If the feasible region of an LPP is bounded and the corresponding objective function is \(Z =5 x -9 y\), then the objective
function attains :

A vector \(\vec{a}\) of magnitude \(3 \sqrt{2}\) making an angle of \(\frac{\pi}{3}\) with \(\hat{i}, \frac{\pi}{4}\) with \(\hat{j}\) and an acute angle \(\theta\) with \(\hat{k}\), is :

The value of the integral \(\int \frac{d x}{e^x+e^{-x}}\) is equal to:

The area enclosed between the curves \(y^2=x\) and \(y=|x|\) is :

Let \(y=\sin \left(\cos x^2\right)\), then the value of \(\frac{d y}{d x}\) at \(x=\frac{\sqrt{\pi}}{2}\) is equal to:

The value of \(|\vec{a}-\vec{b}|\), if two vectors \(\vec{a}\) and \(\vec{b}\) are such that \(|\vec{a}|=1,|\vec{b}|=4\), and \(\vec{a} \cdot \vec{b}=5\) is :

The value of the determinant \(\left|\begin{array}{ccc}a+b & b+c & c+a \\ c & a & b \\ 1 & 1 & 1\end{array}\right|\) is :

Read the Passage carefully and answer the the questions
The DNA fragments can be separated by a technique known as gel electrophoresis. Since DNA fragments are negatively charged molecules, they can be separated by forcing them to move towards the anode under an electric field through a medium/matrix. The separated DNA fragments can be visualised only after staining the DNA with a compound known as ethidium bromide followed by exposure to UV radiation. The repeated amplification of DNA is achieved by the use of a thermostable DNA polymerase (isolated from a bacterium, Thermus aquaticus). After completion of the biosynthetic stage, the product has to be subjected through a series of processes before it is ready for marketing as a finished product. The downstream processing and quality control testing vary from product to product. The convention for naming restriction enzymes is the first letter of the name comes from the genus and the second two letters come from the species of the prokaryotic cell from which they were isolated.
In agarose gel electrophoresis, DNA fragments move towards _______ under an electric field through a medium.

The relation \(R\) on the set \(N \times N\) defined by \((a, b) R(c, d) \Longleftrightarrow a+d=b+c\), \(\forall(a, b),(c, d) \in N \times N\), where N is the set of natural numbers, is:

Consider the differential equation, \(x \frac{d y}{d x}=y\left(\log _e y-\log _e x+1\right)\), then which of the following are true?
(A) It is a linear differential equation
(B) It is a homogenous differential equation
(C) Its general solution is \(\log _e\left(\frac{y}{x}\right)=C x\), where \(C\) is constant of integration
(D) Its general solution is \(\log _e\left(\frac{x}{y}\right)=C_y\), where \(C\) is constant of integration
(E) If \(y(1)=1\), then its particular solution is \(y=x\)
Choose the correct answer from the options given below:

Nucleotide is obtained by linking nucleoside to phosphoric acid at which position of sugar ?

Which bacteria fix the atmospheric nitrogen into organic form to be utilized by plants as nutrients?

Time period of oscillation of a bar magnet in a uniform magnetic field is \( T_o \). The magnet is cut into 3 equal parts transverse to its length. The new time period of oscillation of one part will be :