The feasible region represented by the constraints \(x+y \leq 50,3 x+y \leq 90, x \geq 0, y \geq 0\) of an LPP is

Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively.
Both pipes A and B are opened together for some time and then pipe B is turned off.
If the tank is filled in 15 minutes, then after how many minutes is pipe B turned off?

Which of the following functions from Z to Z are bijections ? (where Z is the set of integers)

The relation \(R=\{(a, b):\) both \(a\) and \(b\) are either odd or even \(\}\) on the set \(\{1,2,4,5,7,8\}\) is

A person can sell a maximum of 20 units of shirts and pants on which a profit of ₹40 is made on each shirt and a of ₹30 on each pant. A minimum of 2 shirts are being sold, while pants are sold at least 4 times as many as shirts the maximum profit is:

Let \(\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=-\hat{i}+2 \hat{j}+\hat{k}, \vec{c}=3 \hat{i}+\hat{j}\) be three vectors. If \((\vec{a}+\lambda \vec{b})\) is perpendicular to \(\vec{c}\), then the value of \(\lambda\) is

Value of \(\int_2^3 \frac{\sqrt{x}}{\sqrt{x}+\sqrt{5-x}} d x\) is

A 12 V battery is connected to a \( 6 \text{ } \Omega, 10 \text{ H} \) coil, through a closed switch. The switch is suddenly opened in 1 ms. The average induced emf across the coil will be

Read the following passage carefully and answer the given questions.
Plasmodium, a tiny protozoan is responsible for the disease malaria. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. Innate immunity consist of four types of barriers. These are – (i) Physical barriers- skin on our body is the main barrier which prevents entry of the micro-organisms. (ii) Physiological barriers- Acid in the stomach, saliva in the mouth, tears from eyes-all prevent microbial growth. (iii) Cellular barriers- Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. (iv) Cytokine barriers- virus-infected cells secrete proteins called interferons which protect non-infected cells from further viral infection. Allergy is due to the release of chemicals like histamine and serotonin from the mast cells. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused.
Malignant malaria is caused by _____ is the most serious one and can even be fatal.

Read the passage carefully and answer the questions.
Electrochemistry is the study involving two types of processes. One type involves the production of electricity from the energy released during a spontaneous chemical reaction. Galvanic cells like Daniel cells are used to produce electricity from the redox reaction. Nernst equation of a galvanic cell gives the relation between the standard cell potential and the concentration of the species involved in the redox reaction. The second type of study involves the cells in which electrical energy is used to bring about the chemical reactions in a non-spontaneous process. The conductance of electrolytic solution depends on many factors including the nature of the electrolyte and the dimensions of the electrolytic cell.
Faraday's laws of electrolysis are related to:

Which of the following is/are NOT the way(s) to introduce alien DNA into the host cell?
(A) Using vectors like Agrobacterium tumifaciens
(B) Injecting directly into the nucleus of animal cell
(C) Using ethylene dibromide
(D) Using vectors like retroviruses
(E) Using biolistics or gene gun
Choose the correct answer from the options given below:

Which of the following organisms occupy the first trophic level in an ecosystem?

The transfer of pollen grains from one plant to the stigma of a different plant is known as: