If \(P, Q\) and \(R\) are three singular matrices given by
\(P=\left[\begin{array}{cc}2 & 3 a \\4 & 3\end{array}\right], Q=\left[\begin{array}{cc}b & 5 \\2 a & 6\end{array}\right]\)
and \(R=\left[\begin{array}{cc}a^2+b^2-c & 1-c \\ c+1 & c\end{array}\right]\), then the value of \((2 a+6 b+17 c)\) is:

The probability of a shooter hitting a target is \(\frac{2}{3}\)
Minimum how many number of times must the shooter fire so that the probability of hitting the target at least once is more than 0.98.

\(\int \frac{d x}{1+\tan x}\) is equal to:

500 g of jaggery syrup has 30% jaggery in it.
The quantity of jaggery that should be added to make it 50% of syrup is:

If \(\sin ^{-1} x+\sin ^{-1} y=\frac{2 \pi}{3}\), then the value of \(\cos ^{-1} x+\cos ^{-1} y\) is:

If A and B square matrices of order 3 such that |A|= -1, |B|= 5, then the value of |2AB| is:

The area of the triangle with vertices \((1,4),(2,7)\) and \((4,13)\) is:

(A) f(x) = |x| is continuous function on R (the set of real numbers)
(B) f(x) = [x] is continuous function on R
(C) f(x) = sin x is continuous function on R
(D) f(x) = tanx is continuous function on R
(E) f(x) = sinx + cosx is continuous function on R

The differentiation of \(\frac{x^3}{1-x^3}\) w.r.t. \(x^3\) is:

p-block elements are placed in groups 13 to 18 of the periodic table. Group 15 is nitrogen family.
Nitrogen makes various compounds like \(NH _3, HNO _3, N_2 O , NO _2\) etc. Phosphorus exists in the form of white and red phosphorus. White phosphorus glows in dark. \(PH _3\) gas is used as smoke screen. Group 16 is called oxygen family. Dry air contains \(21% O_2\) gas by volume. Combined sulphur exists as sulphates such as gypsum, epsome salt, baryte etc. The allotropic forms of sulphur are Rhombic and monoclinic sulphur. \(S_2\) is paramagnetic like \(O_2\) and it stable at high temperature. Group 17 is Halogen family. \(F _2\) is highly reactive, \(Cl _2\) is greenish yellow gas. Both \(SO _2\) and \(Cl _2\) are used for bleaching. Group 18 is Noble gas family but some noble gases also form compounds.
Complete hydrolysis of \(XeF _6\) gives HF and \(XeO _3\) as main products. The permanent bleaching effect is caused by :

Read the following paragraph carefully and answer the given questions.
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. For determining the cause of allergy, the patient is exposed to or injected with very small doses of possible allergens, and the reactions studied. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Heroin, commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. This is obtained by acetylation of morphine. 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. 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.
Malignant malaria is caused by -

Water soluble vitamins are excreted out of our body through urination. Identify the vitamin which is stored in our body for a number of years?

Let \(A\) be any square matrix of order 3 and \(B=\left[\begin{array}{ccc}0 & -4 & 2 \\ 4 & 0 & 3 \\ -2 & -3 & 0\end{array}\right]\).Then the matrix \(A B A^T\) is a: