KVPY Government Jobs Exams

Let r be a real number and n ∈ N be such that the polynomial 2x^2 + 2x + 1 divides the polynomial (x + 1)^n – r.
Then (n, r) can be-

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KVPY Other Question

Arrange the expansion of
n
1/ 4
1/ 2
2x
1 x 



 + in decreasing powers of x. Suppose the coefficient of the first
three terms form an arithmetic progression. Then the number of terms in the expansion having integer
powers of x is-
(A) 1 (B) 2 (C) 3 (D) more than 3 Suppose a, b are real numbers such that ab ≠ 0. Which of the following four figures represents the curve
(y – ax – b)(bx^2 + ay^2 – ab) = 0