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Find the sum of the sequence 0.4, 0.44, 0.444,….. up to n terms.

S = 0.4 + 0.44 + 0.444 + 0.4444 +....n terms S = 4(0.1 + 0.11 + 0.111 + 0.1111 + .......n terms) Multiplying and dividing by 9, we get; S =... View Article

A 2mW laser operates at a wavelength of 500 nm. The number of photons that will be emitted per second is :[Given Planck’s constant h=6.6×10⁻³⁴Js,speed of light c= 3.0×10⁸m/s]

(a) 5 x 1015 (b) 1.5 x 1016 (c) 1 x 1016 (d) 2 x 1016 Answer: (a) 5 x 1015 Solution: Power = nhc/λ ⇒ n =... View Article

Which of the following is not true?

a) For a point charge, electrostatic potential varies as 1/r b) For a dipole, the potential depends on the magnitude of the position... View Article

A current-carrying wireframe is in the shape of digit eight (8). It is carrying current i_o. If the radius of each loop is R_o, then the net magnetic field dipole moment of the figure is

a) (i0πR02)√2 b) Zero c) (i0 x 2πR02) d) i0 x 4πR0 Answer: b) Zero Solution: M1 = i0 x A = i0x πR02 M2 = i0 x A = i0x πR02 Mnet = M1 - M2 = 0... View Article

What is Biological Nitrogen Fixation? Give One Example.

Answer: Biological nitrogen fixation is the process by which certain bacteria convert atmospheric nitrogen to ammonia. The enzyme nitrogenase... View Article

Different Types of Crops Grown in India in Monsoon are

Answer: Crops that are grown in the monsoon are known as Kharif crops. Different types of crops grown in India during the Monsoon are paddy,... View Article

Who invented Abacus?

Abacus is a calculating tool which has been used since ancient times. The name of the inventor of the Abacus is unknown but it is believed that... View Article

Circle equation polar form

Solution: We write the polar form of the equation of circle for the circle with centre at the origin. x = r cos θ y = r sin... View Article

Derivative of ln(f(x)).

Solution: We know derivative of ln x = 1/x Let y = ln (f(x)) Using chain rule, dy/dx = [1/f(x)]× f’(x) =... View Article

3: 18 : : 13 : ?

Solution: Product of means = product of extremes a:b : : c:d a and d are the extremes and b and c are the means. ad = bc 3: 18 : : 13 :... View Article

How to change standard form to vertex form of a parabola?

The standard form of a parabola is y = ax2 + bx + c. The vertex form is given by y = a(x-h)2 + k In the vertex form, (h, k) represents the... View Article

For a wave propagating in a medium, identify the property that is independent of the others

a) Frequency b) Velocity c) Wavelength d) All the above options Solution: a) Frequency Explanation:The wavelength and velocity of a wave... View Article

A mass 2m lies on a fixed ,smooth cylinder. An ideal string attached to 2m passes over the cylinder to mass m. Then the value of angle θ for which the system is in equilibrium.

Solution: Given, mass=2, length=2m, angle=θ FBD of m T−mg=0 T=mg Now FBD of 2m is: 2mgsinθ=T 2mgsinθ=mg... View Article

A non-conducting cylindrical shell of radius R is placed in uniform magnetic field. The axis of the cylinder is parallel to! the direction of magnetic field. A hole is drilled in cylinder and a particle having charge q and mass m is projected with velocity vo perpendicular to magnetic field and directed towards the axis of cylinder as shown in diagram. The particle collides elastically with inner wall of the cylinder and rebounds. The maximum speed Vo for which it can come out is

a) The minimum number of collisions after which it will emerge is two. b) The maximum speed v_(0) for which it can come out is c) The minimum... View Article

The equation of a simple harmonic wave is given by [latex]y=5sinfrac{pi }{2}(100t-x)[/latex], where x and y are in metre and time is in second. The time period of the wave (m seconds) will be?

Solution: Given... View Article

A 6 μF capacitor is charged from 10 V to 20 V. Increase in energy will be?

Solution:... View Article

Four rods each of length I have been hinged to form a rhombus. Vertex A is fixed to a rigid support, vertex C is being moved along the X− axis with a constant velocity v as shown in the figure. The rate at which vertex B is approaching the x− axis at the momentum the rhombus is in the form of a square is

a) v b) v/2 c) v/4 d) 2v Solution: b) v/2... View Article

Acceleration-time graph of a body is as shown. The corresponding velocity-time graph of the same body is.

a) b) c) d) Solution: Correct option is Option c) Explanation: We can see that the acceleration is constant in the initial phase, and... View Article

A piezoelectric quartz crystal of thickness 0.005 m is vibrating in resonance conditions. Calculate the fundamental frequency f0 for quartz. (γ=8×10^10 Nm^−2 and ρ=2.65×10^3 kg m^−3)

a. 55 MHz b. 0.55 MHz c. 5.5 MHz d. 5.5 kHz Solution: b) 0.55 MHz Explanation:... View Article

A comb run through one’s dry hair attracts small bits of paper. This is due to?

a) Paper is good conductor b) Comb is a good conductor c) The comb possesses magnetic properties d) The atoms in the paper gets polarised by... View Article

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