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 $f_1=100=fo\left(\frac{C}{C-V_S}\right)$

C = Speed of sound

Vs = Speed of source

f₂ = 50 = fo = $\left(\frac{C}{C+V_s}\right)$

$\frac{f_1}{f_2}=2=\frac{C+V_S}{C-V_S}$

$fo=\frac{200}{3}=\frac{x}{3}$

x = 200

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$R=R?A^{1/3}$

$\delta =\frac{mass}{volume}=\frac{mA}{\frac{4}{3}\pi R^3}=\frac{mA}{4/3\pi R_0^{3}A}$

$\Rightarrow$ Density is independent of mass number

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L = 1 m

$\Delta L=0.4\times 10^{-3}m$

$m=1kg$

d = 0.4 × 10^-3 m

$\frac{F}{A}=y\frac{\Delta L}{L}$

$y=\frac{FL}{A\Delta L}=\frac{\left(mg\right)\times 1}{\left(\frac{\pi d^2}{4}\right)\times 0.4\times 10^{-3}}$

$\Delta y=0.1\times 0.199\times 10^{12}=1.99\times 10^{10}$

= 1.99

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Calamine – ZnCO₃ (ore of zinc)

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Cryolite – Na₃AlF₆ (ore of aluminium)

 $a_1=\frac{m_{2}g-m_{1}g}{m_1+m_2}=\frac{2mg-mg}{3m}=\frac{g}{3}$

$a_2=\frac{3mg-mg}{4m}=\frac{g}{2}$

$\Rightarrow \frac{a_1}{a_2}=\frac{2}{3}$

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Loss in P.E. = Gain in k.E

2 mg R = $\frac{1}{2}\left(\frac{1}{2}m{R}^2+m{R}^2\right){\omega }^2$

$\omega =\sqrt[]{\frac{8g}{3R}}=4\sqrt[]{\frac{g}{2\times 3R}}$

$x=\frac{g}{2}=5$

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No, to get admission into Certificate courses, candidates are required to complete their Class 12 and must have a passing certificate of their last qualifying examination. According to information available on the official sources, the acceptance of the entrance exam is not explicitly mentioned on the official website of the institution. Moreover, the institute admits the candidates according to the number of seats available at the institution for that course. 

$KE=728\times 1.6\times 10^{-19}=\frac{1}{2}\times 9.1\times 10^{-31}\times V^2$

V = 16 × 106 m/s

For Lorentz force to be zero

eE = eVB

$\Rightarrow E=vB=16\times 10^6\times 12\times 10^{-3}$

= 192 × 103 V/m

y = x5 (1 - x) = x tanθ $\left(1-\frac{x}{R}\right)$

tan = 5, R = 1

$sin\theta =\frac{5}{\sqrt[]{26}},cos\theta =\frac{1}{\sqrt[]{26}}$

$R=\frac{u^{2}sin2\theta }{g}=1$

$\Rightarrow u^2=26\Rightarrow u=\sqrt[]{26}m/s$

y - component of initial velocity

= u sinθ 

= $=\sqrt[]{26}\times \frac{5}{\sqrt[]{26}}$

= 5 m/s

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The eligibility criteria to get admission into certificate courses at ISAS Pune are simple, in which candidates must complete their Class 12/HSC or equivalent with a decent score and must have a passing certificate. Additionally, the admission process of the course is based on the number of seats available in the institution and the batches and their available timings.

Bharatiya Engineering Science and Technology Innovation University is one of the best university to pursue BTech. While the university has some positive aspects like decent infrastructure, experienced faculty, and some international collaborations, it also faces criticism regarding location and work-life balance. The BTech programmes offered at the university cover core courses in the areas of Bio Technology, Agricultural, CSE, Data Science, Cyber Security, and others. 

The institute provides good placement packages to its graduating PGDM students. Check out the table below to know the key highlights of the Firebird Institute of Research in Management placement during 2025: