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The x-t graph of a particle moving along a straight line is shown in figure The distance-time graph of the particle is correctly shown by

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The correct answer is:

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The x-t graph of a particle moving along a straight line is shown in figure The a-t graph of the particle is correctly shown by

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A particle of mass 1 kg is acted upon by a force 'F' which varies as shown in the figure. If initial velocity of the particle is 10 ms–1, the maximum velocity attained by the particle during the period is

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The acceleration of a particle which moves along the positive x-axis varies with its position as shown. If the velocity of the particle is 0.8 m/s at x = 0, the velocity of the particle at x = 1.4 is (in m/s)

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A man moves in x-y plane along the path shown. At what point is his average velocity vector in the same direction as his instantaneous velocity vector. The man starts from point P

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Acceleration versus velocity graph of a particle moving in a straight line starting from rest is as shown in figure. The corresponding velocity-time graph would be

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If position time graph of a particle is sine curve as shown, what will be its velocity-time graph

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The value of not stretchy integral subscript negative 2 end subscript superscript 3 end superscript vertical line 1 minus x to the power of 2 end exponent vertical line d x is‐

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If I subscript n end subscript equals not stretchy integral subscript 0 end subscript superscript pi divided by 4 end superscript t a n to the power of n end exponent blank x d x then the value of n left parenthesis I subscript n minus 1 end subscript plus I subscript n plus 1 end subscript right parenthesis is‐

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Statement‐I:: not stretchy sum subscript r equals 0 end subscript superscript n minus 1 end superscript fraction numerator 1 over denominator n end fraction left parenthesis square root of fraction numerator r over denominator n end fraction end root plus 1 right parenthesis less than not stretchy integral subscript 0 end subscript superscript 1 end superscript left parenthesis square root of x plus 1 right parenthesis d x less than not stretchy sum subscript r equals 1 end subscript superscript n end superscript fraction numerator 1 over denominator n end fraction left parenthesis square root of fraction numerator r over denominator n end fraction end root plus 1 right parenthesis comma n element of N.
Statement‐II:: If f left parenthesis x right parenthesis is continuous and increasing in left square bracket 0 , 1 right square bracket, then not stretchy sum subscript r equals 0 end subscript superscript n minus 1 end superscript fraction numerator 1 over denominator n end fraction f left parenthesis fraction numerator r over denominator n end fraction right parenthesis less than not stretchy integral subscript 0 end subscript superscript 1 end superscript f left parenthesisxXlx less than not stretchy sum subscript r equals 1 end subscript superscript n end superscript fraction numerator 1 over denominator n end fraction f left parenthesis fraction numerator r over denominator n end fraction right parenthesis , where n element of N

Statement‐I:: not stretchy sum subscript r equals 0 end subscript superscript n minus 1 end superscript fraction numerator 1 over denominator n end fraction left parenthesis square root of fraction numerator r over denominator n end fraction end root plus 1 right parenthesis less than not stretchy integral subscript 0 end subscript superscript 1 end superscript left parenthesis square root of x plus 1 right parenthesis d x less than not stretchy sum subscript r equals 1 end subscript superscript n end superscript fraction numerator 1 over denominator n end fraction left parenthesis square root of fraction numerator r over denominator n end fraction end root plus 1 right parenthesis comma n element of N.
Statement‐II:: If f left parenthesis x right parenthesis is continuous and increasing in left square bracket 0 , 1 right square bracket, then not stretchy sum subscript r equals 0 end subscript superscript n minus 1 end superscript fraction numerator 1 over denominator n end fraction f left parenthesis fraction numerator r over denominator n end fraction right parenthesis less than not stretchy integral subscript 0 end subscript superscript 1 end superscript f left parenthesisxXlx less than not stretchy sum subscript r equals 1 end subscript superscript n end superscript fraction numerator 1 over denominator n end fraction f left parenthesis fraction numerator r over denominator n end fraction right parenthesis , where n element of N

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not stretchy integral subscript 2 end subscript superscript 3 end superscript fraction numerator square root of x over denominator square root of left parenthesis 5 minus x right parenthesis end root plus square root of x end fraction d x equals

not stretchy integral subscript 2 end subscript superscript 3 end superscript fraction numerator square root of x over denominator square root of left parenthesis 5 minus x right parenthesis end root plus square root of x end fraction d x equals

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