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Phenol, when it first react with concentrated sulphuric acid and then with concentrated nitric acid, gives

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The major product obtained on interaction of phenol with sodium hydroxide and carbon dioxide is

The sum of the series$_{20}C_{0}−_{20}C_{1}+_{20}C_{2}−_{20}C_{3}+…−…+_{20}C_{10}$ is:

The ellipse $x_{2}+4y_{2}=4$is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is

The organic chloro compound, which shows complete stereochemical inversion during a $S_{N}2$ reaction, is

The sum of the series $2!1 −3!1 +4!1 −…$ upto infinity is

For real x, let $f(x)=x_{3}+5x+1$, then

If $u,v,w$ are noncoplanar vectors and p, q are real numbers, then the equality $[3u,pv,pw]−[pv,w,qu]−[2w,qv,qu]=0$ holds for(A) exactly one value of (p, q)(B) exactly two values of (p, q)(C) more than two but not all values of (p, q)(D) all values of (p, q)

A parabola has the origin as its focus and the line $x=2$as the directrix. Then the vertex of the parabola is at