Which of the following are types of statistical inferences?
(A) Point estimation
(B) Interval estimation
(C) Marginal estimation
(D) Hypothesis testing
Choose the correct answer from the options given below :

If \(\left[\begin{array}{ccc}a-b & 0 & 0 \\ 0 & b-c & 0 \\ 0 & 0 & c-2\end{array}\right]\) is a scalar matrix such that a + b + c = 0, then, which of the following are TRUE?
(A) a = 0
(B) b = 0
(C) a = 1
(D) c = 1
Choose the correct answer from the options given below:

If the lines \(\frac{1-x}{3}=\frac{y-2}{2 \lambda}=\frac{z-3}{2}\) and \(\frac{x-1}{3 \lambda}=\frac{y-1}{1}=\frac{6-z}{5}\) are perpendicular, then the value of \(\lambda\) is:

If \(f: R \rightarrow R\) is defined by \(f(x)=x^2-3 x+2\) then \(f(f(x))\) is :

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

In a pair of adjacent coils, if current in one coil changes from 0 A to 10 A in 0.25 s , causing a magnetic flux change of 15 Wb in the adjacent coil, the mutual inductance of the coils is :

Consider \(Z = x + y\) subject to the constraints \(2x + y \le 3, 2x - y \ge 0, x \ge 0, y \ge 0\). The maximum value of Z is:

Read the given paragraph carefully and answer the following questions:
Since the DNA is enclosed within the membranes, we have to break the cell open to release DNA along with other macromolecules such as RNA, proteins, polysaccharides and also lipids. This can be achieved by treating the bacterial cells/plant or animal tissue with enzymes such as lysozyme (bacteria), cellulase (plant cells), chitinase (fungus). There are some basic steps in genetically modifying an organism (i) identification of DNA with desirable genes; (ii) introduction of the identified DNA into the host; (iii) maintenance of introduced DNA in the host and transfer of the DNA to its progeny. Agrobacterium tumifaciens, a pathogen of several dicot plants is able to deliver a piece of DNA known as 'T-DNA' to transform normal plant cells into a tumor and direct these tumor cells to produce the chemicals required by the pathogen. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol. Selection of recombinants due to inactivation of antibiotics is a cumbersome procedure because it requires simultaneous plating on two plates having different antibiotics. Therefore, alternative selectable markers have been developed which differentiate recombinants from non-recombinants on the basis of their ability to produce colour in the presence of a chromogenic substrate. In this, a recombinant DNA is inserted within the coding sequence of an enzyme, ß-galactosidase. This results into inactivation of the gene for synthesis of this enzyme, which is referred to as insertional inactivation.
The purified DNA ultimately precipitates after the addition of:

If \(A = \begin{bmatrix} 1 & 0 \\ -1 & 5 \end{bmatrix}\) and \(I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}\), then the value of k so that \(A^2 = 6A + kI\) is given by:

Two similar magnetic poles having pole strengths in the ratio 1 : 4 are placed 6 cm apart. The distance from a smaller pole in strength where net magnetic field is zero will be :

Let \(e^{\alpha y}+e^{\beta y}+\gamma x^2+\delta \log |x|+C=0\), where \(C \in R ,\) be a particular solution of the differential equation
\(x\left(e^{2 y}-1\right) d y+\left(x^2-1\right) e^y d x=0\) and passes through the point \((1,1)\).
The value of \((\alpha+\beta+\gamma+\delta-C)\) is:

\(\int_0^2 \frac{\sqrt{x}}{\sqrt{x}+\sqrt{2-x}} d x\) is equal to:

According to the Raoult's law, vapour pressure of a solution is directly proportional to: