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10 months ago

Class 12th Physics Ray Optics and Optical Instruments

Given below are two statements : one is labeled as Assertion A and the other is labeled as Reason R.

Assertion A : For a simple microscope, the angular size of the object equals the angular size of the image.

Reason R : Magnification is achieved as the small object can be kept much closer to the eye that 25cm and hence it subtends a large angle.

In the light of the above statements, choose the most appropriate answer from the options given below:

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10 months ago

Class 12th Physics Electromagnetic Waves

A radiation is emitted by 1000W bulb and it generates an electric field and magnetic field at P, placed at a distance of 2m.Th efficiency of the bulb is 1.25%. The value of peak electric field at P is x * 10^-1 V/m. Value of x is----------. (Rounded – off to the nearest integer)

[Take $ε_{0} = 8.85 * 1 0^{- 12} C^{2} N^{- 1} m^{- 2}, c = 3 * 1 0^{8} m s^{- 1}]$

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Payal Gupta

Contributor-Level 10

$l = \frac{1}{2} c ε_{0} E_{0}^{2} = η * (\frac{P}{4 π r^{2}})$ Here $η$ is the efficiency

$E_{0} = \sqrt[]{\frac{η P}{2 π r^{2} c ε_{0}}} = \sqrt[]{\frac{1.25}{100} * \frac{1000}{2 * 3.14 * 4 * 3 * 1 0^{8} * 8.85 * 1 0^{- 12}}}$

$\Rightarrow E_{0} = \sqrt[]{\frac{12.5}{8 * 3.14 * 3 * 8.85 * 1 0^{- 4}}} = 13.69 V m = 136.9 * 1 0^{- 1} V / m$

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10 months ago

Class 12th Maths

If f : R ->R is a function defined by f(x) = $[x - 1] c o s (\frac{2 x - 1}{2}) π,$ where[.] denotes the greatest integer function, then f is:

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alok kumar singh

Contributor-Level 10

$f (x) = [x - 1] c o s (\frac{2 x -}{2}) π$

$I f x = k, k \in I$

then f(x) = 0 as $c o s (\frac{2 k - 1}{2}) π = 0, \forall k \in I$

LHL = $\underset{h \to 0}{L t} [k - h - 1] c o s (\frac{2 k - 2 h - 1}{2}) π = \underset{h \to 0}{L t} (k - 2) c o s (\frac{2 k - 1}{2}) π \to 0$

$R H L = \underset{h \to 0}{L t} [k + h - 1] c o s (\frac{2 k + 2 h - 1}{2}) π = \underset{h \to 0}{L t} (k - 1) c o s (\frac{2 k - 1}{2}) π \to 0$

$∴ f (x)$ is continuous $\forall x \in R$

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10 months ago

Class 12th Electromagnetic Induction

An aeroplane, with its wings spread 10m, is flying at a speed of 180 km/h in a horizontal direction. The total intensity of earth's field at that part is 2.5 * 10^-⁴Wb/m² and the angle of dip is 60°. The emf induced between the tips of the plane wings will be………….

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Vishal Baghel

Contributor-Level 10

Bv = B sin 60°

$B_{v} = 2.5 * 1 0^{- 4} * \frac{\sqrt[]{3}}{2}$

$E m f = B_{v} * v * l = 2.5 * 1 0^{- 4} * \frac{\sqrt[]{3}}{2} * 180 * \frac{5}{18} * 1 = 108.25 * 1 0^{- 3} v o l t s$

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10 months ago

Class 12th Physics Alternating Current

In a series LCR resonant circuit, the quality factor is measured as 100. If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be--------.

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Payal Gupta

Contributor-Level 10

As we know that Q = $\frac{ω L}{R}$

$\Rightarrow \frac{Q'}{Q} = \frac{L'}{R'} * \frac{R}{L} = (\frac{L'}{L}) * (\frac{R}{R'}) = 2 * 2 \Rightarrow Q' = 4 Q = 4 * 100 = 400$

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10 months ago

Class 12th Physics Electrostatic Potential and Capacitance

If 'C' and 'V' represent capacity and voltage respectively then what are the dimensions of $λ$ where C/V = $λ$

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Vishal Baghel

Contributor-Level 10

$λ = \frac{c}{v} = \frac{Q^{3}}{W^{2}} = \frac{I^{3} T^{3}}{M^{2} L^{4} T^{- 4}} \Rightarrow [λ] = [M^{- 2} L^{- 4} T^{7} l^{3}]$

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10 months ago

Class 12th Maths

$\underset{x \to 0}{l i m} \frac{\int_{0}^{x^{2}} (s i n \sqrt[]{t}) d t}{x^{3}}$ is equal to:

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alok kumar singh

Contributor-Level 10

$\underset{x \to 0}{l i m} \frac{\int_{0}^{x^{2}} (s i n \sqrt[]{t}) d t}{x^{3}}$ $(\frac{0}{0})$ applying L' Hospital rule

$= \underset{x \to 0}{l i m} \frac{s i n (\sqrt[]{x^{2}}) . 2 x}{3 x^{2}}$

$= \frac{2}{3}, f o r x > 0$

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10 months ago

Class 12th Physics

The maximum and minimum amplitude of an amplitude modulated wave is 16V and 8V respectively. The modulation index for this amplitude wave x * 10^-2. The value of x is----------.

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Payal Gupta

Contributor-Level 10

Modulation Index $(μ) = \frac{A_{m a x} - A_{m i n}}{A_{m a x} + A_{m i n}} = \frac{16 - 8}{16 + 8} = \frac{1}{3} = 0.33 = 33 * 1 0^{- 2}$

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10 months ago

Class 12th Physics

In an electrical circuit, a battery is connected to pass 20 C of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at 15V. The work done by the battery is--------- J.

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Payal Gupta

Contributor-Level 10

$W = q Δ V = 20 * 15 = 300 J$

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10 months ago

Class 12th Physics

The circuit contains two diodes each with a forward resistance of 50 $Ω$ and with infinite reverse resistance. If the battery voltage is 6 V, the current through the 120 $Ω$ resistance is---------mA.

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Payal Gupta

Contributor-Level 10

D₁ is forward biased & D₂is reverse biased.

$l = \frac{6}{120 + 130 + 50} = \frac{6}{300} = 2 * 1 0^{- 2} A = 20 * 1 0^{- 3} A = 20 m A$

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