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Physics-

General

Easy

Question

The displacement-time graph of a particle executing SHM is shown. Which of the following statements is/are true?

The velocity is maximum at t = T/2
The acceleration is maximum at t = T
The force is zero at t = 3T/4
The potential energy equals the oscillation energy at t = T/2.

The correct answer is: The acceleration is maximum at t = T

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Two particles undergo SHM along parallel lines with the same time period (T) and equal amplitudes. At a particular instant, one particle is at its extreme position while the other is at its mean position. They move in the same direction. They will cross each other after a further time

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A man is swinging on a swing made of 2 ropes of equal length L and in direction perpendicular to the plane of paper. The time period of the small oscillations about the mean position is

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Let u(x) be a twice differenctiable function defined in $0 less or equal than x less or equal than 1 comma$ holds the relation $u to the power of ´ ´ end exponent left parenthesis x right parenthesis equals e to the power of x end exponent u left parenthesis x right parenthesis text in end text x element of left square bracket 0 , 1 right square bracket. text If end text 0 less than x subscript 0 end subscript less than 1 comma$ then

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If $f open parentheses x close parentheses equals fraction numerator x to the power of 2 end exponent minus 1 over denominator x to the power of 2 end exponent plus 1 end fraction comma$ for every real number, then minimum value of f

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The maximum value of the function $f left parenthesis x right parenthesis equals fraction numerator left parenthesis 1 plus x right parenthesis to the power of 0.6 end exponent over denominator 1 plus x to the power of 0.6 end exponent end fraction$ in the interval [0, 1] is

The maximum value of the function $f left parenthesis x right parenthesis equals fraction numerator left parenthesis 1 plus x right parenthesis to the power of 0.6 end exponent over denominator 1 plus x to the power of 0.6 end exponent end fraction$ in the interval [0, 1] is

How many real values of x satisfy the inequaligy $e to the power of x end exponent less or equal than x plus 1$ ?

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If the function $f left parenthesis x right parenthesis equals c o s invisible function application vertical line x vertical line minus 2 a x plus b$ increases along the entire number scale, the range of value of a is given by

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Let $f left parenthesis x right parenthesis equals fraction numerator ln invisible function application x over denominator x end fraction for all x greater than 0 comma$ then
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Statement 2 : $f open parentheses x subscript 1 end subscript close parentheses greater than f open parentheses x subscript 2 end subscript close parentheses for all x subscript 1 end subscript element of open parentheses 2 comma 4 close parentheses text and end text x subscript 2 end subscript element of open parentheses 0 comma 2 close parentheses union open parentheses 4 comma infinity close parentheses$

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Statement 2 : $f open parentheses x subscript 1 end subscript close parentheses greater than f open parentheses x subscript 2 end subscript close parentheses for all x subscript 1 end subscript element of open parentheses 2 comma 4 close parentheses text and end text x subscript 2 end subscript element of open parentheses 0 comma 2 close parentheses union open parentheses 4 comma infinity close parentheses$

If f(x) is a polynomial function such that $f open parentheses x close parentheses f open parentheses fraction numerator 1 over denominator x end fraction close parentheses equals f open parentheses x close parentheses plus f open parentheses fraction numerator 1 over denominator x end fraction close parentheses$ for all non zero real values of x and f(4) = -15 then f(3) + f(-3) =

If f(x) is a polynomial function such that $f open parentheses x close parentheses f open parentheses fraction numerator 1 over denominator x end fraction close parentheses equals f open parentheses x close parentheses plus f open parentheses fraction numerator 1 over denominator x end fraction close parentheses$ for all non zero real values of x and f(4) = -15 then f(3) + f(-3) =

parallel

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