If \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0\) then
\(\left|\begin{array}{ccc}1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c\end{array}\right|\) is equal to :

The value of the definite integral \(I=\int_0^2 x \sqrt{2-x} d x\) is :

Which of the following statements are correct?
(A) Direction ratios of the line \(\frac{x-1}{2}=\frac{y+2}{3}=\frac{z-3}{4}\) are 2, 3, 4
(B) Direction ratios of the line \(\frac{x-1}{2}=\frac{2-y}{7}=\frac{2 z-1}{6}\) are 2, -7, 3
(C) Direction cosines of z axis are 0, 1, 0
(D) Direction ratios of the line joining the point (1, 2, -3) and (4, 5, 6) are 1, 1, 3
(E) Direction cosines of a line which makes equal angles with the coordinate axes are \(\frac{1}{3}, \frac{-1}{3}, \frac{1}{3}\)
Choose the correct answer from the options given below:

\(\tan ^{-1} \frac{1}{\sqrt{3}}-\sin ^{-1} \frac{1}{2}\) is equal to :

If \(f(x) = \begin{cases} \frac{\sqrt{4+x}-2}{x}, & \text{if } x \neq 0 \\ k, & \text{if } x = 0 \end{cases}\) is continuous at \(x = 0\), then the value of k is:

The area enclosed by the curves \(x y=4, y=x, x=e^2\) and the \(x\)-axis, is :

The area bounded by the curve \(y=x|x|, x\)-axis and the ordinates \(x=-1\) and \(x=1\) is given by:

When a steady current flows in a metalic conductor of non-uniform cross section. Which of these quantities is constant along the conductor?
A. Current
B. Electric field
C. Drift speed
D. Current density
E. Potential gradient
Choose the correct answer from the options given below:

If \(A=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\), then \(A^2=\)

For an AC circuit, a phase diagram shows emf on X-axis, and current I is at angle \( \theta \) to emf. Angle \( \theta \) is phase angle between emf and current. Current I is resolved into two components, \( I \cos \theta \) is along emf on X-axis. \( I \sin \theta \) is along perpendicular direction to emf.
(A) Component \( I \cos \theta \) will draw the power from the source
(B) Component \( I \sin \theta \) will draw the power from the source
(C) \( I \cos \theta \) is called the powerless current
(D) \( I \sin \theta \) is called the powerless current
Choose the correct answer from the options given below:

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.
Malignant malaria is caused by -

The mean of the number of heads in the two tosses of a coin is

Which of the following will have 46 chromosomes?