On a multiple choice examination with 4 possible answers (out of which one is correct)
for each of the five questions, the probability that a candidatewould get 4 or more correct answers just by guessing is:

The radius of a spherical ball is increasing at the rate of 1 m/sec. At the radius equal to 3m, the volume of the ball is increasing at the rate given by :

If \(\int_0^1\left(3 x^2+2 x+5 k\right) d x=0\), then the value of \(k\) is:

The number of letters posted in a certain city on each day for a week is given as follows : 40, 55, 28, 25, 31, 52, 43
Which of the following is NOT an entry in the three-day moving averages?

The function \(f(x)=\left\{\begin{array}{ll}\frac{x^2+2 x-3}{x-1}, & \text { if } x \neq 1 \\ 0, & \text { if } x=1\end{array}\right.\) is

The function \(f(x)=x^3+1\) is:

Let \(x\) denote the number of doublets in three throws of a pair of dice with the following probability distribution.

\(x\)	\(0\)	1	2	3
\(P(x)\)	\(\frac{25}{72} k\)	\(\frac{15}{72} k\)	\(\frac{3}{72} k\)	\(\frac{1}{360} k\)

If value of \(k\) is equal to \(\frac{m}{n}, \operatorname{gcd}(m, n)=1\), then \(m+n\) is equal to

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.
Heroin, commonly called smack is chemically _________ which is a white, odourless, bitter crystalline compound.

A heater coil is rated 100 W, 200 V. It is cut into two identical parts. Both parts are connected together in parallel to the same source of 200 V. The energy liberated per second in the new combination is:

Which one of the following infections is completely curable?

If a person \(A\) speaks the truth in \(80 \%\) cases and the person \(B\) speaks the truth in \(75 \%\) cases, then the probability that they contradict each other in a statement is:

A magnet of magnetic moment \( 50 \hat{i} \text{ A m}^2 \) is placed along the X-axis in a magnetic field \( \vec{B} = (0.5 \hat{i} + 3.0 \hat{j}) \text{ T} \). The torque acting on it is

Match List-I with List-II

List-I	List-II
(A) Gyromagnetic ratio	(I) \( 4 \times 10^{-5} \text{ T} \)
(B) Permeability of free space	(II) \( 9.27 \times 10^{-24} \text{ Am}^2 \)
(C) Earth's magnetic field at equator	(III) \( 8.8 \times 10^{10} \text{ C/kg} \)
(D) Bohr magneton	(IV) \( 12.56 \times 10^{-7} \text{ TmA}^{-1} \)

Choose the correct answer from the options given below: