In the following matrix equation, the value of \(x\) is :
\(\left[\begin{array}{cc}x+y & 4 \\ -5 & 3 y\end{array}\right]=\left[\begin{array}{cc}3 & 4 \\ -5 & 6\end{array}\right]\)

If \(A=\left[\begin{array}{ccc}x+z & 2 & -3 \\ x & 0 & 4 \\ 3 & x-y & 0\end{array}\right]\) is a skew-symmetric matrix, then which of the following are true?
(A) \(y>z>x\)
(B) \(x>y\)
(C) \(x+y+z>0\)
(D) \(z>z\)
Choose the correct answer from the options given below :

The two positive numbers whose sum is 16 and the sum of whose squares is minimum then the positive numbers are :

If \(a>b\) and \(c<0\), then which of the following is NOT correct?
\(a c < b c\)
\(a+c<b+c\)
\(a-c < b-c\)
\(a c>b c\)
Choose the correct answer from the options given below :

If \(y=\log x^5\), then \(\frac{d^2 y}{d x^2}\) is given by :

The domain of the function \(\sin ^{-1}(4 x-1)\) is:

The maximum profit that a company can make if the profit function is
\(P(x)=41+24 x-18 x^2\) is :

The rate of biomass production is expressed in terms of __________ to compare the productivity of different ecosystems.

Read the passage given below and answer the question.
Phenols and Alcohol have the same function group (-OH) but phenols are stronger acids than alcohol due the resonance stabilization of phenoxide ion than alkoxide ion (-RO\(^{-}\)). Electron withdrawing groups tend to increase the acidic strength while electron releasing groups tend to decrease it.
Compound 'A' on reaction with Conc. HCl and anhydrous \(ZnCl_2\), gives turbidity immediately.
Compound 'A' is :

Which of the following statements are correct about the structure of a sperm?
A. It is composed of head, thorax, neck and tail
B. The neck region contains a lot of mitochondria
C. The mitochondria produces energy for the movement of tail
D. The tail facilitate sperm motility essential for fertilisation
Choose the most appropriate answer from the options given below:

The initial idea of triplet nature of codon was proposed by:

Phenol can be distinguished from ethanol by the following reagent :

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.
Transformation is a procedure through which: