If A is an invertible matrix of order 2 ; then \(\operatorname{det}\left(A^{-1}\right)\) is equal to:

The unit's digit of \(12^{12}\) is equal to :

For what value of \(k\), the matrix \(A=\left[\begin{array}{ll}1 & 3 \\ k & 4\end{array}\right]\) is singular ?

The angle between the lines \(\vec{r}=3 \hat{i}+2 \hat{j}-4 \hat{k}+\lambda(\hat{i}+2 \hat{j}+2 \hat{k})\) and \(\vec{r}=5 \hat{j}-2 \hat{k}+\mu(3 \hat{i}+2 \hat{j}+6 \hat{k})\) is:

The vector equation of the plane which is at a distance of 6 units from the origin and has \(2,-1,2\) as the direction ratios of normal to it, is :

The function \(f(x)=\tan x-x\):

Consider the following statement regarding sample parameter and statistic; statistical inference and t-test:
A. There are only three types of probability sampling: stratified, simple and systematic.
B. Since a = probability of the Type-I error, then \((1-\alpha)\) is probability of not rejecting \(H_o\) when \(H_a\) is true.
C. t-value is represented as; \(t=\frac{\text { Mean - Comparison value }}{\text { Standard error }}\)
D. A sample of less than 30 is considered to be sufficient to hold Central Limit Theorem (CLT).
E. A confidence interval consists of three components: confidence level, sample statistic and margin of error.

Choose the appropriate term for the rate of formation of new organic matter by consumers:

In the given circuit, if the potential at A is 50 V, then potential at B is

Answer the question on the basis of passage given below:
In the periodic table, the d-block contains the elements of group \(3\) to \(12\). The d-orbitals are progressively filled in each of the four long periods. The elements of d block referred as transition metals have partly filled d orbitals and exhibit certain characteristic properties such as variety of oxidation states, formation of coloured ions, act as catalyst and show paramagnetic behaviour.
The two inner transition metals series \(4f\) and \(5f\) are known as Lanthanoids and Actinoids respectively. The lanthanoids resemble one another more closely as compared to ordinary transition elements in any series.
In context of the Lanthanoids, which of the following statements is/are NOT correct?
A. There is a gradual decrease in the radii of the members with increasing atomic number in the series
B. Availability of \(4f\) electrons results in the formation of compounds in \(+4\) oxidation state for all the members of the series
C. Because of similar properties, the separation of lanthanoids is not easy
D. \(La(OH)_3\) is least basic among hydroxides of lanthanoids
E. Ce can act as an oxidising agent
Choose the correct answer from the options given below:

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

If 525 = (10 + K) (mod 7) where \(K \in N\), then the least value of K is:

Answer the question on the basis of passage given below :
Formaldehyde is the first member of the aldehydic series. It is present in green leaves of plants where its presence is supposed to be due to the reaction of \(CO_2\) with water in the presence of sunlight and chlorophyll. Commercially, formaldehyde is obtained by the controlled oxidation of methane in the presence of molybdenum oxide (\(MoO\)) acting as a catalyst. Formaldehyde is a constituent of a number of polymers also called resins. These are non volatile solids or semi solids which are obtained directly from certain plants and can be synthesized in the laboratory.
Question: How is formalin useful?