The slope of the tangent to the curve \(x=a t^2, y=2 a t\) at ' \(t\) ' is :

A spherical balloon has a variable radius. The rate at which its volume is increasing with respect to its radius when the radius is 5 cm is:

The order and degree of differential equation \(\left[1+\left(\frac{d y}{d x}\right)^2\right]^2=\frac{d^2 y}{d x^2}\) respectively, are

The value of b for which the function \(f(x) = \sin x - bx + C\), where b and C are constants is decreasing for \(x \in R\) is given by

If \(x=t^4, y=t\), then \(\frac{d^2 y}{d x^2}\) is given by ______________

The absolute maximum value of the function \(f(x)=4 x-\frac{1}{2} x^2\) in the interval \(\left[-2, \frac{9}{2}\right]\) is

A random variable X has the following probability distribution

X	2	3	4	5
P(X)	5/k	7/k	9/k	11/k

Then the value of \(\frac{k}{4}\) is

If \(A=\left[\begin{array}{ccc}5 & 1 & 0 \\ 6 & 2 & -1\end{array}\right], B^T=\left[\begin{array}{cc}2 & 1 \\ -2 & 0 \\ 1 & 3\end{array}\right]\), then \(B A^T\) is :

A glass prism of angle 60° has an angle of minimum deviation of 30° for a given colour of light. The refractive index of glass for that colour of light is :

p-block elements are placed in groups 13 to 18 of the periodic table. Group 15 is nitrogen family. Nitrogen makes various compounds like \(NH _3, HNO _3, N_2 O , NO _2\) etc. Phosphorus exists in the form of white and red phosphorus. White phosphorus glows in dark. \(PH _3\) gas is used as smoke screen. Group 16 is called oxygen family. Dry air contains \(21\% O _2\) gas by volume. Combined sulphur exists as sulphates such as gypsum, epsome salt, baryte etc. The allotropic forms of sulphur are Rhombic and monoclinic sulphur. \(S_2\) is paramagnetic like \(O_2\) and it stable at high temperature.
Group 17 is Halogen family. \(F_2\) is highly reactive, \(C l_2\) is greenish yellow gas. Both \(S O_2\) and \(C l_2\) are used for bleaching. Group 18 is Noble gas family but some noble gases also form compounds.
Complete hydrolysis of \(XeF _6\) gives HF and \(XeO _3\) as main products.
Sulphate of magnesium of the following is :

Read the given paragraph carefully and answer the following questions:
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). There are some basic steps in genetically modifying an organism (i) identification of DNA with desirable genes; (ii) introduction of the identified DNA into the host; (iii) maintenance of introduced DNA in the host and transfer of the DNA to its progeny. Agrobacterium tumifaciens, a pathogen of several dicot plants is able to deliver a piece of DNA known as 'T-DNA' to transform normal plant cells into a tumor and direct these tumor cells to produce the chemicals required by the pathogen. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol. Selection of recombinants due to inactivation of antibiotics is a cumbersome procedure because it requires simultaneous plating on two plates having different antibiotics. Therefore, alternative selectable markers have been developed which differentiate recombinants from non-recombinants on the basis of their ability to produce colour in the presence of a chromogenic substrate. In this, a recombinant DNA is inserted within the coding sequence of an enzyme, ß-galactosidase. This results into inactivation of the gene for synthesis of this enzyme, which is referred to as insertional inactivation.
Which enzyme is not used to lyse the cells for extraction of DNA?

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:

A reaction is second order with respect to a reactant. If the concentration of the reactant is increased by 1.5 times, the
rate of the reaction