A bag contains 12 white and 18 red balls. Two balls are drawn in succession without replacement. The probability that the first is red and the second is white is:

Let \(A=\left[\begin{array}{ccc}1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1\end{array}\right]\), where \(0 \leq \theta \leq 2 \pi\), then which of the following are true?
(A) \(|A|=2+2 \sin ^2 \theta\)
(B) \(|A|=2+\sin ^2 \theta\)
(C) minimum value of \(|A|\) is 1
(D) maximum value of \(|A|\) is 4.
Choose the correct answer from the options given below:

If \(A=\left[\begin{array}{ccc}0 & 0 & \sqrt{3} \\ 0 & \sqrt{3} & 0 \\ \sqrt{3} & 0 & 0\end{array}\right]\), then \(|\operatorname{adj} A|\) is equal to:

The function \(f(x)=\left\{\begin{array}{ll}\frac{\sin x}{x}+\cos x, & \text { if } x \neq 0 \\ k, & \text { if } x=0\end{array}\right.\) is continuous at \(x=0\), then the value of \(k\) is :

\(\int_2^5|x-3| d x\) equals

The point which lies in the half plane \(2 x-y \geq 6\) is:

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

If the net flux through a cube is \( \Phi = 1.05 \, N \, m^2 C^{-1} \), what will be the total charge inside the cube?
(Given: The permittivity of free space is \( \epsilon_0 = 8.85 \times 10^{-12} \, C^2 N^{-1} m^{-2} \)).

An electron in a hydrogen atom emits wavelengths during the transitions given below. Arrange these wavelengths in ascending order.
(A) from n = 3 to n = 2
(B) from n = 2 to n = 1
(C) from n = \( \infty \) to n = 1
(D) from n = \( \infty \) to n = 3
(E) from n = 4 to n = 1
Choose the correct answer from the options given below:

Read the passage carefully and answer the given questions.
DNA Fingerprinting
Polymorphism in DNA sequence is the basis of genetic mapping of the human genome as well as of DNA fingerprinting. DNA fingerprinting involves identification of differences in some specific regions in the DNA sequence called repetitive DNA. It works on the principle of polymorphisms in DNA sequences. The repetitive DNA are separated from bulk genomic DNA. The bulk DNA forms a major peak and the other small peaks are referred to as satellite DNA. These repetitive/satellite DNA sequences show a high degree of polymorphisms and form the basis of DNA fingerprinting.
Which one of the following techniques is involved in DNA fingerprinting?

Total internal reflection can take place only, if

The function \(f(x)=x+\frac{1}{x}\) has

The vapour pressure of pure water at \(25^{\circ} C\) is 23.75 mmHg.
The vapour pressure of the solution obtained by dissolving 34.2 g of sucrose \(\left( C _{12} H _{22} O _{11}\right)\) in 100 g of water will be :