For a manufacturer, total cost function is given by \(C=\frac{x^2}{25}+2 x\). Which of the following are correct ?
A. 2.6 is the marginal cost when 5 units are produced.
B. \(\frac{2 x}{25}+2\) is the marginal cost function.
C. \(\frac{x}{25}+2\) is the average cost function.
D. 2.4 is the marginal cost when 5 units are produced.
E. \(\frac{x}{25}+1\) is the average cost function.
Choose the correct answer from the options given below:

\(y=e^{x+e^{\infty+e^{x+\cdots \infty}}}\) then \(\frac{d y}{d x}=\) ______________

A card is picked at random from a pack of 52 playing cards. Given that the picked card is a queen, the probability of this card to be a card of spade is:

If \(\left|\begin{array}{cc}3 x & 4 \\ 7 & x\end{array}\right|=\left|\begin{array}{ll}6 & 3 \\ 2 & 1\end{array}\right|\) then :

The area (in square units) bounded by the curve \(y=\cos x\) between \(x=0\) and \(x=2 \pi\) in first quadrant is equal to :

The corner points of the feasible region of the LPP: Minimize \(Z=-50 x+20 y\) subject to
\(2 x-y \geq-5,3 x+y \geq 3,2 x-3 y \leq 12\) and \(x, y \geq 0\) are:

The value of \(\int_{-5}^5|x+3|\) \(dx\) is

If \(\hat{a}, \hat{b}\) and \(\hat{c}\) are three units vectors and \(\hat{a}+\hat{b}+\hat{c}=\overrightarrow{0}\), then the angle between \(\hat{a}\) and ( \(-\hat{b}\) ) is

The relation below correctly represents the frequency of light emitted when an electron in a hydrogen atom jumps from a higher \( (n_i) \) energy level to \( (n_f) \) a lower energy level: \( \nu = Rc \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) \). Predict the values of \( n_i, n_f \), respectively for the Paschen series, which will give the highest wavelength in the series

The rate of biomass production is expressed in terms of __________ to compare the productivity of different ecosystems.

If \(A=\left[a_{i j}\right]_{3 \times 3}\), where \(a_{i j}=\frac{(-1)^{i+j}-1, i=j}{(-1)^{i+j}, i \neq j}\) then the value of \(A+A^T\) is:

Match List-I with List-II

List-I (Types of solutions)	List-II (Examples)
(A) Gas in Gas solution	(I) Oxygen dissolved in water
(B) Gas in Liquid solution	(II) Copper dissolved in gold
(C) Liquid in Solid solution	(III) Mixture of oxygen and nitrogen gases
(D) Solid in Solid solution	(IV) Amalgam of mercury with sodium

Choose the correct answer from the options given below:

Read the given passage carefully and answer the questions
Salmonella typhi is a pathogenic bacterium which causes typhoid fever in human beings. Sustained high fever (39° to 40°C), weakness, stomach pain, constipation, headache and loss of appetite are some of the common symptoms of this disease. Typhoid fever could be confirmed by Widal test. Plasmodium enters the human body as sporozoites. The parasites initially multiply within the liver cells and then attack the red blood cells (RBCs) resulting in their rupture. The rupture of RBCs is associated with release of a toxic substance, haemozoin, which is responsible for the chill and high fever recurring every three to four days. There is lymphoid tissue also located within the lining of the major tracts (respiratory, digestive and urogenital tracts) called mucosa-associated lymphoid tissue (MALT). In our body, cell growth and differentiation is highly controlled and regulated. In cancer cells, there is breakdown of regulatory mechanisms. Normal cells show a property called contact inhibition by virtue of which contact with other cells inhibits their uncontrolled growth. Cancerous cells just continue to divide giving rise to masses of cells called tumors. Tumors are of two types: benign and malignant. Cannabinoids are a group of chemicals, which interact with cannabinoid receptors present principally in the brain. Generally taken by inhalation and oral ingestion, these are known for their effects on cardiovascular system of the body.
Which one of the following statements is not true?