A man wishes to ensure that he gets Rs. 75,000/- at the end of each year indefinitely. The amount that he invest now to produce the desired cash flow, if money is worth 2.5% compounded annually is:

The least non-negative remainder, when \(5^{61}\) is divided by 7 , is

If \(\left|\begin{array}{ccc}-a^2 & a b & a c \\ a b & -b^2 & b c \\ a c & b c & -c^2\end{array}\right|=\lambda a^2 b^2 c^2\), then the value of \(\lambda\) is:

For the system of equations \(A X=B\), which of the following is correct?

Identify the equations of lines through origin which intersect the line \(\frac{x-3}{2}=\frac{y-3}{2}=\frac{z}{1}\) at an angle \(\frac{\pi}{3}\).
(A) \(\frac{x}{1}=\frac{y}{2}=\frac{z}{-1}\)
(B) \(\frac{x}{1}=\frac{y}{-2}=\frac{z}{1}\)
(C) \(\frac{x}{-1}=\frac{y}{-1}=\frac{z}{-2}\)
(D) \(\frac{x}{-1}=\frac{y}{1}=\frac{z}{-2}\)
Choose the correct answer from the options given below:

For the curve xy = 6, the value of \(\frac{d^2 y}{d x^2}\) at y = 3 is:

In a meeting, 70% of the members favour and 30% oppose a certain proposal.
A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour.
Then, E(X) is:

While charging the lead storage battery......

Which of the following statement is correct about the half life period?
A. It is proportional to initial concentration of zero order reaction.
B. Half life period can be used to determine the order of the reaction.
C. Half life period for lst order reaction is independent of concentration.
D. Catalyst does not affect half life time period.

Choose the correct statement from the following:

In a moving coil galvanometer, the coil is wound over a metallic frame in order to

Large Identify "Y" in the following reaction:
\(R-Mg-X+CO_2 \xrightarrow{\text { Dry ether }} X \xrightarrow{H_3 O^{+}} Y\)
The options for \(Y\) are:

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 -