Electric potential at any point \(V=-(\sqrt{23} x+4 y+5 z)\), then magnitude of electric field is

Consider the following statements
(A) Corpuscular model predicted that if the ray of light bends towards the normal after refraction then the speed of light would be greater in the second medium
(B) In optical fibre, the refractive index of the core is kept higher than cladding.
(C) Diffraction due to clouds is efficient in equal measures for all wavelengths
(D) Light travels faster in glass than in air.
(E) When light reflects from an air glass plate interface, the reflected wave suffers a phase change of \( \pi \).
Choose the correct answer from the options given below :

Match List-I with List-II for convex lens (symbols have their usual meanings)

List-I (Position of Object)	List-II (Details of image)
(A) at 2F	(l) \(m>1\), virtual
(B) at F	(II) \(m <1\), real
(C) between lens and F	(III) m = 1 , real
(D) between \(\infty\) and 2F	(IV) \(m \gg 1\), real

Choose the correct answer from the options given below :

For an astronomical telescope with 10 m focal length objective and 10 cm eyepiece, tube length and magnification are:

An unpolarized light of intensity \(I_0\) is passed through a polariser and is incident on an analyser making an angle of \((\pi/6) \text{ rad}\) with that of the polariser. The intensity of the light transmitted from the analyzer is

An astronomical telescope of ten fold angular magnification has a length of 44 cm. The focal length of the objective is:

Which of the following statements are correct?
(A) Permeability of soft iron < permeability of steel
(B) Susceptibility of soft iron > susceptibility of steel
(C) Retentivity of soft iron > Retentivity of steel
(D) Coercivity of soft iron > coercivity of steel
Choose the correct answer from the options given below :

The probability distribution of a random variable \(X\) is given under :
\(
P(X=x)=\left\{\begin{array}{ll}
k x^2 & \text { for } x=1,2,3 \\
2 k x & \text { for } x=4,5,6 \\
0 & \text { for otherwise }
\end{array}\right.
\)
Then \(P(X \geq 4)\) is :

The points on the ellipse \(\frac{x^2}{9}+\frac{y^2}{25}=1\) at which the tangents are parallel to the \(x\)-axis are:

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 -

The maximum slope of the curve \(y=-x^3+3 x^2+9 x-27\) is:

The differential equation that represents the family of lines parallel to x + y = 2 is:

Match List-I with List-II

List-I (EM Waves)	List-II (Production)
(A) Infra-red rays	(I) Electrons in atoms emit light when they move from one energy level to a lower level
(B) Visible light rays	(II) Radioactive decay of the nucleus
(C) Ultraviolet rays	(III) Vibration of molecules
(D) Gamma rays	(IV) Inner shell electrons in atoms moving from one energy level to a lower level

Choose the correct answer from the options given below: