KVPY Government Jobs Exams

A polynomial P(x) with real coefficients has the property that P''(x) ≠ 0 for all x. Suppose P(0) = 1 and P'(0) = –1.
What can you say about P(1)

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KVPY Other Question

Let (x, y) be a variable point on the curve 4x^2 + 9y^2 – 8x –36y + 15 = 0. Then
min(x ^2 − 2x + y^2 − 4y + 5) + max(x^ 2 − 2x + y^2 − 4y + 5) is A man tosses a coin 10 times, scoring 1 point for each head and 2 points for each tail. Let P(K) be the probability
of scoring at least K points. The largest value of K such that P(K) > ½ is