Ferromagnetic material in transformers should have :

Find the value of k making the following function continuous at x = 5
\(f(x)=\left\{\begin{array}{ll}2 k x-1, & x \geq 5 \\ 2 x+3, & x<5\end{array}\right.\)

Match List-I with List-II.
If the random variable z has the following distribution:

X	0	1	2	otherwise
P(x)	k	k	2k	0

List-l & List-ll

List-I	List-II
(A) k	(I) \(\frac{3}{4}\)
(B) \(P(x \geq 2)\)	(II) \(1 / 4\)
(C) \(P(x \leq 2)\)	(III) \(\frac{1}{2}\)
(D) \(P(0<x \leq 2)\)	(IV) 1

Choose the correct answer from the options given below:

If \(\cos y=x \cos (a+y)\), then \(\frac{d y}{d x}=\)

The corner points of the feasible region of a LPP with the constraints \(x+2 y \leq 40,3 x+y \geq 30,4 x+3 y \geq 60, x, y \geq 0\) are

The product of the order and degree of the following differential equation :
\(x \left( \frac{d^2y}{dx^2} \right)^2 + \left( \frac{dy}{dx} \right)^3 + y^2 = 0\)

The equation of the normal to the curve \(y=4 x^3+2 \sin x\) at \((0,3)\) is :

Forward biasing of a p-n junction

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 the nomenclature of restriction enzymes -

Darwin's finches are the example of :

Match List - I with List - II.

List - I (Name of microorganism)	List - II (Chemical)
(A) Aspergillus niger	(I) Citric acid
(B) Acetobacter aceti	(II) Acetic acid
(C) Clostridium butylicum	(III) Butyric acid
(D) Lactobacillus	(IV) Lactic acid

The corner points of the bounded feasible region determined by the system of linear constraints are (15,0), (40,0), (4, 18) and (6, 12). If objective function is Z = 30x + 20y then the sum of the maximum and the minimum values of Z is

If \(A\) is a \(3 \times 3\) matrix such that \(|\operatorname{adj} A|=9\) and \(\left|k A^{-1}\right|=9\), then the value of \(k\) are :