Class 12th

A modulating signal 2sin (6.28 * 10⁶)t is added to the carrier signal 4 sin(12.56 *10⁹)t for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passes through a band pass filter. The bandwidth of the output signal of band pass filter will be_________ MHz.

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alok kumar singh

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Modulating signal 2sin (6.28 * 10⁶)t

Carrier signal 4 sin (12.56 * 10⁹)t

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11 months ago

As shown in the figure, in steady state, the charge stored in the capacitor is ____________* 10^-⁶C.

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Contributor-Level 10

$q = C V_{100 Ω}$

$= (1.1 * 1 0^{- 6}) (\frac{10}{R + r} R)$

$= 1.1 * 1 0^{- 6} (\frac{10}{110} * 100)$

$= 10 μ C$

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11 months ago

A conducting circular loop is placed in X – Y plane in presence of magnetic field $\vec{B} = (3 t^{3} \hat{j} + 3 t^{2} \hat{k})$ in SI unit. If the radius of the loop is 1m. The induced emf in the loop, at time, t = 2s is npV. The value of n is__________.

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$? = \vec{B} . \vec{A}$

$= (3 t^{3} \hat{j} + 3 t^{2} \hat{k}) . (π {(1)}^{2} \hat{k})$

$? = 3 t^{2} π$

$E_{i n d} = | \frac{d ?}{d t} | = 6 t π$

at t = 2, E_ind = 12

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11 months ago

A thin prism of angle 6° and refractive index for yellow light (n_Y) 1.5 is combined with another prism of angle 5° and n_Y = 1.55. The combination produces no dispersion. The net average deviation $(δ)$ produced by the combination is ${(\frac{1}{x})}^{o}$ . The value of x is____________.

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$δ = A (μ_{y} - 1) - A^{1} (μ_{y}^{1} - 1)$

$= 6 (1.5 - 1) - 5 (1.55 - 1)$

$= \frac{1}{4}$

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11 months ago

In the given figure of meter bridge experiment, the balancing length AC corresponding to null deflection of the galvanometer is 40 cm. The balancing length, if the radius of the wire AB is doubled, will be__________cm.

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Class 12th Physics Wave Optics

Contributor-Level 10

Independent of are a is case of uniform wire

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11 months ago

Nearly 10% of the power of a 110 W light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of 1 m from the bulb to a distance of 5 m is a * 10^‑2 W/m². The value of 'a' will be________.

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alok kumar singh

Contributor-Level 10

P = 10% of 110W = 11W

(Visible)

$I_{1} - I_{2} = \frac{ρ}{4 π} (\frac{1}{r_{1}^{2}} - \frac{1}{r_{2}^{2}})$

$= \frac{11}{4 * \frac{22}{7}} (\frac{1}{1} - \frac{1}{25})$

$\frac{7}{8} * (\frac{24}{25}) = a * 1 0^{- 2} W / m^{2}$

$\frac{28 * 24}{8} * 1 0^{- 2} = a * 1 0^{- 2}$

=84 * 10^-2 = a * 10^-2 = a = 84

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11 months ago

Class 12th Maths

Let S $= {z \in C : z^{2} + \bar{Z} = 0} .$ Then $\sum_{z \in R}^{} (R e (z) + I m (z))$ is equal to

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Contributor-Level 10

take z = x + iy

$z^{2} + \bar{z} = 0$

$\Rightarrow x^{2} - y^{2} + x + i 2 x y - y i = 0$

$\Rightarrow x^{2} - y^{2} + x = 0 a n d y (2 x - 1) = 0$

if y = 0 x = 0, 1

$i f x = \frac{1}{2} \Rightarrow y = \pm \frac{\sqrt[]{3}}{2}$

$Σ (R e (z) + l m (z)) = (0 - 1 + \frac{1}{2} + \frac{1}{2}) + (0 + 0 + \frac{\sqrt[]{3}}{2} - \frac{\sqrt[]{3}}{2}) = 0$

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11 months ago

Class 12th Maths Matrices

Let S be the set containing all 3 * 3 matrices with entries from ${- 1, 0, 1}$ . The total number of matrices $A \in S$ such that the sum of all the diagonal elements of A^TA is 6 is

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Contributor-Level 10

Let A = $[\begin{matrix} a & b & c \\ d & e & f \\ 9 & h & i \end{matrix}]$

Now A^TA

trace will be $a^{2} + b^{2} + c^{2} + d^{2} + e^{2} + f^{2} + 9^{2} + h^{2} = 6$

total ways = ⁹C₆.2⁶.1.1.1 = 5376

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11 months ago

Class 12th Maths

Let f(x) = 2x² – x – 1 and $S = {n \in Z : | f (n) | < 800} .$ Then, the value of $\sum_{n \in S}^{} f (n)$ is equal to

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$| f (x) | \leq 800 \Rightarrow 2 n^{2} - n - 1 \leq 800$

$\Rightarrow 2 n^{2} - n - 801 \leq 0$

$\sum_{x \in S}^{} f (x) = \sum_{}^{} (2 x^{2} - x - 1)$

$= 2 (1 9^{2} + 1 8^{2} + . . . . . . . . 1^{2} + 0^{2} + 1^{2} + . . . . . + 2 0^{2})$

= 10620

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11 months ago

Class 12th Maths

Let M and N be the number of points on the curve y⁵ – 9xy + 2x = 0, where the tangents to the curve are parallel to x-axis and y-axis, respectively. Then the value of M + N equals

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