
Exam
Let a solution y = y(x) of the differential equation
x x^2 - 1 dy (-y) y^2 - 1 dx = 0 satisfy y(2) = 23.
STATEMENT -1 : y(x) = sec sec 1 x^6
and
STATEMENT -2 : y(x) is given by 2
1 2 3 1 1 y x x = -
(A) STATEMENT 1 is True, STATEMENT -2 is True; STATEMENT -2 is a correct explanation for STATEMENT -1
(B) STATEMENT -1 is True, STATEMENT -2 is True; STATEMENT -2 is NOT a correct explanation for STATEMENT -1.
(C) STATEMENT -1 is True, STATEMENT -2 is False
(D) STATEMENT -1 is False, STATEMENT -2 is True
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IIT-JEE Other Question
Suppose four distinct positive numbers a1, a2, a3, a4 are in G.P. Let b1 = a1, b2 = b1 + a2, b3 = b2 + a3 and b4 = b3 + a4.
STATEMENT -1 : The numbers b1, b2, b3, b4 are neither in A.P. nor in G.P.
and
STATEMENT -2 : The numbers b1, b2, b3, b4 are in H.P.
(A) STATEMENT -1 is True, STATEMENT -2 is True; STATEMENT -2 is a correct explanation for STATEMENT -1
(B) STATEMENT -1 is True, STATEMENT -2 is True; STATEMENT -2 is NOT a correct explanation for STATEMENT -1.
(C) STATEMENT +1 is True, STATEMENT -2 is False
(D) STATEMENT +1 is False, STATEMENT -2 is True
Which of the following is true?
(A) f(x) is decreasing on (-1, 1) and has a local minimum at x = 1
(B) f(x) is increasing on (-1, 1) and has a local maximum at x = 1
(C) f(x) is increasing on (-1, 1) but has neither a local maximum nor a local minimum at x = 1
(D) f(x) is decreasing on (-1, 1) but has neither a local maximum nor a local minimum at x = 1