Tutorial Course

# 24 Jan 2023 - Shift 1

## Physics

QuestionA travelling wave is described by the equation

$y(x,t) = [.05sin(8x-4t)]$

The velocity of the wave is : [ all the quantities are in SI unit ]

(A)0.5 ms-1 (B) 8 ms-1 (C) 2 ms -1 (D) 4 ms-1

Answer$\text{Velocity of Sine Wave} = \frac{\text{Angular Frequency}}{\text{Wave Number}}$

Angular Frequency = 4 and Wave number is 8 So the answer is .5 $m {s}^{-1}$

## Chemistry

AnswerWe know that square root of frequency of x-ray is directly proportional to the atomic number! So square root of v = v raised to n. That's why value of n is 1/2.

## Maths

Question$\lim_{t \to 0} (1^\frac{1}{\sin^2(t)} + 2^\frac{1}{\sin^2(t)} + ... + n^\frac{1}{\sin^2(t)}) ^ {\sin^2(t)}$  is equal to ...
AnswerRemember that  $a^\infty = 0 \text { if 0 < a < 1 }$

So  $\lim_{t \to 0} (1^\frac{1}{\sin^2(t)} + 2^\frac{1}{\sin^2(t)} + ... + n^\frac{1}{\sin^2(t)}) ^ {\sin^2(t)}$

is equal to  $\lim_{t \to 0} (1^{\cos^2(t)} + 2^{\cos^2(t)} + ... + n^{\cos^2(t)}) ^ {\sin^2(t)}$

is equal to  $\lim_{t \to 0} ( (n^{\cos^2(t)}) ^ {\sin^2(t)}) ((\frac{1}{n})^{\cos^2(t)} + (\frac{2}{n})^{\cos^2(t)} + ... + (\frac{n}{n-1})^{\cos^2(t)} + 1) ^ {\sin^2(t)}$

is equal to $n$