Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

Consider the following statements $S$ and $R$ : S: Both $s i n blank$ x&cos $x$ are decreasing functions in the interval $left parenthesis pi divided by 2 comma pi right parenthesis$ .
R: If a differentiable function decreases in an interval $left parenthesis a comma blank b right parenthesis$ , then its derivative also decreases in $left parenthesis a comma blank b right parenthesis$ Which of the following is true ?

both $S$ and $R$ are wrong
both $S$ and $R$ are correct, but $R$ is not the correct explanation for $S$
$S$ is correct and $R$ is the correct explanation for $S$
$S$ is correct and $R$ is wrong.

The correct answer is: $S$ is correct and $R$ is wrong.

Related Questions to study

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank The two sides having fence are of same length $x$ The maximum area enclosed by the park is‐

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank The two sides having fence are of same length $x$ The maximum area enclosed by the park is‐

Let $y equals f left parenthesis x right parenthesis$ be a thrice derivable fu nction such that $f left parenthesis a right parenthesis f left parenthesis b right parenthesis less than 0 comma$ $f left parenthesis b right parenthesis f left parenthesis c right parenthesis less than 0 comma$ $f left parenthesis c right parenthesis f left parenthesis d right parenthesis less than 0$ where $a less than b less than c less than d blank$ Also the equations $f$ (x) $equals$ O& $f to the power of ’ ’ end exponent left parenthesis x right parenthesis equals 0$ have no common roots.
Statement‐I:: The equation $f left parenthesis x right parenthesis left parenthesis f to the power of ’ ’ end exponent left parenthesis x right parenthesis right parenthesis to the power of 2 end exponent plus f left parenthesis x right parenthesis f to the power of ’ end exponent left parenthesis x right parenthesis f to the power of ’ ’ ’ end exponent left parenthesis x right parenthesis plus left parenthesis f to the power of ’ end exponent left parenthesis x right parenthesis right parenthesis to the power of 2 end exponent f to the power of ’ ’ end exponent left parenthesis x right parenthesis equals 0$ has atleast 5 real roots.
Statement‐II:: The equation $f left parenthesis x right parenthesis equals 0$ has atleast 3 real distinct roots&if $f left parenthesis x right parenthesis equals 0$ has $k$ real distinct roots, then $f to the power of ´ end exponent left parenthesis x right parenthesis equals 0$ has atleast k‐l distinct roots.

Let $y equals f left parenthesis x right parenthesis$ be a thrice derivable fu nction such that $f left parenthesis a right parenthesis f left parenthesis b right parenthesis less than 0 comma$ $f left parenthesis b right parenthesis f left parenthesis c right parenthesis less than 0 comma$ $f left parenthesis c right parenthesis f left parenthesis d right parenthesis less than 0$ where $a less than b less than c less than d blank$ Also the equations $f$ (x) $equals$ O& $f to the power of ’ ’ end exponent left parenthesis x right parenthesis equals 0$ have no common roots.
Statement‐I:: The equation $f left parenthesis x right parenthesis left parenthesis f to the power of ’ ’ end exponent left parenthesis x right parenthesis right parenthesis to the power of 2 end exponent plus f left parenthesis x right parenthesis f to the power of ’ end exponent left parenthesis x right parenthesis f to the power of ’ ’ ’ end exponent left parenthesis x right parenthesis plus left parenthesis f to the power of ’ end exponent left parenthesis x right parenthesis right parenthesis to the power of 2 end exponent f to the power of ’ ’ end exponent left parenthesis x right parenthesis equals 0$ has atleast 5 real roots.
Statement‐II:: The equation $f left parenthesis x right parenthesis equals 0$ has atleast 3 real distinct roots&if $f left parenthesis x right parenthesis equals 0$ has $k$ real distinct roots, then $f to the power of ´ end exponent left parenthesis x right parenthesis equals 0$ has atleast k‐l distinct roots.

Statement‐I:: The largest term in the sequence $a subscript n end subscript equals fraction numerator n to the power of 2 end exponent over denominator 3 end fraction n element of N$ is the $7 to the power of t h end exponent$ term.
$n plus 200$ ’
Statement‐II:: The function $f left parenthesis x right parenthesis equals fraction numerator x to the power of 2 end exponent over denominator x to the power of 3 end exponent plus 200 end fraction$ attains local maxima at $x equals 7.$

Statement‐I:: The largest term in the sequence $a subscript n end subscript equals fraction numerator n to the power of 2 end exponent over denominator 3 end fraction n element of N$ is the $7 to the power of t h end exponent$ term.
$n plus 200$ ’
Statement‐II:: The function $f left parenthesis x right parenthesis equals fraction numerator x to the power of 2 end exponent over denominator x to the power of 3 end exponent plus 200 end fraction$ attains local maxima at $x equals 7.$

parallel

The area of the region bounded in first quadrant by $y equals x to the power of 1 divided by 3 end exponent semicolon y equals negative x to the power of 2 end exponent plus 2 x plus 3 semicolon y equals 2 x minus 1$ and the axis of ordinates is:

The area of the region bounded in first quadrant by $y equals x to the power of 1 divided by 3 end exponent semicolon y equals negative x to the power of 2 end exponent plus 2 x plus 3 semicolon y equals 2 x minus 1$ and the axis of ordinates is:

The area of the region bounded by the curve $a to the power of 4 end exponent y to the power of 2 end exponent equals left parenthesis 2 a minus x right parenthesis x to the power of 5 end exponent$ is to that of the circle whose radius is $a$ , is given by the ratio

