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Physics-

General

Easy

Question

A boat is moving with velocity of $3 stack i with hat on top plus 4 stack j with hat on top$ in river and water is moving with a velocity of $negative 3 stack i with hat on top minus 4 stack j with hat on top$ with respect to ground. Relative velocity of boat with respect to water is :

$- 6 \hat{i} - 8 \hat{j}$
$6 \hat{i} + 8 \hat{j}$
$8 \hat{i}$
$6 \hat{i}$

The correct answer is: $6 stack i with hat on top plus 8 stack j with hat on top$

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A man is 45 m behind the bus when the bus start accelerating from rest with acceleration 2.5 m/s² With what minimum velocity should the man start running to catch the bus?

A man is 45 m behind the bus when the bus start accelerating from rest with acceleration 2.5 m/s² With what minimum velocity should the man start running to catch the bus?

Physics-General

The position of a particle moving along the x-axis at certain times is given below :

Which of the following describes the motion correctly :

The position of a particle moving along the x-axis at certain times is given below :

Which of the following describes the motion correctly :

physics-General

For a moving body at any instant of time :

For a moving body at any instant of time :

Physics-General

parallel

The velocity of a body depends on time according to the equation u = 20 + 0.1t² The body is undergoing:

The velocity of a body depends on time according to the equation u = 20 + 0.1t² The body is undergoing:

Physics-General

If $integral s e c to the power of fraction numerator 4 over denominator 9 end fraction end exponent invisible function application x times c o s invisible function application e to the power of fraction numerator 14 over denominator 9 end fraction end exponent x d x equals a t a n to the power of b end exponent invisible function application x plus c$ then a+b= ___

If $integral s e c to the power of fraction numerator 4 over denominator 9 end fraction end exponent invisible function application x times c o s invisible function application e to the power of fraction numerator 14 over denominator 9 end fraction end exponent x d x equals a t a n to the power of b end exponent invisible function application x plus c$ then a+b= ___

The value of constant a>0 such that $stretchy integral subscript 0 end subscript superscript a end superscript open square brackets tan to the power of negative 1 end exponent invisible function application square root of x close square brackets d x equals stretchy integral subscript 0 end subscript superscript a end superscript open square brackets cot to the power of negative 1 end exponent invisible function application square root of x close square brackets d x$ where [.] denotes G.I.F is

The value of constant a>0 such that $stretchy integral subscript 0 end subscript superscript a end superscript open square brackets tan to the power of negative 1 end exponent invisible function application square root of x close square brackets d x equals stretchy integral subscript 0 end subscript superscript a end superscript open square brackets cot to the power of negative 1 end exponent invisible function application square root of x close square brackets d x$ where [.] denotes G.I.F is

parallel

Let $text end text f colon R to the power of plus end exponent rightwards arrow R$ be a differentiable function with $f left parenthesis A right parenthesis equals 3$ and satisfying $stretchy integral subscript 1 end subscript superscript x y end superscript f left parenthesis t right parenthesis d t equals y stretchy integral subscript 1 end subscript superscript x end superscript f left parenthesis t right parenthesis d t plus x stretchy integral subscript 1 end subscript superscript y end superscript f left parenthesis t right parenthesis d t for all x comma y element of R to the power of plus end exponent comma text then end text f left parenthesis x right parenthesis equals$

Let $text end text f colon R to the power of plus end exponent rightwards arrow R$ be a differentiable function with $f left parenthesis A right parenthesis equals 3$ and satisfying $stretchy integral subscript 1 end subscript superscript x y end superscript f left parenthesis t right parenthesis d t equals y stretchy integral subscript 1 end subscript superscript x end superscript f left parenthesis t right parenthesis d t plus x stretchy integral subscript 1 end subscript superscript y end superscript f left parenthesis t right parenthesis d t for all x comma y element of R to the power of plus end exponent comma text then end text f left parenthesis x right parenthesis equals$

Area bounded by the curve $y to the power of 2 end exponent equals x plus 4$ and the line x+2y=4 is _____ sq. units

Area bounded by the curve $y to the power of 2 end exponent equals x plus 4$ and the line x+2y=4 is _____ sq. units

