Let f : r r and g : r r be continuous functions, then the-Turito

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Easy

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Let f : R →R and g : R →R be continuous functions, then the value of $not stretchy integral subscript negative pi divided by 2 end subscript superscript pi text /2 end text end superscript blank$ (f(x) + f(-x)) (g(x) – g(-x)) dx, is equal to

Maths-General

– 1
0
1
None of these

Answer:The correct answer is: 0

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Horizontal component of velocity of

A

c o s blank 6 0 degree

5 blank m s to the power of negative 1 end exponent

which is equal to the velocity of

B

in horizontal direction. They will collide at

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if time of flight of the particles are equal or

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fraction numerator 2 u sin invisible function application theta over denominator g end fraction equals square root of fraction numerator 2 h over denominator g end fraction end root open parentheses therefore h equals fraction numerator 1 over denominator 2 end fraction g t subscript B end subscript superscript 2 end superscript close parentheses

h equals fraction numerator 2 u to the power of 2 end exponent sin to the power of 2 end exponent invisible function application theta over denominator g end fraction

equals fraction numerator 2 open parentheses 10 close parentheses to the power of 2 end exponent open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses to the power of 2 end exponent over denominator 10 end fraction equals 15 blank m

A particle $A$ is projected from the ground with an initial velocity of $10 blank m s to the power of negative 1 end exponent$ at an angle of 60 $degree$ with horizontal. From what height $h$ should an another particle $B$ be projected horizontally with velocity $5 m s to the power of negative 1 end exponent$ so that both the particles collide in ground at point $C$ if both are projected simultaneously? $left parenthesis g equals 10 blank m s to the power of negative 2 end exponent right parenthesis$

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Horizontal component of velocity of

A

c o s blank 6 0 degree

5 blank m s to the power of negative 1 end exponent

which is equal to the velocity of

B

in horizontal direction. They will collide at

C

if time of flight of the particles are equal or

t subscript A end subscript equals t subscript B end subscript

fraction numerator 2 u sin invisible function application theta over denominator g end fraction equals square root of fraction numerator 2 h over denominator g end fraction end root open parentheses therefore h equals fraction numerator 1 over denominator 2 end fraction g t subscript B end subscript superscript 2 end superscript close parentheses

h equals fraction numerator 2 u to the power of 2 end exponent sin to the power of 2 end exponent invisible function application theta over denominator g end fraction

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