A person wishes to purchase a house for ₹ \(39,65,000\) with a down payment of ₹ \(5,00,000\) and balance in equal monthly installments (EMI) for 25 years.
If bank charges \(6 \%\) per annum compounded monthly, then EMI on reducing balance payment method is:
[Given \((1.005)^{300}=4.465\) ]

If the matrix \(A=\left[\begin{array}{cc}2-x & 3 \\ 2 & 1-x\end{array}\right]\) is singular, then value(s) of \(x\) are :

\(\lim _{x \rightarrow \frac{\pi}{4}} \frac{4 \sqrt{2}-(\cos x+\sin x)^5}{1-\sin 2 x}\) is equal to :

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)

For the given five values, \(16,25,19,34,43\), the three year moving averages are

If \(x+\frac{1}{x}=2\), the principal value of \(\sin ^{-1} x\) is :

Which of the region shown in the given figures represents the feasible region bounded by the following constraint?
\(4 x+y \geq 80,2 x+y \geq 60, x+y \leq 80, x \geq 0, y \geq 0\)

Read the following passage carefully and answer the given questions.
Plasmodium, a tiny protozoan is responsible for the disease malaria. 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. Innate immunity consist of four types of barriers. These are – (i) Physical barriers- skin on our body is the main barrier which prevents entry of the micro-organisms. (ii) Physiological barriers- Acid in the stomach, saliva in the mouth, tears from eyes-all prevent microbial growth. (iii) Cellular barriers- 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. (iv) Cytokine barriers- virus-infected cells secrete proteins called interferons which protect non-infected cells from further viral infection. Allergy is due to the release of chemicals like histamine and serotonin from the mast cells. 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.
Malignant malaria is caused by _____ is the most serious one and can even be fatal.

If x, y \(\in R\) then match List - I with List - II

List - I	List - II
(A) \(|x|<|y|\)	(I) iff \(x^2>y^2\)
(B) \(|x|>|y|\)	(II) iff \(x^2 \leq y^2\)
(C) \(|x| \leq |y|\)	(III) iff \(x^2<y^2\)
(D) \(|x| \geq |y|\)	(IV) iff \(x^2 \geq y^2\)

Choose the correct answer from the options given below:

Which of the following represents Fehling solution B?

Which of the following is a barrier method of contraception?

The integral \(I=\int \frac{e^x}{1-e^{2 x}} d x\) is equal to :

The objective function of an LPP is \(z=a x+\beta y,(a, \beta>0)\) that has to be maximized/minimized subject to the constraints \(x+y \leq 2, x \geq 0, y \geq 0\).
Then \(\max (z)-\min (z)\) is equal to :