Shown below is the graph of parabola \(y^2=x\), the area (in sq. units) of the shaded region is:

The values of \(\lambda\) for which the following system of equations has unique solution:
\(\begin{array}{l}\lambda x+3 y-z=1 \\x+2 y+z=2 \\-\lambda x+y+2 z=-1\end{array}\)

The area (in sq. units) of the region bounded by \(y=-1, y=2, x=y^3\) and \(x=0\) is equal to

In a 900 meters race, Ram gives Shyam a start of 150 meters and defeats him by 50 seconds. If the speed of Ram is 4.5 m/sec, then the speed of Shyam is

A measurable characteristic of a population is called:

A conducting ring of radius \(r\) in a magnetic field varying at rate \(x\) has electric field intensity at any ring point as :

Which of the following statements are correct in reference to the linear programming problem (LPP):
Maximize \(Z =5 x +2 y, Z =5 x +2 y, Z =5 x +2 y\)
subject to the following constraints
\(3 x+5 y \leq 15,5 x+2 y \leq 10, x \geq 0, y \geq 0\)
(A) The LPP has a unique optimal solution at \((2,0)\) only.
(B) The feasible region is bounded with corner points \((0,0),(2,0),(20 / 19,45 / 19)\) and \((0,3)\).
(C) The optimal value is unique, but there are an infinite number of optimal solutions.
(D) The feasible region is unbounded.
Choose the correct answer from the options given below:

A point charge is kept at the centre of a metallic insulated spherical shell. Then :

Read the passage carefully and answer the Questions
The concentration dependence of the rate of a reaction is called the differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by calculating the slope of the tangent at point 't' in the concentration vs time plot. This makes it difficult to determine the rate and hence the order of the reaction. This difficulty is overcome by integrating the differential rate equation. This integrated rate equation gives a direct relation between concentrations at different times and the rate constant. The integrated rate equations are different for the reactions having different reaction orders.
A certain amount of \(N _2 O _5\) decomposes to half of its initial amount in 50 minutes.
If the decomposition is a first order reaction, the rate constant of the reaction is.

Lichens are an example of -

'GEAC' stands for -

A metal plate is getting heated. It can be because of:
A. An alternating current is passing through the plate.
B. It is placed in a time varying magnitude field.
C. A direct current is passing through the plate.
D. It is placed in a space varying magnitude field, but does not vary with time.
E. It is placed in a time constant magnetic filed.
Choose the correct answer from the options given below:

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 one gives blue colored colonies if the plasmid in the bacteria does not have an insert?