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Question

The function $f open parentheses x close parentheses equals fraction numerator ln invisible function application left parenthesis pi plus x right parenthesis over denominator ln invisible function application left parenthesis e plus x right parenthesis end fraction comma$ is

Increasing on $[0, \infty)$
Decreasing on $[0, \infty)$
Increasing on $[0, π / e)$ and decreasing on $[π / e, \infty)$
Decreasing on $[0, π / e)$ and increasing on $[π / e, \infty)$

The correct answer is: Decreasing on $left square bracket 0 comma infinity right parenthesis$

Given, $f open parentheses x close parentheses equals cos invisible function application x plus cos invisible function application square root of 2 x$
$rightwards double arrow blank f to the power of ´ end exponent open parentheses x close parentheses equals negative sin invisible function application x minus square root of 2 sin invisible function application square root of 2 x$

$rightwards double arrow blank f to the power of ´ ´ end exponent open parentheses x close parentheses equals negative cos invisible function application x minus 2 cos invisible function application square root of 2 x$

For extremum value, put $f to the power of ´ end exponent open parentheses x close parentheses equals 0$

$rightwards double arrow blank minus sin invisible function application x minus square root of 2 sin invisible function application square root of 2 x equals 0 blank rightwards double arrow blank x equals 0$

$therefore$ At $x equals 0 comma blank f to the power of ´ ´ end exponent open parentheses x close parentheses less than 0$ , maxima

$therefore blank f left parenthesis x right parenthesis$ Is maximum only once.

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The circumference of a circle is measured as 28 cm with an error of $0.01$ cm. The percentage error in the area is

The circumference of a circle is measured as 28 cm with an error of $0.01$ cm. The percentage error in the area is

The number of values of $x$ where $f open parentheses x close parentheses equals cos invisible function application x plus cos invisible function application square root of 2 x$ attains its maximum is

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A function $f$ is defined by $f open parentheses x close parentheses equals 2 plus open parentheses x minus 1 close parentheses to the power of 2 divided by 3 end exponent$ in [0, 2]. Which of the following is not correct?

A function $f$ is defined by $f open parentheses x close parentheses equals 2 plus open parentheses x minus 1 close parentheses to the power of 2 divided by 3 end exponent$ in [0, 2]. Which of the following is not correct?

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q₁, q₂ , q₃ and q₄ are point charges located at points as shown in the figure and S is a spherical Gaussian surface of radius R. Which of the following is true according to the Gauss’s law?

q₁, q₂ , q₃ and q₄ are point charges located at points as shown in the figure and S is a spherical Gaussian surface of radius R. Which of the following is true according to the Gauss’s law?

Let $f open parentheses x close parentheses equals square root of x minus 1 end root plus square root of x plus 24 minus 10 square root of x minus 1 end root end root comma blank 1 less or equal than x less or equal than 26$ be real valued function, then $f to the power of ´ end exponent left parenthesis x right parenthesis$ for $1 less than x less than 26$ is

Let $f open parentheses x close parentheses equals square root of x minus 1 end root plus square root of x plus 24 minus 10 square root of x minus 1 end root end root comma blank 1 less or equal than x less or equal than 26$ be real valued function, then $f to the power of ´ end exponent left parenthesis x right parenthesis$ for $1 less than x less than 26$ is

The minimum value of $2 log subscript 10 end subscript invisible function application x minus log subscript x end subscript invisible function application 0.01 comma blank x greater than 1$ , is

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Let $f colon R ⟶ R blank$ be defined by $f open parentheses x close parentheses equals open curly brackets table row cell k minus 2 x comma blank i f blank x less or equal than negative 1 end cell row cell 2 x plus 3 comma blank i f x greater than negative 1 blank end cell end table close$
If $f$ has a local minimum at $x equals negative 1 comma blank t h e n blank a blank p o s s i b l e blank v a l u e blank o f blank k blank i s$

Let $f colon R ⟶ R blank$ be defined by $f open parentheses x close parentheses equals open curly brackets table row cell k minus 2 x comma blank i f blank x less or equal than negative 1 end cell row cell 2 x plus 3 comma blank i f x greater than negative 1 blank end cell end table close$
If $f$ has a local minimum at $x equals negative 1 comma blank t h e n blank a blank p o s s i b l e blank v a l u e blank o f blank k blank i s$

The slope of the tangent to the curve $y equals cos to the power of negative 1 end exponent invisible function application left parenthesis cos invisible function application x right parenthesis a t blank x equals negative fraction numerator pi over denominator 4 end fraction$ , is

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The function $f open parentheses x close parentheses equals x to the power of 2 end exponent e to the power of negative x end exponent$ increases in the interval

The function $f open parentheses x close parentheses equals x to the power of 2 end exponent e to the power of negative x end exponent$ increases in the interval

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The equation of tangent to the curve $y equals b e to the power of negative x divided by a end exponent$ at the point where it crosses $blank y minus$ axis, is

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Then the equation $f to the power of ´ end exponent open parentheses x close parentheses equals 0$

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