If A is any non-zero square matrix, then the matrix \(P=\frac{1}{2}\left(A-A^T\right)\) is:

Which of the following statements are correct in reference to the linear programming problem (LPP):
Maximize \(Z =5 x +2 y, Z =5 x +2 y, Z =5 x +2 y\)
subject to the following constraints
\(3 x+5 y \leq 15,5 x+2 y \leq 10, x \geq 0, y \geq 0\)
(A) The LPP has a unique optimal solution at \((2,0)\) only.
(B) The feasible region is bounded with corner points \((0,0),(2,0),(20 / 19,45 / 19)\) and \((0,3)\).
(C) The optimal value is unique, but there are an infinite number of optimal solutions.
(D) The feasible region is unbounded.
Choose the correct answer from the options given below:

If \(f(x)=3 x^2+10 x-5\), then by using the concept of differentials, the approximate value of \(f(2.03)\) is :

If the area above x - axis, bounded by the curves \((y = 3^{\beta x}), \; x = 0\) and \(x = 3\) is \(\frac{(26)}{\log(e)} 3\), then the value of \(\beta\) is:

Let \(y(x)=a(x+1) \log (x+1)+b x+5\) be the solution of the differential equation \(e^{\frac{d y}{d x}}=x+1, y(0)=5\), then the value of \((a+b)\) is :

The equation of trend line for five years (2004-2008) for the profit of a company is \(y_t=150+8 x\)The predicted profit for the year 2011 is:

The value of the determinant \(\left|\begin{array}{ccc}\cos ^2 \theta & \cos \theta \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right|\) is equal to

A wire of resistance \( 5 \, \Omega \) is drawn out so that its length is increased to thrice its original length. The new resistance would be :

An atom has a positively charged point nucleus of charge Ze surrounded by a uniform density of negative charge up to a radius R. The atom is taken as neutral. The electric field at a distance r < R from the nucleus is given by:

Various types of skin colour in humans is an example of :

Observe the table and answer the given question :

Identify the amino acids with one codon each?

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?

To demonstrate the phenomenon of interference, we require two sources, which emit radiation of