If A and B are two events such that \(P(A) = 0.2, P(B) = 0.4\) and \(P(A \cup B) = 0.5\) then value of \(P(A/B)\) is:

If \(x \neq y \neq z\) then \(\left|\begin{array}{lll}1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2\end{array}\right|\) is equal to

If the corner points of the bounded feasible region of an LPP are (0,2), (3,0), (6,0), (6,8) and (0,5) then the minimum value of the objective function F = 4x+6y occurs at

The area (in sq. units) of the region in the first quadrant bounded by \(y=3 \sqrt{1-x^2}, x \in[0,1]\) and the x-axis is equal to

If \(\left[\begin{array}{ll}x-y & 0 \\ x+y & 1\end{array}\right]\) is an identity matrix and \(\left[\begin{array}{ll}x & y \\ x & x\end{array}\right]\) is a singular matrix then :

If \(x=e^t\) and \(y=e^{2 t}\) then \(\frac{d^2 y}{d x^2}=\)

A simple random sample consists of three observations \(1,3,5\). The point estimate of the population standard deviation is :

Answer the question on the basis of passage given below :
Nitrogen differs from rest of the members of group 15 due to its small size, high electronegativity, high ionization enthalpy and non-availability of d orbitals. Nitrogen has unique ability to form pa - pa multiple bonds with itself and with other elements having small size and high electronegativity. Heavier elements of this group do not form pa - pr bonds as their atomic orbitals are so large and diffuse that they cannot have effective overlapping.
Arrange the following in decreasing order of their basic strength :
A. PH3 \(_3\)
B. \(AsH _3\)
C. \(NH _3\)
D. \(SbH _3\)
E. \(BiH _3\)
Choose the correct answer from the options given below:

Let \(L_1\) and \(L_2\) be two lines, represented as,
\(L_1: \vec{r}=\hat{i}+\hat{j}+\lambda(2 \hat{i}-\hat{j}+\hat{k})\) and \(L_2: \vec{r}=2 \hat{i}+\hat{j}-\hat{k}+\mu(4 \hat{i}-2 \hat{j}+2 \hat{k})\), where \(\lambda\) and \(\mu\) are scalars. Then which of the following are true?
(A)\(L_1\) is perpendicular to \(L_2\)
(B) \(L_1\) is parallel to \(L_2\)
(C) \(L_1\) passes through the point (1,1,0)
(D) \(L_2\) passes through the point (2,1,-1)
Choose the correct answer from the options given below:

If k be the kinetic energy and m the mass of a moving particle then the de-Broglie wavelength of the particle is :

The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x^3+x \cos x+\tan ^5 x+1\right) d x\) is:

The basic steps involved in the genetic modification of an organism inlcude -
(A) Identification of DNA with desirable genes
(B) Production and clinical trial of drugs
(C) Introduction of the identified DNA into the host
(D) Maintenance of introduced DNA in the host and transfer of the DNA to its progeny
Choose the most appropriate combination from the options given below.

An ac source has a frequency of 60 Hz. The time taken for the voltage to change from peak value to zero is :