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 of the region bounded by \(y^2=2 x+1\) and x - y = 1 is:

If the corner points of the bounded feasible region of an LPP with objective function maximize \(Z=2 x+3 y\) are \((0,0),(1,2)\) and \((1,1)\), then its optimal value is

The corner points of the bounded feasible region determined by the system of linear constraints are \((0,0),(5,0),(3,4)\) and \((0,5)\). Let \(Z=p x+q y\) where \(p, q>0\). Condition on \(p\) and \(q\) so that the maximum of \(Z\) occurs at both \((5,0)\) and \((3,4)\) is

If \(f(x)=\left\{\begin{array}{ll}\frac{\tan \left(\frac{\pi}{4}-x\right)}{\cot 2 x}, & x \neq \frac{\pi}{4} \\ K, & x=\frac{\pi}{4}\end{array}\right.\) is continuous at \(x=\frac{\pi}{4}\), then the value of \(K\) is :

A bag contains 12 white and 18 red balls. Two balls are drawn in succession without replacement. The probability that the first is red and the second is white is:

For the system \(\left[\begin{array}{cc}2 & -3 \\ -4 & 6\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}5 \\ -10\end{array}\right]\), which of the following statements are correct?
(A) The system has no solution.
(B) The system is consistent.
(C) It has infinitely many solutions.
(D) It has a unique solution.
Choose the correct answer from the options given below :

The equipotential surfaces due to an isolated point charge \( q < 0 \) are:

Two identical metal balls, A and B, with similar charges Q are suspended with insulating threads. They repel each other with a force F. Another identical uncharged metal ball C is first touched with metal ball A and then touched with metal ball B and finally removed. The new force of repulsion between A and B will be

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:

Pipe A can fill a tank in 24 hours and pipe B in 32 hours. If both the pipes are opened in an empty tank at the same time, then the time taken to fill the tank is:

Read the following paragraph and answer the given questions.
Cancer detection is based on biopsy and histopathological studies. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Do you know why mother's milk is considered very essential for the new-born infant? The yellowish fluid colostrum secreted by mother during the initial days of lactation has abundant antibodies (IgA) to protect the infant. 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. The exaggerated response of the immune system to certain antigens present in the environment is called allergy. 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. Morphine is a very effective sedative and painkiller, and is very useful in patients who have undergone surgery.
Which one of the following is not used for detection of cancer?

Which is not an example of broadly utilitarian concept of biodiversity conservation?