The area of the region bounded by the curve $a to the power of 4 end exponent y to the power of 2 end exponent equals left parenthesis 2 a minus x right parenthesis x to the power of 5 end exponent$ is to that of the circle whose radius is $a$ , is given by the ratio

Statement‐I : The area of the curve $y equals s i n to the power of 2 end exponent x$ from $0$ to $pi$ will be more than that of curve $y equals s stack m with dot on top x$ from $0$ to $pi.$
Statement‐II : $t to the power of 2 end exponent greater than t$ if $t element of R minus left square bracket O comma blank 1 right square bracket.$

Statement‐I : The area of the curve $y equals s i n to the power of 2 end exponent x$ from $0$ to $pi$ will be more than that of curve $y equals s stack m with dot on top x$ from $0$ to $pi.$
Statement‐II : $t to the power of 2 end exponent greater than t$ if $t element of R minus left square bracket O comma blank 1 right square bracket.$

parallel

The area bounded by the curve y=f(x) , the $x$ ‐axis &the ordinates x=1 &x =b is (b‐l)sin $left parenthesis 3 b plus 4 right parenthesis$ Then f(x) is:

The area bounded by the curve y=f(x) , the $x$ ‐axis &the ordinates x=1 &x =b is (b‐l)sin $left parenthesis 3 b plus 4 right parenthesis$ Then f(x) is:

The value of $not stretchy integral subscript a end subscript superscript b end superscript left parenthesis x minus a right parenthesis to the power of 3 end exponent left parenthesis b blank short dash x right parenthesis$ 4dx is $fraction numerator left parenthesis b minus a right parenthesis to the power of m end exponent over denominator n end fraction$ Then $left parenthesis m comma blank n right parenthesis$ is

The value of $not stretchy integral subscript a end subscript superscript b end superscript left parenthesis x minus a right parenthesis to the power of 3 end exponent left parenthesis b blank short dash x right parenthesis$ 4dx is $fraction numerator left parenthesis b minus a right parenthesis to the power of m end exponent over denominator n end fraction$ Then $left parenthesis m comma blank n right parenthesis$ is

The tangent to the graph of the function $y equals f left parenthesis x right parenthesis$ at the point with abscissa $x equals 1$ form an angle of $pi divided by 6$ and at the point $x equals 2$ , an angle of $pi divided by 3$ and at the point $x equals 3$ , an angle of $pi divided by 4$ The value of $not stretchy integral subscript 1 end subscript superscript 3 end superscript f to the power of ’ end exponent left parenthesis x right parenthesis f to the power of ’ ’ end exponent left parenthesis x right parenthesis d x plus not stretchy integral subscript 2 end subscript superscript 3 end superscript f to the power of ’ ’ end exponent left parenthesis x right parenthesis d x$ ( $f to the power of ’ end exponent left parenthesis x right parenthesis$ is supposed to be continuous) is:

The tangent to the graph of the function $y equals f left parenthesis x right parenthesis$ at the point with abscissa $x equals 1$ form an angle of $pi divided by 6$ and at the point $x equals 2$ , an angle of $pi divided by 3$ and at the point $x equals 3$ , an angle of $pi divided by 4$ The value of $not stretchy integral subscript 1 end subscript superscript 3 end superscript f to the power of ’ end exponent left parenthesis x right parenthesis f to the power of ’ ’ end exponent left parenthesis x right parenthesis d x plus not stretchy integral subscript 2 end subscript superscript 3 end superscript f to the power of ’ ’ end exponent left parenthesis x right parenthesis d x$ ( $f to the power of ’ end exponent left parenthesis x right parenthesis$ is supposed to be continuous) is:

parallel

The integral $stretchy integral subscript negative fraction numerator 1 over denominator 2 end fraction end subscript superscript fraction numerator 1 over denominator 2 end fraction end superscript open parentheses left square bracket x right square bracket plus l n open parentheses fraction numerator 1 plus x over denominator 1 minus x end fraction close parentheses close parentheses d x$ equals‐

The integral $stretchy integral subscript negative fraction numerator 1 over denominator 2 end fraction end subscript superscript fraction numerator 1 over denominator 2 end fraction end superscript open parentheses left square bracket x right square bracket plus l n open parentheses fraction numerator 1 plus x over denominator 1 minus x end fraction close parentheses close parentheses d x$ equals‐

If $g left parenthesis x right parenthesis equals not stretchy integral subscript 0 end subscript superscript x end superscript blank c o s blank 4 t d t$ , then $g left parenthesis x plus pi right parenthesis$ equals :

If $g left parenthesis x right parenthesis equals not stretchy integral subscript 0 end subscript superscript x end superscript blank c o s blank 4 t d t$ , then $g left parenthesis x plus pi right parenthesis$ equals :

The figure shows a network of four resistances and three batteries Choose the correct alternative

The figure shows a network of four resistances and three batteries Choose the correct alternative

physics-General

parallel

The figure shows a network of resistances in which the point A is earthed.
The point which has the least potential is

The figure shows a network of resistances in which the point A is earthed.
The point which has the least potential is

physics-General

The figure shows a network of five resistances and two batteries The current through the 30V battery is

The figure shows a network of five resistances and two batteries The current through the 30V battery is

physics-General

If X, Y and Z in figure are identical lamps, which of the following changes to the brightnesses of the lamps occur when switch S is closed?

If X, Y and Z in figure are identical lamps, which of the following changes to the brightnesses of the lamps occur when switch S is closed?

physics-General

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.