Year(x)	2011	2012	2013	2014	2015	2016	2017
Sales (in lakh Rs. ) (y)	65	68	70	72	75	67	73

If \(y=70+0.964(x-2014)\) be a straight line trend fitted by the method of the least squares to the above data, then the trend value for the year 2015 is :

Match List-I with List-II (where \(c\) is an arbitrary constant)

List-I	List-II
(A) \(\int \tan x d x\)	(I) \(\log |\sec x+\tan x|+c\)
(B) \(\int \cot x d x\)	(II) \(\log |\sec x|+c\)
(C) \(\int \sec x d x\)	(III) \(\log |\sin x|+c\)
(D) \(\int \operatorname{cosec} x d x\)	(IV) \(\log |\operatorname{cosec} x-\cot x|+c\)

Choose the correct answer from the options given below :

If \(A=\left[\begin{array}{cc}4 & 3 \\ 2 & -1 \\ 1 & 0\end{array}\right]\) and \(B^T=\left[\begin{array}{ccc}1 & 2 & 3 \\ 2 & 1 & -1\end{array}\right]\), then \(A-B\) is equal to

If \(\vec{a}=2 \hat{i}-\hat{j}+3 \hat{k}\) and \(\vec{b}=2 \hat{i}+2 \hat{j}+\hat{k}\) then
Match List-I with List-II

List-I	List-II
(A) Projection of \(\vec{a}\) on \(\vec{b}\) is	(I) \(-7 \hat{i}+4 \hat{j}+6 \hat{k}\)
(B) \(\vec{a} \times \vec{b}\) is	(II) \(\frac{1}{\sqrt{101}}(-7 \hat{i}+4 \hat{j}+6 \hat{k})\)
(C) Unit vector along \(\vec{a}+\vec{b}\) is	(III) \(\frac{5}{3}\)
(D) Unit vector perpendicular to both \(\vec{a}\) and \(\vec{b}\) is	(IV) \(\frac{1}{\sqrt{33}}(4 \hat{i}+\hat{j}+4 \hat{k})\)

Choose the correct answer from the options given below :

The value of c in Rolle's theorem for the function \(f(x)=x^3-3 x\) in the interval \([0, \sqrt{3}]\) is :

Match List-I with List-II

List-I (Matrix)	List-II (Inverse of the Matrix)
(A) \(\left[\begin{array}{cc}1 & 7 \\ 4 & -2\end{array}\right]\)	(I) \(\left[\begin{array}{cc}2 / 15 & 1 / 10 \\ -1 / 15 & 1 / 5\end{array}\right]\)
(B) \(\left[\begin{array}{cc}6 & -3 \\ 2 & 4\end{array}\right]\)	(II) \(\left[\begin{array}{cc}1 / 5 & -2 / 15 \\ -1 / 10 & 7 / 30\end{array}\right]\)
(C) \(\left[\begin{array}{cc}5 & 2 \\ -5 & 4\end{array}\right]\)	(III) \(\left[\begin{array}{cc}\frac{1}{15} & \frac{7}{30} \\ 2 / 15 & -1 / 30\end{array}\right]\)
(D) \(\left[\begin{array}{ll}7 & 4 \\ 3 & 6\end{array}\right]\)	IV) \(\left[\begin{array}{cc}2 / 15 & -1 / 15 \\ 1 / 6 & 1 / 6\end{array}\right]\)

Choose the correct answer from the options given below:

\(\int \frac{(x-3) e^x}{(x-1)^3} d x\) is equal to

Read the given passage carefully and answer the questions
Salmonella typhi is a pathogenic bacterium which causes typhoid fever in human beings. Sustained high fever (39° to 40°C), weakness, stomach pain, constipation, headache and loss of appetite are some of the common symptoms of this disease. Typhoid fever could be confirmed by Widal test. Plasmodium enters the human body as sporozoites. The parasites initially multiply within the liver cells and then attack the red blood cells (RBCs) resulting in their rupture. The rupture of RBCs is associated with release of a toxic substance, haemozoin, which is responsible for the chill and high fever recurring every three to four days. There is lymphoid tissue also located within the lining of the major tracts (respiratory, digestive and urogenital tracts) called mucosa-associated lymphoid tissue (MALT). In our body, cell growth and differentiation is highly controlled and regulated. In cancer cells, there is breakdown of regulatory mechanisms. Normal cells show a property called contact inhibition by virtue of which contact with other cells inhibits their uncontrolled growth. Cancerous cells just continue to divide giving rise to masses of cells called tumors. Tumors are of two types: benign and malignant. Cannabinoids are a group of chemicals, which interact with cannabinoid receptors present principally in the brain. Generally taken by inhalation and oral ingestion, these are known for their effects on cardiovascular system of the body.
The rupture of RBCs is associated with release of a toxic substance__________, which is responsible for the chill and high fever recurring every three to four days.

Which of the following component was not the part of S.L. Miller's experiment?

Read the passage carefully and answer the given questions.
DNA Fingerprinting
Polymorphism in DNA sequence is the basis of genetic mapping of the human genome as well as of DNA fingerprinting. DNA fingerprinting involves identification of differences in some specific regions in the DNA sequence called repetitive DNA. It works on the principle of polymorphisms in DNA sequences. The repetitive DNA are separated from bulk genomic DNA. The bulk DNA forms a major peak and the other small peaks are referred to as satellite DNA. These repetitive/satellite DNA sequences show a high degree of polymorphisms and form the basis of DNA fingerprinting.
Which one of the following techniques is involved in DNA fingerprinting?

The following statements are based on the osmotic pressure of solutions. The correct statements are
(A) Molar concentration is same for isotonic solutions
(B) Solutions which have same osmotic pressure at same temperature arecalled isotonic solutions
(C) No osmosis occurs when isotonic solutions are separated by semipermeable membrane
(D) A 1.9% Sodium Chloride solution has equivalent osmotic pressure to that of fluid inside blood cells
Choose the correct answer from the options given below:

A Linear Programming Problem (LPP) consists of which of the following components?
(A) Decision variables
(B) The graphical compliment
(C) The objective function
(D) The linear constraints
Choose the correct answer from the options given below :

Match List-I with List-II
Let \(f: A \rightarrow B\) be a function given by \(f(x)=x^2\)

List - I (Domain and Co-domain)	List - II (Kind)
(A) \(A= R\) and \(B= R\)	(I) \(f\) is both one-one and onto
(B) \(A= R\) and \(B=[0, \infty]\)	(II) \(f\) is one-one but not onto
(C) \(A=B=[0, \infty]\)	(III) \(f\) is not one-one but onto
(D) \(A=[0, \infty], B= R\)	(IV) \(f\) is neither one-one nor ont

Choose the correct answer from the options given below :