An infinitely long line charge distribution produces an electric field of \( 9 \times 10^4 \text{ N/C} \) at a distance of 2 cm. The linear charge density of the distribution is :

A source emits sound of frequency 600 Hz inside water. The frequency heard in air (velocity of sound in water is 1500 m/s and velocity of sound in air is 300 m/s) will be :

If an object moves towards a convex mirror with a speed of 10 m/s, what would be the speed of image when the object is 49m away? (Given focal length of convex mirror is 1m)

The light from a point source placed in air is incident on a convex spherical glass surface of radius of curvature 30 cm.
The refractive index of the glass is 1.5. The distance of light source from the glass surface is 120 cm. The distance of the image formed from the glass surface is

Work done in moving a charge q along a closed path of length l by an electric field \(\vec{E}\) is given by:

The speed of light in a material medium is given by :

When white light consisting of wavelengths ranging from 400 nm to 700 nm passes through water (u = 4/3), then the wavelength range in water will be :

The angle between two vectors \(\vec{a}\) and \(\vec{b}\) with magnitudes \(\sqrt{3}\) and 4 respectively and \(\vec{a} \cdot \vec{b}=2 \sqrt{3}\) is :

Which of following statements are true about DNA structure?
A. DNA is made of two polynucleotide chains
B. The two chains have anti-parallel polarity
C. The two chains are coiled in a left-handed fashion
D. Distance between a base pairs in a helix is approximately equal to 3.4 nanometre
Choose the correct answer from the options given below:

Read the passage carefully and answer the Questions
\(KMnO _4\) is prepared by the fusion of \(MnO _2\) with an alkali metal hydroxide and an oxidizing agent like \(KNO _3\) to give a dark-green manganate ion which disproportionate to give permanganate as follows.
\(\begin{array}{l}2 MnO _2+4 KOH + O _2 \rightarrow 2 K_2 MnO _4+2 H _2 O \\ 3 K_2 MnO _4+4 H ^{+} \rightarrow 2 KMnO _4+ MnO _2+2 H _2 O \end{array}\)
On heating \(K _2 MnO _4\) decomposes at 513 K to give \(K _2 MnO _4\). Permanganate ion is tetrahedral and diamagnetic
Acidified \(KMnO _4\) acts a strong oxidizing agent which oxidizes oxalic acid, ferrous ions, nitrite ion and iodides.
When one mole of \(KMnO _4\) is used for the oxidation of oxalic acid, how many moles of \(CO _2\) will be produced?

Match List I with List II

List - I	List - II
(A) Convergent evolution	(I) Speciation
(B) Divergent evolution	(II) Analogous organs
(C) Adaptive radiation	(III) Homologous organs
(D) Natural selection	(IV) Australian marsupials

Choose the correct answer from the options given below:

Which of the following functions are increasing on \(x \in\left(0, \frac{\pi}{2}\right)\) ?
(A) \(f(x)=\sin x\)
(B) \(f(x)=\cos x\)
(C) \(f(x)=\tan x\)
(D) \(f(x)=\cos 3 x\)
Choose the correct answer from the options given below :

A random variable X has the following probability distribution

X	0	1	2
\(P ( X )\)	\(1 / 4\)	\(1 / 2\)	\(1 / 4\)

then, which of the following is correct?