In a survey question for a sample of 250 individuals, 120 persons gave response 'yes', 80 persons gave response 'no' and 50 gave 'no response'. The point estimate of the proportion in the population who responded 'yes' is:

Given that \(\vec{a}=-3 \hat{i}-6 \hat{j}+4 \hat{k}, \quad \vec{b}=9 \hat{i}-\lambda \hat{j}-12 \hat{k}\)
If \(\vec{a} \times \vec{b}=\overrightarrow{0}\), then the value of \(\lambda\) is

The value of \(\tan ^2\left(\sec ^{-1} 2\right)+\cot ^2\left(\operatorname{cosec}^{-1} 3\right)\) is:

The coordinates of the image of the point \(\mathbf{P}(5,4,2)\) in the line \(\vec{r}=(-\hat{i}+3 \hat{j}+\hat{k})+\lambda(2 \hat{i}+3 \hat{j}-\hat{k})\), where \(\lambda\) is a parameter, is

The effective rate that is equivalent to a nominal rate of 16 % compounded semi-annually is :

If the random variable \(X\) is normally distributed with mean 16 and standard deviation 4,
then the standard normal variable \(Z\) corresponding to \(X=17\) is

If \(\left[\begin{array}{ccc}x-2 & 3 & -2 \\ y & 0 & -4 \\ 2 & z & 0\end{array}\right]\) is a skew symmetric matrix, then the value of \(x+y+z\) is

Australian marsupials show the phenomena of:

If set A has 5 elements and set B has 7 elements then number of one-one and onto mapping from A to B is:

If you place blood cells in a solution containing more than 0.9% (mass/volume) sodium chloride, water will flow out of the cells and they will shrink. Such a solution is called

The number of arbitrary constants in general solution of a differential equation of third order is :

After how many half lives a radioactive substance will decay to 6.25% of its original value :

Read the passage carefully and answer the questions
Many halogen containing organic compounds are present in nature and some of them are clinically useful. These classes of organic compounds find a wide range of applications in our daily life as well as in industries. Many of the polyhalogen compounds are useful too in agriculture. However, some of these compounds cannot be easily decomposed and are thus considered to be environmental hazards. These halo compounds are prepared via different synthetic routes where a variety of organic compounds can be used as substrates such as amines, hydrocarbons etc. They are used as solvents for relatively non-polar compounds. These compounds exhibit substitution and elimination reactions, in addition to their reactions with different metals, which leads to the formation of a versatile starting material for others organic compounds.
The reaction of aryl halide with sodium and dry ether is known as