The function \(f(x)=\frac{x}{(x-2)(x-3)(x-5)}, x \in R\) is :

The equation of motion of a missile is x = 3t, y = -4t, z = t where time 't' is in seconds and the distance is measured in kilometres.
If the position of rocket at a certain instant of time is (5, -8, 10), then what will be the height of the rocket from the ground? (Ground is considered as xy plane)

Let \(\vec{a}\) and \(\vec{b}\) be unit vectors. If \(\sqrt{3} \vec{a}-\vec{b}\) is a unit vector, then the angle between \(\vec{a}\) and \(\vec{b}\) is

The solution of \(y^{\prime}-y^{\prime \prime}=2 x\) is:
A. \(y=x^2+2 x+2\)
B. \(y=x^2+2 x+1\)
C. \(y=x+2\)
D. \(y=x^2-2 x+1\)
Choose the correct answer from the options given below :

A player participates in 3 matches against three teams \(T_1, T_2\) and \(T_3\). The probability of winning a match against teams \(T_1, T_2\) and \(T_3\) are \(0.2,0.3\) and 0.9 respectively. If 'wins' can be regarded as independent events, then the probability that he
(A) wins all the 3 matches is 0.054
(B) wins no match is 0.054
(C) wins exactly two matches is 0.348
(D) wins exactly one match is 0.542
Choose the correct answer from the options given below :

The probability distribution of a random variable X is given by

X	0	1	2
P(X)	k	2k	3k

If \(k>0\), then \(P(0 < X \leq 2)\) is equal to

Which of the following is a vertex of the positive region bounded by the inequalities:
\(4 x+y \geq 80 ; \quad 2 x+y \geq 60 ; \quad x, y \geq 0\)

A solenoid with \(2\times 10^4\) turns per meter, diameter 0.1 m, has a coil of 100 turns and 0.01 m radius placed inside. If solenoid current decreases from 4 A to 0 in 0.05 s, total charge through coil is :

For the protection from herbivore animals, the plant Calotropis secretes the highly poisonous compound known as -

Reproductive capacity of a flowering plant can be appreciated by finding out the:
(A) Size of the embryo sac in the ovule
(B) Number of eggs in the embryo sac
(C) Size of eggs in the embryo sac
(D) Number of ovules in the ovary
Choose the most appropriate answer from the options given below:

The magnetic field at a distance r from a long wire carrying current I is 0.4 T. The magnetic field at a distance 2r from the wire is

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.
Which of the following cells are involved in phagocytosis and destruction of microbes?

Which one of the following is NOT a method of molecular diagnosis for early detection of a disease?