JEE Mains
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
AnswerVelocity of Sine Wave=Wave NumberAngular Frequency
Angular Frequency = 4 and Wave number is 8 So the answer is .5 ms−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
Questionlimt→0(1sin2(t)1+2sin2(t)1+...+nsin2(t)1)sin2(t) is equal to ...
AnswerRemember that a∞=0 if 0 < a < 1
So limt→0(1sin2(t)1+2sin2(t)1+...+nsin2(t)1)sin2(t)
is equal to limt→0(1cos2(t)+2cos2(t)+...+ncos2(t))sin2(t)is equal to limt→0((ncos2(t))sin2(t))((n1)cos2(t)+(n2)cos2(t)+...+(n−1n)cos2(t)+1)sin2(t)
is equal to n