Mr. X wishes to purchase a flat for Rs. 44, 60, 800 with a down payment of Rs. 10,00,000 and the balance in equal monthly instalments (EMI) for 20 years. If the bank charges 7.5% per annum compounded monthly, then the EMI is :
[Given that \((1.00625)^{240}=4.4608\) ]

A die is thrown twice and the sum of the numbers appearing is observed to be 6 .
The probability that the number 4 has appeared at least once is:

The function \(f(x)=|x-1|, x \in R\) is:

The maximum slope of the curve \(y=-x^3+3 x^2+9 x-27\) is:

Interval in which the function \(f\) given by \(f(x)=\tan x-4 x, x \in\left(0, \frac{\pi}{2}\right)\) is strictly decreasing is

If \(A=\left[\begin{array}{ccc}2 & 0 & 3 \\ -1 & 1 & 3 \\ 0 & -4 & 0\end{array}\right]\), then the value of \(\operatorname{det}(2 A)\) is

Let \(f: R -\left\{\frac{3}{5}\right\} \rightarrow R\) be defined by \(f(x)=\frac{3 x+2}{5 x-3}\), then

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

A plane wave is incident on a concave mirror of radius R. The shape of the reflected wavefront will be

Read the passage carefully and answer the questions given along
Our immune system plays the major role in preventing diseases when we are exposed to disease-causing agents. Immunity is of two types: (i) Innate immunity and (ii) Acquired immunity. The human immune system consists of lymphoid organs, tissues, cells and soluble molecules like antibodies. The immune system also plays an important role in allergic reactions, auto-immune diseases and organ transplantation. The primary lymphoid organs are bone marrow and thymus. The secondary lymphoid organs are spleen, lymph nodes, tonsils, Peyer's patches of small intestine and appendix. There is lymphoid tissue also located within the lining of the major tracts (respiratory, digestive and urogenital tracts) called mucosa associated lymphoid tissue (MALT). It is important to note that HIV/AIDS is not spread by mere touch or physical contact; it spreads only through body fluids. AIDS has no cure, prevention is the best option. Adolescence is accompanied by several biological and behavioural changes and surveys and statistics show that use of drugs and alcohol has been on the rise especially among the youth. Factors associated with drug and alcohol abuse among adolescents are a child's natural curiosity, stress, the perception among youth that it is 'cool' or progressive to smoke, media exposure and an unstable or unsupportive family structures and peer pressure. It is best to identify the situations that may push an adolescent towards use of drugs or alcohol, and to take remedial measures well in time.
Which one of the following structures is not an example of a cellular barrier in innate immunity?

Transmission of HIV-Infection occurs by-
(A). Using infected needles by the health staff or by drug abusers
(B). Transfusion of contaminated blood and blood product
(C). Sexual contact with infected person
(D). Sharing food and sanitation facilities
Choose the correct answer from the options given below:

If h is the Planck's constant, then the momentum of the photon having frequency \(v\) is represented by

The maximum value of \(\left( \frac{1}{x} \right)^x\) is :