The area bounded by \(y^2=4 x\) and \(x^2=4 y\) is

Let \(A, B, C\) are subsets of set \(X\). Then consider the validity of the following set theoretic statement :

Let \(n\) be a positive even integer. If the ratio of the largest coefficient and the 2nd largest coefficient in the expansion of \((1+x)^{n}\) is \(11: 10 .\) Then, the number of terms in the expansion of \((1+x)^{n}\) is

Given an A.P. and a G.P. with positive terms, with the first and second terms of the progressions being equal. If \(a_n\) and \(b_n\) be the \(n^{\text {th }}\) term of A.P. and G.P. respectively then

The locus of the mid-points of all chords of the parabola \(y^{2}=4 a x\) through its vertex is another parabola with directrix

If \(a, b \in\{1,2,3\}\) and the equation \(a x^{2}+b x+1=0\) has real roots, then

If \(\cot \frac{2 x}{3}+\tan \frac{x}{3}=\operatorname{cosec} \frac{k x}{3},\) then the value of \(k\) is

Which of the following is correct?

In aluminium extraction by the Bayer process, alumina is extracted from bauxite by sodium hydroxide at high temperature and pressures :
\(\mathrm{Al}_2 \mathrm{O}_3(\mathrm{~s})+2 \mathrm{OH}^{-}(\mathrm{aq}) \rightarrow 2 \mathrm{Al}_2 \mathrm{O}_2(\mathrm{aq})+\mathrm{H}_2 \mathrm{O}(1)\)

Solid impurities such as \(\mathrm{Fe}_2 \mathrm{O}_3\) and \(\mathrm{SiO}_2\) are removed and then \(\mathrm{Al}(\mathrm{OH})_4^{-}\)is reprecipitated : \(2 \mathrm{Al}(\mathrm{OH})_4^{-} \rightarrow \mathrm{Al}_2 \mathrm{O}_3 \cdot 3 \mathrm{H}_2 \mathrm{O}(\mathrm{s})+2 \mathrm{OH}^{-}\)(aq) . In the industrial world :

If the pressure, temperature and density of an ideal gas are denoted by \(p, T\) and \(\rho\), respectively, the velocity of sound in the gas is

Which of the following orbitals will have zero probability of finding the electron in the yz plane ?

A very long charged solid cylinder of radius 'a' contains a uniform charge density \(\rho\). Dielectric constant of the material of the cylinder is \(\mathrm{k}\). What will be the magnitude of electric field at a radial distance ' \(x^{\prime}(x < a)\) from the axis of the cylinder?

Let \(f: R \rightarrow R\) be such that \(f\) is injective and \(f(x) f(y)=f(x+y) \quad\) for \(\quad\) all \(\quad x, y \in R, \quad\) if \(f(x), f(y)\) and \(f(z)\) are in \(G P,\) then \(x, y\) and \(z\) are in