If the coefficient of x10 in the binomial expansion of \(\left(\frac{\sqrt{x}}{5^{\frac{1}{4}}} + \frac{\sqrt{5}}{x^{\frac{1}{3}}}\right)^{60}\)is 5k.l, where l, k∈N and l is co-prime to 5, then k is equal to ___________.
Let \(A1 = {(x,y):|x| <= y^2,|x|+2y≤8} \)and \(A2 = {(x,y) : |x| +|y|≤k}. \)If 27(Area A1) = 5(Area A2), then k is equal to :
Let the eccentricity of an ellipse \(\frac {x^2}{a^2}+\frac {y^2}{b^2}=1\), \(a>b\), be \(\frac 14\). If this ellipse passes through the point \((−4\sqrt {\frac 25},3)\), then \(a^2 + b^2\) is equal to :
When the excited electron of a H atom from n = 5 drops to the ground state, the maximum number of emission lines observed are ____.
Let a triangle ABC be inscribed in the circle\(x² - \sqrt2(x+y)+y² = 0\)such that ∠BAC= π/2. If the length of side AB is √2, then the area of the ΔABC is equal to :
Negation of the Boolean statement (p ∨ q) ⇒ ((~ r) ∨ p) is equivalent to
Let \(\vec{a}=α\hat{i}+\hat{j}−\hat{k}\ and\ \vec{b}=2\hat{i}+\hat{j}−α\hat{k},α>0\). If the projection of \(\vec{a}×\vec{b}\) on the vector \(−\hat{i}+2\hat{j}−2\hat{k}\) is 30, then α is equal to
The area enclosed by y2 = 8x and y = √2x that lies outside the triangle formed by \(y=√2x,x=1,y=2√2\), is equal to
The equation of a common tangent to the parabolas y = x2 and y = –(x – 2)2 is
Let f be a real valued continuous function on [0, 1] and\(f(x) = x + \int_{0}^{1} (x - t) f(t) \,dt\)Then, which of the following points (x, y) lies on the curve y = f(x)?