Mathematics Tes...

The approximate value of square root of 25.2 is

If one root of the quadratic equation \(a x^{2}+b x+c=0\) is equal to the \(n^{\text {th }}\) power of the other root, then the value of \(\left(a c^{n}\right)^{\frac{1}{n+1}}+\left(a^{n} c\right)^{\frac{1}{n+1}}\)

If \(3 \sin ^{-1} \frac{2 x}{1+x^{2}}-4 \cos ^{-1} \frac{1-x^{2}}{1+x^{2}}+2 \tan ^{-1} \frac{2 x}{1+x^{2}}=\frac{\pi}{3}\) then \(x=\)

If \(\lim _{x \rightarrow 0}(1+a \sin x)^{\text {cosec x}}=3,\) then a is

If the tangent to the curve \(\sqrt{x}+\sqrt{y}=\sqrt{a}\) at any point on it cuts the axes OX and OY at P and Q respectivelv. then \(\mathrm{OP}+\mathrm{OQ}\) is

\(\sin \left(\frac{1}{2} \cos ^{-1} \frac{4}{5}\right)=\)

With reference to a universal set, the inclusion of a subset in another, is relation, which is

The value of \(\sqrt{\left(\log _{0.5}^{2} 4\right)}\) is

Let \(g(x)\) be an antiderivative for \(f(x) .\) Then \(\ln \left(1+(g(x))^{2}\right)\) is an antiderivate for