KVPY Government Jobs Exams

The product (1 + tan 1º) (1 + tan 2º) (1 + tan 3º) …. (1 + tan 45º) equals-

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KVPY Other Question

The number of roots of the equation cos^7θ – sin^4θ = 1 that lie in the interval [0, 2π] is-
(A) 2 (B) 3 (C) 4 (D) 8 Let f : R → R be a differentiable function such that f (a) = 0 = f (b) and f ′(a) f ′(b) > 0 for some a < b. Then
the minimum number of roots of f ′(x = 0 in the interval (a, b) is-
(A) 3 (B) 2 (C) 1 (D) 0