The region represented by the constraints \(x \geq 0, y \geq 0\) of an LPP is

The values of \(\lambda\) for which the system of equation \(x+2 y+z=14,-x+y+z=10, x+\lambda y+z=2\) has unique solution is :

The nearest integral value of the shaded area shown below is :

A 50 Hz AC current of crest 1 A flows through a transformer primary. With mutual inductance \(0 . 5 ~ H\), the crest voltage induced in secondary is :

If a line makes angles \(\alpha, \beta, \gamma\) with the positive directions of \(x\)-axis, \(y\)-axis and \(z\)-axis respectively, then \(\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma\) is equal to:

The points on the curve \(\frac{x^2}{9} + \frac{y^2}{16} = 1\) at which the tangents are parallel to x-axis :

The increase in the sale of shawls during winters is an example of :

According to Gause's Competitive Exclusion Principle:

An electron is accelerated through a potential difference of \( V = 36 \text{ V} \). The de-Broglie wavelength associated with it will be

The total cost function is given by \(C(x)=\frac{1}{3} x^3-5 x^2+30 x-15\) and selling price per unit is Rs. 6. The profit is maximum if the value of x is:

The refractive index of the material of an equilateral prism is \(\sqrt{2}\). The angle of minimum deviation of that prism is :

The half life of decaying \({ }^{14} C\) is 6000 years approximately. How much time is needed to decaying \(80 \%\) of \({ }^{14} C ?[\log 5=0.6990]\)

"Choose the reactions given by \(\text{Cr}_2\text{O}_7^{2-}\)
(A)\(\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6\text{Fe}^{2+} \rightarrow 2\text{Cr}^{3+} + 6\text{Fe}^{3+} + 7\text{H}_2\text{O}\)
(B) \(\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 3\text{H}_2\text{S} \rightarrow 2\text{Cr}^{3+} + 3\text{SO}_4^{2-} + 7\text{H}_2\text{O}\)
(C) \(\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 3\text{Sn}^{2+} \rightarrow 2\text{Cr}^{3+} + 3\text{Sn}^{4+} + 7\text{H}_2\text{O}\)
(D) \(\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ \rightarrow 3\text{Cr}^{3+} + 2\text{H}_2\text{O}\)
(E) \(\text{Cr}_2\text{O}_7^{2-} + 2\text{OH}^- \rightarrow 2\text{CrO}_4^{2-} + \text{H}_2\text{O}\)
Choose the correct answer from the options given below:"