The number of distinct real roots of the equation x5(x3 – x2 – x + 1) + x (3x3 – 4x2 – 2x + 4) – 1 = 0 is ______ .
If the coefficients of x and x2 in the expansion of (1 + x)p (1 – x)q, p, q≤15, are – 3 and – 5 respectively, then coefficient of x3 is equal to ______.
If \(n(2n+1)\int_{0}^{1}(1−xn)^{2n}dx=1177\int_{0}^{1}(1−x^n)^{2n+1}dx\),then n ∈ N is equal to ______.
Let a curve y = y(x) pass through the point (3, 3) and the area of the region under this curve, above the x-axis and between the abscissae 3 and \(x(>3)\ be\ (\frac{y}{x})^3\). If this curve also passes through the point (α,6√10) in the first quadrant, then α is equal to _______.
The Integral\(\int \frac{(1 - \frac{1}{\sqrt{3}})(\cos x - \sin x)}{1 + \frac{2}{\sqrt{3}}\sin2 x} \,dx\)is equal to
The structure of A in the given reaction is:
Major product ‘B’ of the following reaction sequence is
Match List-I with List-II
Choose the correct answer from the options given below:
Match List-I with List-IIChoose the correct answer from the options given below:
The number of functions f, from the set\(A = {x∈N: x^2-10x+9≤0} \)to the set \(B = {n62:n∈N}\)such that\(f(x)≤(x-3)^2+1\), for every \(x∈A,\)is ______.
