The vector equation of line passing through (2, -1, 3) and perpendicular to the lines \(\frac{x-2}{3}=\frac{y-1}{1}=\frac{z+2}{2} \quad\) and \(\quad \frac{x+3}{-4}=\frac{y-5}{-3}=\frac{z+1}{2}\)
(Here \(\lambda\) is a parameter)

The value of \(\lim _{x \rightarrow 0} \frac{1-\cos x}{2 x^2}\) is:

\(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{d x}{1+\sqrt{\tan x}}\) is equal to:

The shortest distance between the lines \(\vec{r}_1=\hat{i}+\hat{j}+\lambda(2 \hat{i}-\hat{j}+\hat{k})\) and \(\vec{r}_2=2 \hat{i}+\hat{j}-\hat{k}+\mu(4 \hat{i}-2 \hat{j}+2 \hat{k})\) is :

Which of the following statements is incorrect?

At what rate will the present value of a perpetuity of Rs.1000 payable at the end of each quarter be Rs.50000?

A \(95 \%\) confidence interval for a population mean was reported to be 152 to 160 , if sample standard deviation \(\sigma=15\), then sample size used in this study is (Given \(Z_{0.025}=1.96\) )

The dehydration of alcohol follows the order :

Read the following passage carefully and answer the given questions
The separated DNA fragments can be visualized only after staining the DNA with ethidium bromide followed by exposure to UV radiation. Bright orange colored bands of DNA in ethidium bromide stained gel exposed to UV light can be seen. The separated bands of DNA are cut out from the agarose gel and extracted from the gel piece. This step is known as elution. The DNA fragments purified in this way are used in constructing recombinant DNA by joining them with a cloning vector.
The DNA fragments are separated by-

Which of the following is the wrong statement? Coulomb's law describes the electric force that

When a protein in its native form, is subjected to physical or chemical change, then its

The intervals in which the function \(f(x) = 2x^3 + 9x^2 + 12x + 20\) is increasing is given by:

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 technique is not very useful to detect the cancers of internal organs?