Let \(A=\{x \in R, x \neq 0,-4 \leq x \leq 4\} \quad\) and \(f: A \rightarrow R\) defined by \(f(x)=\frac{|x|}{x}\) for \(x \in A\). Then, the range of \(f\) is

\(A\left(x_1, y_1\right)\) is the internal centre of similitude and \(\mathrm{B}\left(x_2, y_2\right)\) is the external centre of similitude of two circles \(C_1\) and \(C_2\) whose centres are \(\mathrm{P}(\alpha, \beta)\) and \(\mathrm{Q}(\gamma, \delta)\) respectively. If \(\mathrm{PA}=3, \mathrm{AB}=5, \mathrm{QB}=2\), then ratio of the radii of the two circles is

If \(\alpha, \beta, \gamma, \delta\) are the roots of the equation \(x^4-8 x^3+11 x^2+32 x-60=0\) and \(\alpha < \beta < \gamma < \delta\), then \(4 \alpha+3 \beta+2 \gamma+\delta=\)

The correct match is

For \(h, k \in N\), let \(\mathrm{P}(h, k)\) be the point of intersection of the curves \(x^2 y-x^3=8\) and \(y^3-x y^2=32\). If \(\theta\) is the acute angle between these two curves at \(P, \operatorname{then} \tan \theta=\)

If \(\lim _{x \rightarrow 0} \frac{3^{x^3}-\left(1-x^3\right)^{2 / 3}}{x^2 \sin x}=p+\log q\) then \(p q=\)

If \(\ell, \mathrm{m}, \mathrm{n}\) and \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are direction cosines of two lines then

If the equilibrium constant for the reaction, \(\mathrm{H}_2(g)+\mathrm{I}_2(g) \rightleftharpoons 2 \mathrm{HI}(g) \text { is } K\) what is the equilibrium constant of \(\mathrm{HI}(g) \rightleftharpoons \frac{1}{2} \mathrm{H}_2(g)+\frac{1}{2} \mathrm{I}_2(g) ?\)

Number of bonding electron pairs and number of lone pairs of electrons in \(\mathrm{ClF}_3, \mathrm{SF}_4, \mathrm{BrF}_5\) respectively are

Sulphur on boiling with \(\mathrm{NaOH}\) solution forms

Consider the following statements \(A\) and \(B\). Identify the correct choice in the given answer. A. \(p-n, p-p\) and \(n-n\) forces between nucleons are not equal and charge dependent. B. In nuclear reactor the fission reaction will be in accelerating state if the value of neutron reproduction factor \(A>1\).

The standard reduction potentials of \(\mathrm{Zn}^{2+}\left|\mathrm{Zn}, \mathrm{Cu}^{2+}\right| \mathrm{Cu}\) and \(\mathrm{Ag}^{+} \mid \mathrm{Cu}\) and \(\mathrm{Ag}^{+} \mid \mathrm{Ag}\) are respectively \(-0.76,0.34\) and \(0.8 \mathrm{~V}\). The following cells were constructed : (1) \(\mathrm{Zn}\left|\mathrm{Zn}^{2+}\right|\left|\mathrm{Cu}^{2+}\right| \mathrm{Cu}\) (2) \(\mathrm{Zn}\left|\mathrm{Zn}^{2+}\right|\left|\mathrm{Ag}^{+}\right| \mathrm{Ag}\) (3) \(\mathrm{Cu}\left|\mathrm{Cu}^{2+} \| \mathrm{Ag}^{+}\right| \mathrm{Ag}\) What is the correct order of \(E_{\text {cell }}^{\circ}\) of these cells?

The mean deviation from the mean for the observations \(1,3,5,7,11,13,17,19,23\) is