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Maths-

General

Easy

Question

Let $I equals stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator sin invisible function application x over denominator square root of x end fraction d x text and end text J equals stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator cos invisible function application x over denominator square root of x end fraction d x text . end text$ Then which one of the following is true ?

$I > \frac{2}{3} and J > 2$
$I < \frac{2}{3} and J < 2$
$I < \frac{2}{3} and J > 2$
$I > \frac{2}{3} and J < 2$

The correct answer is: $I less than fraction numerator 2 over denominator 3 end fraction text and end text J less than 2$

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$text Iff end text text . end text minus y minus e to the power of y end exponent comma g comma negative y minus y comma y greater than 0 text end text$ andE.. $t minus stretchy integral subscript 0 end subscript superscript t end superscript f left parenthesis t minus y right parenthesis g left parenthesis y right parenthesis d y text , end text$ then-

$text Iff end text text . end text minus y minus e to the power of y end exponent comma g comma negative y minus y comma y greater than 0 text end text$ andE.. $t minus stretchy integral subscript 0 end subscript superscript t end superscript f left parenthesis t minus y right parenthesis g left parenthesis y right parenthesis d y text , end text$ then-

If for a non-zero x, af $x plus b f open parentheses fraction numerator 1 over denominator x end fraction close parentheses equals fraction numerator 1 over denominator x end fraction minus 5 text , end text$ where $a to the power of not equal to end exponent b text , end text$ then $stretchy integral subscript 1 end subscript superscript 2 end superscript$ f(x)dx=

If for a non-zero x, af $x plus b f open parentheses fraction numerator 1 over denominator x end fraction close parentheses equals fraction numerator 1 over denominator x end fraction minus 5 text , end text$ where $a to the power of not equal to end exponent b text , end text$ then $stretchy integral subscript 1 end subscript superscript 2 end superscript$ f(x)dx=

Which of the following is correct?

Which of the following is correct?

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In the thermal power stations, electricity is produced by producing heat energy from the burning of coal. This is an example of ..

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physics-General

A pendulum bob is swinging in a vertical plane such that its angular amplitude is less than 900 . At its highest point, the string is cut. Which trajectory is possible for the bob afterwards.

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Find the acceleration of 3 kg mass when acceleration of 2 kg mass is 2 ms^–2 as shown in figure.

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physics-General

A rope of mass 5 kg is moving vertically in vertical position with an upwards force of 100 N acting at the upper end and a downwards force of 70 N acting at the lower end. The tension at midpoint of the rope is

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A ball is hit by a batsman at an angle of 37° as shown in figure. The man standing at P should run at what minimum velocity so that he catches the ball before it strikes the ground. Assume that height of man is negligible in comparison to maximum height of projectile.

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