Some important general properties of the electric field lines are given below:
(A) Field lines start from positive charges and end at negative charges
(B) In a charge-free region, electric field lines can be taken to be continuous curves without any breaks
(C) Electrostatic field lines form closed loops
(D) Two field lines can never cross each other
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There are four media in which light is traveling. The speed of light in each medium along with relative permeability of the medium are given as below. Arrange the relative permittivity of each of the medium in increasing order.
(A) Medium I: \( v_1 = 2 \times 10^8 \, \text{m/s}, \mu_r = 1 \)
(B) Medium II: \( v_{II} = 1.5 \times 10^8 \, \text{m/s}, \mu_r = 1 \)
(C) Medium III: \( v_{III} = 3 \times 10^8 \, \text{m/s}, \mu_r = 1 \)
(D) Medium IV: \( v_{IV} = 2 \times 10^8 \, \text{m/s}, \mu_r = 2 \)

The internal resistance of primary cell is \( 3 \Omega \). It generates a current of \( 0.3 \text{ A} \) in an external resistance of \( 22 \Omega \). The rate at which chemical energy is consumed in providing the current is:

According to Bohr's Model :
(A) The radius is directly proportional to 'n'.
(B) The speed is directly proportional to \(\frac{1}{n} \) .
(C) The magnitude of total energy is directly proportional to \(\frac{1}{n^2} \).
(D) The radius is directly proportional to \(n^2\)

According to Einstein's photoelectric equation :

The current in a solenoid changes from 0.0A to 10.0A in 0.1 sec. If an average emf of 2V is induced in the circuit, the value of self-inductance is:

Two point charges, \( q_1 = 4\mu C \) and \( q_2 = -3\mu C \) (with no external field) are placed at (\(-6 \, cm, 0, 0\)) and (\(6 \, cm, 0, 0\)), respectively. The amount of work required to separate the two charges infinitely away from each other will be

Applying the Kirchhoff's rule to the loop (a) ABCA and (b) BCDEB, two correct equations are given

(A) \(8-4 I_2-2\left(I_2+I_3\right)-I_1=0\)
(B) \(4-2\left(I_2+I_3\right)-4\left(I_2+I_3-I_1\right)=0\)
(C) \(4+2\left(I_2-I_3\right)-4\left(I_2+I_3-I_1\right)=0\)
(D) \(8+4 I_2+2\left(I_2-I_3\right)-I_1=0\)
Choose the correct answer from the options given below:

Match List - I with List - II.

LIST-I ((Function)y)	LIST-II (\((\) Derivative \() \frac{d y}{d x}\))
(A) \(y=\cos \sqrt{x}\)	(I) \(\frac{\sec (\tan \sqrt{x}) \tan (\tan \sqrt{x}) \sec ^2 \sqrt{x}}{2 \sqrt{x}}\)
(B) \(y=\sqrt{\sin x}\)	(II) \(-3 x^2 \cos \left(x^3\right) \sin \left(\sin \left(x^3\right)\right)\)
(C) \(y=\sec (\tan \sqrt{x})\)	(III) \(\frac{\cos x}{2 \sqrt{\sin x}}\)
(D) \(y=\cos \left(\sin \left(x^3\right)\right)\)	(IV) \(-\frac{1}{2 \sqrt{x}} \sin \sqrt{x}\)

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Read the given passage carefully and answer the questions
Antibiotics have greatly improved our capacity to treat deadly diseases such as plague, whooping cough (kali khansi), diphtheria (gal ghotu) and leprosy (kusht rog), which used to kill millions all over the globe.
Streptokinase produced by the bacterium Streptococcus and modified by genetic engineering is used as a 'clot buster' for removing clots from the blood vessels of patients who have undergone myocardial infarction leading to heart attack. Microbes are diverse-protozoa, bacteria, fungi and microscopic animal and plant viruses, viroids and also prions that are proteinacious infectious agents. The puffed-up appearance of dough is due to the production of CO₂ gas. Similarly the dough, which is used for making bread, is fermented using baker's yeast (Saccharomyces cerevisiae). Primary sewage treatment basically involve physical removal of particles - large and small from the sewage through filtration and sedimentation. These are removed in stages; initially, floating debris is removed by sequential filtration. Then the grit (soil and small pebbles) are removed by sedimentation. All solids that settle form the primary sludge, and the supernatant forms the effluent. The effluent from the primary settling tank is taken for secondary treatment. The primary effluent is passed into large aeration tanks, where it is constantly agitated mechanically and air is pumped into it. This allows vigorous growth of useful aerobic microbes into flocs. While growing, these microbes consume the major part of the organic matter in the effluent.
The puffed-up appearance of dough in the baking industry is due to the production of -

Out of students in a school, it is known that \(65 \%\) reside in hostel and \(35 \%\) are day scholars. Previous year results report that \(40 \%\) of the students who reside in hostel attain A grade and \(20 \%\) of day scholars attain A grade in their annual examination.
At the end of the year, one student is chosen at random from the class.
Probability of the selected student attaining grade \(A\) is:

The condition where one species is harmed whereas the other is
unaffected is called

The degree of the differential equation \(\left(1+\frac{d y}{d x}\right)^4=\left(\frac{d^2 y}{d x^2}\right)^2\) is: