The shortest distance between the lines \(l_1\) and \(l_2\) given by
\(l_1: \vec{r}=\hat{i}+2 \hat{j}-4 \hat{k}+\lambda(2 \hat{i}+3 \hat{j}+6 \hat{k})\) and \(l_2: \vec{r}=3 \hat{i}+3 \hat{j}-5 \hat{k}+\mu(2 \hat{i}+3 \hat{j}+6 \hat{k})\) is :

The solution of the differential equation \(\frac{d y}{d x}=\left(1+x^2\right)\left(1+y^2\right)\) is (Here \(C\) is an arbitrary constant)

If \(\left|\begin{array}{ccc}1 & \cos \theta & 0 \\ \sin \theta & 1 & \cos \theta \\ \cos \theta & 1 & -\sin \theta\end{array}\right|=A \sin \theta+B \cos \theta+C \sin \theta \cos \theta\) then :

500 g of jaggery syrup has 30% jaggery in it.
The quantity of jaggery that should be added to make it 50% of syrup is:

Sudhir had Rs 45,000. He lent a part of it at 4% p.a. and the remaining at 10% p.a. simple interest. He earned a total profit at 8% p.a. on the money lent, what sum did he lend at 10% p.a ?

The integrating factor of differential equation \(\frac{d y}{d x}+y \tan x=\sec x\) is:

If \(y=\log \left(x+\sqrt{x^2+a^2}\right)\) then \(\frac{d y}{d x}\) =

Arrange the following PCR steps in the correct sequence.
A. Extension of Primers
B. Amplification of DNA
C. Annealing of Primers
D. Denaturation of DNA fragment
Choose the correct answer from the options given below:

Which of the following compounds will show highest acidic strength?

For a full wave rectifier, if the input frequency is 50 Hz, the output frequency will be:

Read the passage carefully and give the answers to the question :
India was amongst the first countries in the world to initiate action plans and programmes at a national level to attain total reproductive health as a social goal.
These programmes called 'family planning' were initiated in 1951 and were periodically assessed over the past decades. Improved programmes covering wider reproduction-related areas are currently in operation. Creating awareness among the people about various reproduction-related aspects and providing facilities and support for building up a reproductively healthy society are the major tasks under these programmes.
Which of the following is not a Sexually Transmitted Disease?

Area bounded by \(y=|x-5|\) and the \(x\)-axis between \(x=2\) and \(x=4\) is:

Match the complex given in List-I with type of hybridisation given in List-II.

List-I (Complex)	List-II (Hybridisation)
(A) \([Ni(CO)_4]\)	(I) \(sp^3d^2\)
(B) \([Ni(CN)_4]^{2-}\)	(II) \(dsp^2\)
(C) \([Co(NH_3)_6]^{3+}\)	(III) \(d^2sp^3\)
(D) \([CoF_6]^{3-}\)	(IV) \(sp^3\)

Choose the correct answer from the options given below: