If the area of the triangle with vertices \(A(1,3), B(2,0), C(k, 2 k)\) is \(\frac{k^2}{2}\) sq. units, then the value(s) of \(k\) is/are:

Consider the function \(f(x)=x^3-3 x\). Then Match List-I with List-II:

List-I	List-II
(A) Point of local Maxima	(I) 1
(B) Point of local Minima	(II) -1
(C) Local maximum value	(III) 2
(D) Local minimum value	(IV) - 2

Choose the correct answer from the options given below:

In the formula for Z -test statistic \(Z=\frac{\bar{x}-\mu_0}{\sigma / \sqrt{n}}\), mark the incorrect statement.

The degree of the differential equation \(\left(1+\frac{d y}{d x}\right)^3=\left(\frac{d^2 y}{d x^2}\right)^2\) is:

The feasible region corresponding to the linear constraints of a Linear Programming Problem (LPP) is represented by the shaded region in the given figure. Which of the following is not a constraint to the given LPP?

A simple random sample consists of three observations \(1,3,5\). The point estimate of the population standard deviation is :

If \(\cos ^{-1} \alpha+\cos ^{-1} \beta+\cos ^{-1} \gamma=3 \pi\) then the value of \(\alpha^2 \beta^2 \gamma^2+3(\alpha+\beta+\gamma)\) is:

Medical termination of pregnancy (MTP) is considered relatively safe -

A uniform metallic wire of resistance \(4 \Omega\) is bent to form a circle. What is the effective resistance between the end of its diameter?

Read the passage carefully and answer the Questions
Carbonyl compounds such as aldehydes, ketones, and carboxylic acids play an important role in the biochemical process of plants and animal kingdom.
Many aldehydes and ketones find applications in dye, perfumery and other industries.
The carbonyl carbon atom is \(s p^2\)-hybridized forming three sigma and one pi-bond with oxygen.
C-O bonds are polar bond due to high electronegativity of oxygen than carbon.
Hence the carbonyl carbon behaves as an electrophilic center and oxygen as a nucleophilic centre.
Primary and secondary alcohols yield aldehydes and ketones respectively upon oxidation with variety of oxidizing agents.
The boiling points of aldehydes and ketones differ from hydrocarbons and ethers.
Aldehydes and ketones undergo nucleophilic addition reaction due to presence of electrophilic carbonyl carbon.
Nucleophile and a proton add across the carbon oxygen double bond.
Formalin which is used to preserve biological specimen is an aqueous solution of

The angle between the lines
\(l_1: \frac{x+1}{1}=\frac{2-y}{2}=\frac{z-1}{1}\) and \(l_2: \frac{x-1}{4}=\frac{2 y-4}{6}=\frac{z-1}{2}\), is:

Arrange the given structures starting from chalazal end to micropylar end in a mature embryo sac?
(A) Central cell
(B) Antipodals
(C) Synergids
(D) Egg
Choose the correct answer from the options given below:

There are two kinds of nucleases - exonucleases and endonucleases. Exonucleases remove nucleotides from the ends of the DNA whereas, endonucleases make cuts at specific positions within the DNA. The cutting of DNA by restriction endonucleases results in the fragments of DNA. These 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. Small volume cultures cannot yield appreciable quantities of products. To produce in large quantities, the development of bioreactors, where large volumes (100 - 1000 litres) of culture can be processed, was required. Thus, bioreactors can be thought of as vessels in which raw materials are biologically converted into specific products, individual enzymes, etc., using microbial plant, animal or human cells. PCR stands for Polymerase Chain Reaction. In this reaction, multiple copies of the gene (or DNA) of interest are synthesised in vitro using two sets of primers (small chemically synthesised oligonucleotides that are complementary to the regions of DNA) and the enzyme DNA polymerase.
Identify the incorrect fact about the PCR?