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4 months ago

Class 11th Physics

An observer is riding on a bicycle and moving towards a hill at 18 kmh^-1. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is 640 Hz and velocity of the sound in air is 320 m/s, the beat frequency between the two sounds heard by observer will be _________ Hz.

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Vishal Baghel

Contributor-Level 10

$v_{S} = 0, v_{O_{b}} = 5 m / s$

$f_{d i r e c t} = (\frac{320 - 5}{320}) 640 = 630 H z$

$f_{b e a t} = (650 - 630) = 20 H z$

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4 months ago

Class 11th Physics

A unit scale is to be prepared whose length dows not change with temperature and remains 20cm, using a bimetallic strip made of bass and iron each of different length. The length of both components would change in such a way that difference between their length remains constant. If length of brass is 40cm and length of iron will be ________cm.

$(α_{i r o n} = 1.2 * 1 0^{- 5} K^{- 1} a n d α_{b r a s s} = 1.8 * 1 0^{- 5} K^{- 1}) .$

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Vishal Baghel

Contributor-Level 10

$l_{B} (1 + α_{B} Δ T) - l i (1 + α_{i} Δ T) = l_{B} - l_{i}$

$\Rightarrow α_{B} l_{B} = l_{i} α_{i}$

$l_{i} = 60 c m$

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4 months ago

Class 11th Mechanical Properties of Fluids

A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force F, its length increases by 5cm. Another wire of the same material of length 4L and radius 4r pulled by a force 4F under same conditions. The increases in length of this wire is _________cm.

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Vishal Baghel

Contributor-Level 10

$Δ L_{1} = \frac{F L}{A Y} = \frac{F L}{π r^{2} Y} = 5 c m$

$Δ L_{2} = \frac{4 F 4 L}{π 16 r^{2} y}$ = $\frac{F L}{π r^{2} Y} = 5 c m$

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4 months ago

Class 11th Physics

Four forces are acting at a point P in equilibrium as shown in figure. The ratio of force F₁ to F₂ is 1: x where x = _________.

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Vishal Baghel

Contributor-Level 10

$F_{2} = 1 c o s 45 ° + 2 c o s 45 ° = 3 c o s 45 ° = \frac{3}{\sqrt[]{2}} N$

$\begin{array}{l} F_{1} + 1 c o s 45 ° = 2 s i n 45 ° \\ \frac{F_{1}}{F_{2}} = 1 : 3 \end{array}$

x = 3

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4 months ago

Class 11th Physics

A car is moving with speed of 150 km/h and after applying the break it will move 27m before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling _________m distance.

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Vishal Baghel

Contributor-Level 10

Stopping distance = $\frac{v^{2}}{2 a} = d$ $\frac{^{}}{}$

If speed is made $\frac{1}{3} r d$ $\frac{}{}$

$d^{1} = \frac{d}{9}, d^{1} = \frac{27}{9} = 3 m$

Braking acceleration Remains same.

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4 months ago

Class 11th Maths

Let AB be a chord of length 12 of the circle ${(x - 2)}^{2} + {(y + 1)}^{2} = \frac{169}{4} .$

If tangents drawn to the circle at points A and B intersect at the point P, then five times the distance of point P form chord AB is equal to……………

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Payal Gupta

Contributor-Level 10

Let C be the centre and M be the mid point of AB

$Δ A P C : s i n θ = \frac{13 / 2}{p c} = \frac{5}{13} \Rightarrow p C = \frac{169}{10}$

$Δ A M C : c o s θ = \frac{6}{13 / 2} = \frac{12}{13}$

PC = $\frac{169}{10}, M C = \frac{13}{2} s i n θ = \frac{13}{2} \cdot \frac{5}{13}$

PM = PC – MC = $\frac{169}{10} - \frac{5}{2} = \frac{144}{10}$

5PM = 72

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4 months ago

Class 11th Maths

The number of natural numbers lying between 1012 and 23421 that can be formed using the digits 2, 3, 4, 5, 6 (repetition of digits is not allowed) and divisible by 55 is

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Payal Gupta

Contributor-Level 10

1012 $\leq$ Number in the question $\leq$ 23421

Also, the number has to use digits {2, 3, 4, 5, 6} without repetition and the number has to be divisible by $\frac{55}{11 * 5}$

As the number has to be divisible by both 5 and 11,

5 → once place

Let us make 4-digit such numbers first:

{2, 3, 4, 6} (digits are not be repeated)

A number is divisible by 11 it difference of sum of its digits at even places and sum of digits at odd place is 0 or multiple of 11.

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4 months ago

Class 11th Maths

Let α,β (α > β) be the roots of the quadratic equation x²– x – 4 = 0. If P_n = αⁿ - βⁿ, n $\in$ N, then $\frac{P_{15} P_{16} - P_{14} P_{16} - P_{15}^{2} + P_{14} P_{15}}{P_{13} P_{14}}$ is equal to…………