The demand function P for maximising a profit monopolist is given by \(P = 274 -\) \(x^2\), while the marginal cost is \(4+3x\) for \(x\) units of commodity. The consumer surplus is

The ratio of the speeds of a motor boat and that of the current of water is \(26: 4\). The boat goes certain distance against the current in 6 hrs . The time taken by the boat to come back is ___________

Match List-I with List-II

List-I (Function f(x))	List-II (Interval)
(A) \(f(x)=x|x|\)	(I) Decreases on \((0, \infty)\)
(B) \(f(x)=x^2+2 x-5\)	(II) Increases on \((3, \infty)\)
(C) \(f(x)=x^2-6 x+9\)	(III) Decreases on \((-\infty,-1)\)
(D) \(f(x)=-x^2\)	(IV) Increases on \((-\infty, \infty)\)

Choose the correct answer from the options given below:

Let \(x=t^2, y=t^3\). Then \(\frac{d^2 y}{d x^2}\) is equal to

Assuming the same rate of change continues for the following data :

Year(X)	2019	2020	2021	2022	2023
Profit in Percentage (y)	38	40	65	72	69

The equation of the straight line trend using the least square method is :

If \(A\) and \(B\) are skew-symmetric matrices, then which one of the following is NOT true?

If \(A\) and \(B\) are two invertible matrices, then which of the following statements are correct?
(A) \(\left|A^{-1}\right|=|A|^{-1}\)
(B) \(\operatorname{adj} A=|A| A^{-1}\)
(C) \((A B)^{-1}=A^{-1} B^{-1}\)
(D) \((A+B)^{-1}=A^{-1}+B^{-1}\)
Choose the correct answer from the options given below:

Two waves of amplitudes 3 m and 2 m, respectively superimpose at a point in the same phase. The resultant amplitude would be:

A charge of 50 \( \mu C \) is uniformly distributed on the surface of a thin spherical shell of radius 10 cm. The electric field at a point at a distance of 5 cm from the center of the shell is

Read the Passage carefully and answer the the questions
The DNA 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. The separated DNA fragments can be visualised only after staining the DNA with a compound known as ethidium bromide followed by exposure to UV radiation. The repeated amplification of DNA is achieved by the use of a thermostable DNA polymerase (isolated from a bacterium, Thermus aquaticus). After completion of the biosynthetic stage, the product has to be subjected through a series of processes before it is ready for marketing as a finished product. The downstream processing and quality control testing vary from product to product. The convention for naming restriction enzymes is the first letter of the name comes from the genus and the second two letters come from the species of the prokaryotic cell from which they were isolated.
The thermostable DNA polymerase is isolated from -

Toluene reacts with a halogen in the presence of FeCl 3, giving a mixture of ortho and para halo compounds. This type of reaction is called:

On which of the following factors angular fringe width does not depend?

The area (in sq. units) of the region bounded by the parabola \(y^2=8 x\) and the line \(x=2\) is