A metallic wire of uniform area of cross section has a resistance \(R\), resistivity \(\rho\) and power rating P at V volts. The wire is uniformly stretched to reduce the radius to half the original radius. The values of resistance, resistivity and power rating at V volts are now denoted by \(R ^{\prime}, \square\) ' and \(P ^{\prime}\) respectively. The corresponding values are correctly related as ___________ . Fill in the blank with the correct answer from the options given below

The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}(\sin |x|+\cos |x|) d x\), is equal to:

If \(\left|\begin{array}{ll}2 & 4 \\ 5 & 1\end{array}\right|=\left|\begin{array}{cc}2 x & 4 \\ 6 & x\end{array}\right|\), then \(x\) is equal to:

If \(y=\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right), 0 < x < 1\), then \(\frac{d y}{d x}\) is equal to :

Pipe A and B can fill a tank in 15 hours and 20 hours respectively. Pipe C can empty the tank in 25 hours. Pipes A, B and C work together but pipe C is closed after 10 hours, then the time taken by pipe A and B to fill the remaining tank is:

An automobile dealer wishes to buy four luxury cars of different brands with some down payment and balance in equal monthly instalments for 10 years
The bank charges \(9 \%\) interest per annum compounded monthly
Given \(\frac{0.0075(1.0075)^{120}}{(1.0075)^{120}-1}=0.01266\)

Luxury Car	Price of the Car (in Rs.)	Down payment (in Rs.)
P	25,00,000	5,00,000
Q	35,00,000	12,00,000
R	45,00,000	15,00,000
S	42,00,000	15,00,000

Match List I with List II

List-I (Luxury Car)	List-II (EMI (in Rs.))
(A) P	(i) 34,182
(B) Q	(ii) 37,980
(C) R	(iii) 29,118
(D) S	(iv) 25,320

Choose the correct answer from the options given below :

If \(\vec{a}=2 \hat{i}+m \hat{j}-n \hat{k}\) and \(\vec{b}=\hat{l} \hat{i}-3 \hat{j}+4 \hat{k}\) such that \(\vec{a}=2 \vec{b}\), then the value of \(14 l+m+n\) is :

A machine has been producing steel tubes of mean inner diameter of 2 cm.
A sample of 10 tubes gives an inner diameter of 2.01 cm and a standard deviation of 0.063 cm.
Test the hypothesis that the machine is working in the proper order at 5% level of significance and answer, which of the following statements are correct?
[Given that \(t_{0.05}=2.262\)]
(A) The value of the test statistic is t = 0.476
(B) The null hypothesis is rejected at \(5 \%\) level of significance.
(C) The null hypothesis is accepted at \(5 \%\) level of significance.
(D) The degree of freedom is 10
Choose the correct answer from the options given below:

The backbone of a polynucleotide chain is formed by:

In Clemmensen reduction the carbonyl compound is treated with

\(\int \sqrt{1+\frac{x^2}{9}} d x\) is equal to
(Where \(C\) is an arbitrary constant)

The velocity of an EM wave in a given medium is \( \vec{V} = 3 \times 10^8 \hat{j} \). When electric field oscillates along z-axis, then direction of oscillation of magnetic field at that time should be :

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 drugs are commonly used to quickly reduce the symptoms of allergy?