For predicting the straight line trend in the sales of cars (in thousands) on the basis of 5 consecutive years' data, the company uses a 3-year moving averages method.
If the sales of cars for respective years are 15, 24, 18, 33 and 42, then which of the following averages will not be computed?

The solution of the differentiable equation \(2 x \frac{d y}{d x}+y=14 x^3, x>0\), is:

Which of the following statements are true?
(A) The vector joining the points P(2, 3, 0) Q(- 1, - 2, - 4) directed from P to Q is \(\overrightarrow{P Q}\) = - 3i - 5j - 4k
(B) Projection of a vector vec a on other vector \(\vec{b}\) is \(\frac{\vec{a} \cdot \vec{b}}{|\vec{a}|}\)
(C) If \(\vec{a}=i-2 j+k\) and \(\vec{b}=-2 i+4 j+5 k\) then \(\vec{a}+\vec{b}=-i+2 j+6 k\)
(D) If \(\theta\) is the angle between \(\vec{a}\) and \(\vec{b}\) \(\cos \theta=\frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|}\)
Choose the correct answer from the options given below:

Match List 1 with List 2.

List 1 (Differential equation)	List 2 (Sum of order and degree)
(A) \(\frac{d^2 y}{d x^2}+\frac{d y}{d x}+3 y=\sin x\)	(I) 2
(B) \(\frac{d y}{d x}=\sin (x+y)\)	(II) 3
(C) \(\sqrt{1+\left(\frac{d y}{d x}\right)^2}=\frac{d^2 y}{d x^2}\)	(III) 4
(D) \(x^2\left(\frac{d^2 y}{d x^2}\right)^3+y\left(\frac{d y}{d x}\right)^4+y^3=0\)	(IV) 5

Choose the Correct answer from the options given below :

In the interval [-5, -3], the function f(x) = (x + 1)(x - 3) is:

The number of solutions of the system of equations
\(\begin{array}{l}\alpha^2 x+\alpha y=-1 \\\alpha x+\alpha^2 y=1\end{array}\)
is infinite. Then \(\alpha\) is:

The area of the region bounded by the lines x = 2y + 3, x = 0, y = 1 and y = - 1 is:

Consider the differential equation \(\frac{d y}{d x}+y \tan x=\sec x\), then which of the following statements are correct?
(A) It is homogeneous
(B) It has \(\sec x\) as its integrating factor
(C) Its general solution is \(y \sec x=\tan x+c\), where \(c\) is an arbitrary constant.
(D) Its degree is not defined
Choose the correct answer from the options given below :

Arrange the given structures involved in packaging of DNA Helix.
(A). Chromatin
(B). Chromatin fibers
(C). Nucleosome
(D). Euchromatin
Choose the correct answer from the options given below:

The value of \(\tan ^{-1} \frac{2}{11}+\tan ^{-1} \frac{7}{24}\) is :

In order to link the alien DNA, the vector needs to have very few, preferably single, recognition sites for the commonly used restriction enzymes. Presence of more than one recognition sites within the vector will generate several fragments, which will complicate the gene cloning. In Biolistics or gene gun method cells are bombarded with high velocity micro particles of gold or tungsten coated with DNA. The ligation of alien DNA is carried out at a restriction site present in one of the two antibiotic resistance genes. For example, you can ligate a foreign DNA at the BamH I site of tetracycline resistance gene in the vector pBR322. 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. The RNA can be removed by treatment with ribonuclease whereas proteins can be removed by treatment with protease. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol.
Which one of the following statements is correct with reference to biolistics?

Amniocentesis is not legally used to test:

Match the Integrating factor of the following Differential equations.

List - I	List - II
(A) \(\frac{d y}{d x}-y=\cos x\)	(I) \(e^x\)
(B) \(\frac{d y}{d x}=\cos x-y\)	(II) \(x^2\)
(C) \(x \frac{d y}{d x}+2 y=x^2\)	(III) \(\frac{1}{x^2}\)
(D) \(\frac{d y}{d x}=x+\frac{2}{x} y\)	(IV) \(e^{-x}\)