Two runners, Ajay and Vijay complete a \(600\) m race in \(38\) seconds and \(48\) seconds respectively. By how many meters will Ajay defeat Vijay?

Let \(\vec{a}=\hat{i}+\hat{j}+\hat{k}\) and \(\vec{b}=\hat{i}+2 \hat{j}+3 \hat{k}\), then a unit vector perpendicular to both vectors \((\vec{a}+\vec{b})\) and \((\vec{a}-\vec{b})\) is equal to

If \(A=\left[a_{i j}\right]_{3 \times 2}\), where \(a_{i j}=i+j\), then

(A) A is a square matrix
(B) \(a_{21}+a_{32}=8\)
(C) Number of elements in A is 6
(D) Transpose of \(\mathrm{A}=\left[\begin{array}{ll}2 & 3 \\ 3 & 4 \\ 4 & 5\end{array}\right]\)
Choose the correct answer from the options given below:

The probability that a plant \(A\) survives is \(\frac{3}{4}\) and the probability that another plant \(B\) survives is \(\frac{1}{3}\).
The probability that only one of them survives is :

A container is full of pure milk. From this container, one third of milk is taken out and then an equal amount of water is poured into the container to fill it. This operation is repeated four times. The final ratio of milk and water in the container is :

The function \(f(x)=\frac{x}{(x-2)(x-3)(x-5)}, x \in R\) is :

For what value of \(k\), the following system of equations has infinitely many solutions?
\(x+2 y=5\), \(3 x+k y=15\)

A voltmeter of resistance \( 600 \text{ } \Omega \) is used to measure the potential drop across \( 300 \text{ } \Omega \) resistor. The measured value of potential drop will be

The temp at which the resistance of a conductor becomes 30% more than that of its resistance at \( 47^\circ \text{C} \) will be : (given the value of temperature coefficient of resistance of the conductor is \( 2 \times 10^{-4} \text{ K}^{-1} \))

The technology of biogas production was developed in India mainly due to the efforts of -

The number of equivalence relation on the set {1, 2, 3} containing (1, 2) and (2, 1) is

If the line \(\vec{r}=(\hat{i}-2 \hat{j}+\hat{k})+\lambda(2 \hat{i}+\hat{j}+2 \hat{k})\) is parallel to the plane \(\vec{r} \cdot(3 \hat{i}-2 \hat{j}+m \hat{k})=14\), then value of \(m\) is :

Answer the question on basis of passage given below
The noble gases have closed shell electronic configuration and are monatomic gases under normal conditions. The low boiling points of lighter noble gases are due to the weak dispersion forces between the atoms and the absence of other inter atomic interaction. The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers \(+2, +4\) and \(+6\).
\(\text{XeF}_4\) reacts violently with water to give \(\text{XeO}_3\). The compound of Xenon exhibit stereoisomerism and their geometries can be deduced considering the total number of electrons in the valence shell.
Which noble gas is generally used in illuminating warning signals?