KVPY Government Jobs Exams

The maximum value M of 3^x + 5^x – 9^x + 15^x –25^x, as x varies over reals, satisfies –
(A) 3 < M < 5 (B) 0 < M < 2 (C) 9 < M < 25 (D) 5 < M < 9

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KVPY Other Question

In the real number system, the equation sqrt(x + 3− 4 x −1) + sqrt(x + 8 − 6 x −1) = 1 has
option
(A) No solution
(B) Exactly two distinct solutions
(C) Exactly four distinct solutions
(D) Infinitely may solutions
Suppose two perpendicular tangents can be drawn from the origin to the circle x2 + y2 – 6x –2py + 17 = 0, for
some real p. then |p| =