Two sources of equal emf are connected in series. This combination is connected to an external resistance R.
The internal resistance of two sources are \( r_1 \) and \( r_2 \) (\( r_2 > r_1 \)).
If the potential difference across the source of internal resistance \( r_2 \) is zero, then R equals to:

A wire has a resistance of \( 3 \text{ } \Omega \) at 20°C and \( 5 \text{ } \Omega \) at 100°C. The temperature coefficient of resistance of the wire is:

An eye specialist prescribes spectacles having a combination of a converging lens of focal length 25 cm and a diverging lens of focal length of 20 cm. The power of the combination of two lenses (in dioptre) is

A bar magnet when suspended horizontally and perpendicular to earth's field experiences a torque of \( 3 \times 10^{-4} \text{ N m} \). The Magnetic moment of the magnet would be: (take horizontal component of Earth's magnetic field at the place \( 0.4 \times 10^{-4} \text{ T} \))

Two coherent monochromatic light beams of intensities 16I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are-

A slit of width 'd' is illuminated by red light of wavelength 650 nm. What should be the value of slit width 'd' so that first minimum fall at an angle of diffraction of \(\frac{\pi}{6}\) ?

Two antennas A and B have maximum line of sight range R = 45.5 km. If the height of antenna A is 32 m then the height of antenna B is : (Given radius of earth is = 6400 km)

If \(\int_0^1 \frac{e^x}{1+x} d x=m\), then the value of \(\int_0^1 \frac{e^x}{(1+x)^2} d x\) is :

In a common emitter transistor amplifier current gain is 9 and resistance gain is 20. The voltage gain will be :

If the points \((2,1),(-1,4)\) and \((a, 3)\) are collinear then the value/(s) of a is/(are) :

Read the following passage carefully and answer the given questions.
Bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. Baculoviruses are pathogens that attack insects and other arthropods. The majority of baculoviruses used as biological control agents are in the genus Nucleopolyhedrovirus. These viruses are excellent candidates for species-specific, narrow spectrum insecticidal applications. They have been shown to have no negative impacts on plants, mammals, birds, fish or even on non-target insects. BOD refers to the amount of the oxygen that would be consumed if all the organic matter in one liter of water were oxidised by bacteria. The sewage water is treated till the BOD is reduced. Cheese, is one of the oldest food items in which microbes were used. Different varieties of cheese are known by their characteristic texture, flavour and taste. For example, the large holes in 'Swiss cheese' are due to production of a large amount of CO₂ by a bacterium named Propionibacterium sharmanii.
Bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus-

Which of the following statements about electromagnetic waves is/are correct?
A. Visible Light can be polarised but X-rays cannot.
B. X-rays in vacuum travel faster than visible light waves in vacuum.
C. The energy of X-ray photon is greater than that of a visible light photon.
D. Radio waves are produced by the accelerated motion of charges in conducting wires.
E. An electric dipole is a basic source of electromagnetic waves.
Choose the correct answer from the options given below:

Which of the following are linear first order differential equations?
(A) \(\frac{d y}{d x}+P(x) y=Q(x)\)
(B) \(\frac{d x}{d y}+P(y) x=Q(y)\)
(C) \((x-y) \frac{d y}{d x}=x+2 y\)
(D) \(\left(1+x^2\right) \frac{d y}{d x}+2 x y=2\)
Choose the correct answer from the options given below: