If A and B are two distinct events such that P(A|B) = P(B|A), then which of the following is/are possible?
(A) A = B
(B) P(A) = P(B)
(C) \(A \subset B\) but \(A \neq B\)
(D) \(A \cap B=\phi\)
Choose the correct answer from the options given below:

If \(\cos ^{-1} \sqrt{3} x+\cos ^{-1} x=\frac{\pi}{2}\), then the value of \(x\) is :

The number of all possible matrices of order \(2 \times 2\) with each entry \(0,1,2\), and 3 is:

The solution set of \(6 \leq-3(2 x-4)<12, x \in R\) is :

The value of the integral \(I=\int_0^1 \frac{1}{\sqrt{1+3 \sqrt{x}}} d x\) is:

If \(x=a \cos ^3 \theta, y=a \sin ^3 \theta\). The value of \(\frac{d^2 y}{d x^2}\) at \(\theta=\frac{\pi}{6}\) is :

The general solution of the differential equation \(ydx + xdy = 0\) is:

The electric field amplitude of an electromagnetic wave is \(100 N C ^{-1}\) and its frequency is 50 MHz . What is the magnitude of wave vector \(k\), (given speed of electromagnetic wave is \(3 \times 10^8 m s ^{-1}\) )

Observe the figures and answer the question.

Match List I with List II.

LIST I	LIST II
A. Globular embryo	I. W
B. Mature embryo	II. Y
C. Zygote	III. Z
D. Heart-shaped embryo	IV. X

Choose the correct answer from the options given below:

A 95% confidence interval for a population mean was reported to be 152 to 160. If the standard deviation \(\sigma=15\), then the sample size is (given \(Z_{0.025}=1.96\) ) :

According to the electrochemical series, which of the following statements is incorrect?

The correct structure representing N,N-dimethylethanamine is

p-block elements are placed in groups 13 to 18 of the periodic table. Group 15 is nitrogen family.
Nitrogen makes various compounds like \(NH _3, HNO _3, N_2 O , NO _2\) etc. Phosphorus exists in the form of white and red phosphorus. White phosphorus glows in dark. \(PH _3\) gas is used as smoke screen. Group 16 is called oxygen family. Dry air contains \(21% O_2\) gas by volume. Combined sulphur exists as sulphates such as gypsum, epsome salt, baryte etc. The allotropic forms of sulphur are Rhombic and monoclinic sulphur. \(S_2\) is paramagnetic like \(O_2\) and it stable at high temperature. Group 17 is Halogen family. \(F _2\) is highly reactive, \(Cl _2\) is greenish yellow gas. Both \(SO _2\) and \(Cl _2\) are used for bleaching. Group 18 is Noble gas family but some noble gases also form compounds.
Complete hydrolysis of \(XeF _6\) gives HF and \(XeO _3\) as main products. The permanent bleaching effect is caused by :