Area of the figure contained between the parabola $x to the power of 2 end exponent equals 4 y$ and the curve $y equals fraction numerator 8 over denominator x to the power of 2 end exponent plus 4 end fraction text is end text 2 pi minus K$ then K=

Area of the figure contained between the parabola $x to the power of 2 end exponent equals 4 y$ and the curve $y equals fraction numerator 8 over denominator x to the power of 2 end exponent plus 4 end fraction text is end text 2 pi minus K$ then K=

parallel

The area bounded by mini $left parenthesis vertical line x vertical line comma vertical line y vertical line right parenthesis equals 2 text end text$ and $m a x left parenthesis vertical line x vertical line comma vertical line y vertical line right parenthesis equals 4 text is : end text$

The area bounded by mini $left parenthesis vertical line x vertical line comma vertical line y vertical line right parenthesis equals 2 text end text$ and $m a x left parenthesis vertical line x vertical line comma vertical line y vertical line right parenthesis equals 4 text is : end text$

$f left parenthesis x right parenthesis equals stretchy integral subscript 1 end subscript superscript x end superscript fraction numerator tan to the power of negative 1 end exponent invisible function application t over denominator t end fraction d t semicolon x greater than 0$ then the value of $f open parentheses e to the power of 2 end exponent close parentheses minus f open parentheses fraction numerator 1 over denominator e to the power of 2 end exponent end fraction close parentheses text is end text$

$f left parenthesis x right parenthesis equals stretchy integral subscript 1 end subscript superscript x end superscript fraction numerator tan to the power of negative 1 end exponent invisible function application t over denominator t end fraction d t semicolon x greater than 0$ then the value of $f open parentheses e to the power of 2 end exponent close parentheses minus f open parentheses fraction numerator 1 over denominator e to the power of 2 end exponent end fraction close parentheses text is end text$

$integral left parenthesis square root of c o t invisible function application x end root plus square root of t a n invisible function application x end root right parenthesis d x equals f left parenthesis x right parenthesis plus c text thenf end text left parenthesis x right parenthesis equals$

$integral left parenthesis square root of c o t invisible function application x end root plus square root of t a n invisible function application x end root right parenthesis d x equals f left parenthesis x right parenthesis plus c text thenf end text left parenthesis x right parenthesis equals$

parallel

If $text end text g left parenthesis x right parenthesis equals stretchy integral subscript 0 end subscript superscript x end superscript left parenthesis vertical line s i n invisible function application t vertical line plus vertical line c o s invisible function application t vertical line right parenthesis d t text then end text g open parentheses x plus fraction numerator n pi over denominator 2 end fraction close parentheses$ is equal to where $n element of N$

If $text end text g left parenthesis x right parenthesis equals stretchy integral subscript 0 end subscript superscript x end superscript left parenthesis vertical line s i n invisible function application t vertical line plus vertical line c o s invisible function application t vertical line right parenthesis d t text then end text g open parentheses x plus fraction numerator n pi over denominator 2 end fraction close parentheses$ is equal to where $n element of N$

If the primitive of $text end text s i n to the power of negative 3 divided by 2 end exponent invisible function application x s i n to the power of negative 1 divided by 2 end exponent invisible function application left parenthesis x plus theta right parenthesis text end text text is end text text end text minus 2 c o s e c invisible function application theta square root of f left parenthesis x right parenthesis end root plus C text end text$ then

If the primitive of $text end text s i n to the power of negative 3 divided by 2 end exponent invisible function application x s i n to the power of negative 1 divided by 2 end exponent invisible function application left parenthesis x plus theta right parenthesis text end text text is end text text end text minus 2 c o s e c invisible function application theta square root of f left parenthesis x right parenthesis end root plus C text end text$ then

$integral fraction numerator square root of s i n to the power of 3 end exponent invisible function application 2 x end root over denominator sin to the power of 5 end exponent invisible function application x end fraction d x text is end text$

$integral fraction numerator square root of s i n to the power of 3 end exponent invisible function application 2 x end root over denominator sin to the power of 5 end exponent invisible function application x end fraction d x text is end text$

parallel

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