Mr. Ram took a loan of 4,00,000rupees at 10% annual interest rate and paid 20,000 as monthly instalment under flat rate system. What is the term of the loan?

The slope of normal to the curve \(y=3 x^2-6 x\) at \(x=0\) is:

The corner points of the feasible region determined by the system of Linear Constraints are \((0,3),(1,2)\) and \((3,0)\). Let \(z=p x+q y\), where \(p, q>0\), be the objective function. Find the condition on \(p\) and \(q\) so that the minimum of \(z\) occurs at \((3,0)\) and \((1,2)\) :

If \(\cos^2 y + \sin(xy) = \lambda\), then \(\frac{dy}{dx} =\)

The interval in which where the function \(f(x)=x^3-3 x^2+4 x+1, x \in R\) is increasing, is:

The shortest distance between the lines \(\vec{r}=(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(2 \hat{i}+3 \hat{j}+4 \hat{k})\) and \(\vec{r}=(2 \hat{i}+4 \hat{j}+5 \hat{k})+\mu(4 \hat{i}+6 \hat{j}+8 \hat{k})\) is equal to

The linear constraints, for which the shaded area in the figure is the feasible region of an LPP, are:

Read the following passage carefully and answer the given questions.
Restriction endonuclease on finding its specific recognition sequence, bind to the DNA and cut each of the two strands of the double helix at specific points in their sugar -phosphate backbones. Each restriction endonuclease recognises a specific palindromic nucleotide sequences in the DNA. 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). Now a days the most commonly used matrix is agarose which is a natural polymer extracted from sea weeds. The DNA fragments separate (resolve) according to their size through sieving effect provided by the agarose gel. The first restriction endonuclease-Hind II, whose functioning depended on a specific DNA nucleotide sequence was isolated and characterised five years later. It was found that Hind II always cut DNA molecules at a particular point by recognising a specific sequence of six base pairs. In addition to 'ori', the vector requires a selectable marker, which helps in identifying and eliminating non-transformants and selectively permitting the growth of the transformants. Transformation is a procedure through which a piece of DNA is introduced in a host bacterium. Normally, the genes encoding resistance to antibiotics such as ampicillin, chloramphenicol, tetracycline or kanamycin, etc., are considered useful selectable markers for E. coli
Chitinase is used to disrupt the membranes of:

Match List - I with List - II.

LIST I	LIST II
A. Gobar gas	I. Citric acid
B. Aspergillus niger	II. Methane
C. Saccharomyces cerevisiae	III. Antibiotic
D. Penicillium notatum	IV. Ethanol

Choose the correct answer from the options given below:

If the frequency of an alternating current is doubled while keeping the inductance constant, then the inductive reactance

If the value of the refractive index of a denser medium with respect to the rarer medium is 1.414, then the critical angle is:

The untranslated regions are present on an mRNA at:

Arrange the correct sequence of steps for gel electrophoresis.
(A). Load this DNA into the agarose gel matrix
(B). Cutting the DNA fragments by using a restriction enzyme
(C). Use ethidium bromide for DNA staining
(D). Separated bands of DNA are cut out from agarose gel
Choose the correct answer from the options given below.