A coin is tossed 3 times. If \(X\) denotes the number of heads, then Match List I with List II

LIST I	LIST II
A. \(P(X=0)\)	I. \(\frac{1}{8}\)
B. \(P(X=1)\)	ㅍ. \(\frac{7}{8}\)
C. \(P(X \leq 2)\)	III. \(\frac{4}{8}\)
D. \(P(X \geq 2)\)	IV. \(\frac{3}{8}\)

Choose the correct answer from the options given below:

If \(e^x+e^y=e^{x+y}\), then \(\frac{d y}{d x}\) equals

A square matrix \(B=\left[b_{i j}\right]_{n \times n}\) where
\(b_{i j}=0\) when \(i \neq j\)
\(b_{i j}=k\) when \(i=j\) for some constant \(k\) is called:

Match the electromagnetic waves in Column-I with production methods in Column-II

Column-I (Electromagnetic Waves)	Column-II (Production Methods)
(A) Microwaves	(I) LC oscillator
(B) Infrared	(II) Magnetron
(C) X-rays	(III) Vibration of atoms/molecules
(D) Radio waves	(IV) Bombarding large atomic number metal target with fast-moving electrons

Choose the correct answer from the options given below :

If the line \(\vec{r}=(\hat{i}+\hat{j}+\hat{k})+\lambda(2 \hat{i}+\hat{j}+2 \hat{k})\)
is parallel to the plane \(\vec{r} \cdot(3 \hat{i}-2 \hat{j}+a \hat{k})=11\), then \(a\) is equal to :

A random variable X has the following probability distribution where k is some number :

X	0	1	2
P(X)	k	2k	3k

Find the value of k.

If the matrix \(A =\left(\begin{array}{ll}1 & 3 \\ 2 & 1\end{array}\right)\), then the value of \(\operatorname{det}\left( A ^2-2 A \right)\) is equal to

Ferric oxide in blast furnace's upper half is mainly reduced by :

The pyramid of biomass in the sea is -

The following data are from a random sample : \(5,8,10,7,10,14\), then the point estimate of the population standard deviation is

Let \(A=\left[a_{i j}\right]\) be a square matrix of order 3 with each entry either 0 or 1 .
Then the number of all such possible matrices is :

Which one of the following plants will have many ovules in their gynoecium?

Read the passage carefully and answer the questions based on the passage:
Species diversity on earth is not uniformly distributed. It is generally highest in the tropics and decreases towards the poles. Earth's fossil history reveals the incidences of mass extinctions in the past. Earth's rich biodiversity is vital for the very survival of mankind. It is believed that communities with high diversity tend to be less variable and more productive. The reasons of conserving biodiversity are narrowly utilitarian, broadly utilitarian and ethical. Biodiversity conservation may be in-situ as well as ex-situ.
Which of the following might not account for the greater biological diversity in the tropic region?