The feasible region of a linear programming problem is bounded. The corresponding objective function is \(Z = 3x - 4y\). The objective function attains:

The system of linear equations \(k x+5 y=5,2 x+3 y=5\) will be consistent if

Let \(\left|\begin{array}{cc}x & 2 \\ 18 & x\end{array}\right|=\left|\begin{array}{ll}-4 & -2 \\ -8 &-4\end{array}\right|\). Then :
(A) \(x=-4\)
(B) \(x=-6\)
(C) \(x=4\)
(D) \(x=6\)
Choose the correct answer from the options given below :

Match List-I with List-II

List - I	List - II
(A) \(\sin ^{-1}(-1)\)	(I) \(\frac{5 \pi}{6}\)
(B) \(\cot ^{-1}(-1)\)	(II) \(-\frac{\pi}{2}\)
(C) \(\sec ^{-1}\left(-\frac{2}{\sqrt{3}}\right)\)	(III) \(\frac{\pi}{4}\)
(D) \(\tan ^{-1}(1)\)	(IV) \(\frac{3 \pi}{4}\)

Choose the correct answer from the options given below :

If z = 5x + 8y is the objective function of a LPP and (0,0), (3, 1), (2, 4), (0, 3), (5,0) are corner points of the bounded feasible region, then the maximum value of the objective function is

A function \(f: R \rightarrow R\) defined by \(f(x)=\frac{x}{x^2+1}\) is (where \(R\) is the set of real numbers) :

Two large plane parallel sheets with equal but opposite surface charge densities \(+\sigma\) and \(-\sigma\). A point charge q placed at points P1, P2, and P3 experiences forces F1, F2, and F3 respectively. Then :

Read the passage carefully and answer the questions
Many halogen containing organic compounds are present in nature and some of them are clinically useful. These classes of organic compounds find a wide range of applications in our daily life as well as in industries. Many of the polyhalogen compounds are useful too in agriculture. However, some of these compounds cannot be easily decomposed and are thus considered to be environmental hazards. These halo compounds are prepared via different synthetic routes where a variety of organic compounds can be used as substrates such as amines, hydrocarbons etc. They are used as solvents for relatively non-polar compounds. These compounds exhibit substitution and elimination reactions, in addition to their reactions with different metals, which leads to the formation of a versatile starting material for others organic compounds.
Alkyl halides react with sodium in dry ether and give hydrocarbon containing double the number of carbon atom present in the halides. The reaction is known as:

Down's syndrome is caused by:

At certain places on earth, the angle of dip is \( 30^\circ \). If horizontal component of earth's magnetic field is H, then the total intensity of earth's magnetic field will be :

Read the passage carefully and answer the questions based on the passage:
Species diversity on earth is not uniformly distributed. It is generally highest in the tropics and decreases towards the poles. Earth's fossil history reveals the incidences of mass extinctions in the past. Earth's rich biodiversity is vital for the very survival of mankind. It is believed that communities with high diversity tend to be less variable and more productive. The reasons of conserving biodiversity are narrowly utilitarian, broadly utilitarian and ethical. Biodiversity conservation may be in-situ as well as ex-situ.
Which one of the following does not exhibit narrowly utilitarian argument for conserving biodiversity?

A pipe can fill a tank in 2 hours. Because of a leak in the tank, the pipe takes 2 hours 40 minutes to fill the tank. The time the leakage takes to empty the full tank is :

The water and milk in two vessels are in the ratio 1:1 and 3: 8 respectively. In what ratio, the mixtures in the vessels be mixed to obtain a new mixture containing water and milk in the ratio 4 : 7?