Recent questions tagged p19

Find the rank of the following matrix :$\begin{bmatrix} 1 & -2 & 3 &4 \\-2 & 4 & -1 &-3 \\-1 & 2 & 7 &6 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the rank of the following matrix :$\begin{bmatrix} 1 & 2 & -1 &3 \\2 & 4 & 1 &-2 \\3 & 6 & 3 &-7 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the rank of the following matrix :$\begin{bmatrix} 0 & 1 & 2 &1 \\2 & -3 & 0 &-1 \\1 & 1 & -1 & 0 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the rank of the following matrix :$\begin{bmatrix} 3 & 1 & 2 &0 \\1 & 0 & -1 &0 \\2 & 1 & 3 &0 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the rank of the following matrix :$\begin{bmatrix} 6 & 12 & 6 \\1 & 2 & 1 \\4 & 8 & 4 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the rank of the following matrix :$\begin{bmatrix} 1 & 1 & -1 \\3 & -2 & 3 \\2 & -3 & 4 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

A point on the hypotenuse of a right angled triangle is at distances a and b from the sides. Show that the length of the hypotenuse is at least $ \bigg(a^{2/3}+b^{2/3}\bigg)^{3/2}$

asked Jan 29, 2013 by meena.p

0 answers

Show that the height of the cone of maximum volume that can be inscribed in a sphere of radius 12 cm is 16 cm.

asked Jan 29, 2013 by meena.p

0 answers

Find the maximum slope of the curve $ f(x)=2x+3x^2-x^3-27$

asked Jan 29, 2013 by meena.p

0 answers

Given the sum of the perimeters of a square and a circle show that the sum of their areas is least when the side of the square is equal to the diameter of a circle.

asked Jan 29, 2013 by meena.p

0 answers

Show that the semi vertical angle of the cone of maximum volume and of given slant height is $ \tan ^{-1} \sqrt 2$

asked Jan 29, 2013 by meena.p

0 answers

Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is $\Large\frac{8}{27}$ of the volume of the sphere.

asked Jan 29, 2013 by meena.p

0 answers

Show that the rectangle of maximum area that can be inscribed in a circle of radius 'r' cms is a square of side $\sqrt 2 r$

asked Jan 29, 2013 by meena.p

0 answers

Of all the rectangles each of which has perimeter 40 metres find one which has maximum area.Find the area also.

asked Jan 29, 2013 by meena.p

0 answers

Show that the height of the right circular cylinder of maximum volume that can be inscribed in a given right circular cone of height $h\; is\; h/3$

asked Jan 29, 2013 by meena.p

0 answers

Show that the volume of the greatest cylinder which can be inscribed in a cone of height h and semi vertical angle $ 30^\circ\;is\;\large\frac{4}{81}\pi h^3$

asked Jan 29, 2013 by meena.p

0 answers

A rectangular window is surmounted by an equilateral triangle. Given that the perimeter is 16 cm. Find the width of the window so that the maximum amount of light may enter.

asked Jan 29, 2013 by meena.p

0 answers

Find the area of the greatest isoscles triangle that can be inscribed in a given ellipse $ \Large\frac{x^2}{a^2}+\frac{y^2}{b^2}$=1 with its vertex coinciding with one extremity of the major axis.

asked Jan 29, 2013 by meena.p

0 answers

A window is in the form of a rectangle above which there is a semicircle. If the perimeter of the window is P cm. Show that the window will allow the maximum possible light only when the radius of the semi circle is $\large\frac{p}{\pi+4}cm$

asked Jan 29, 2013 by meena.p

0 answers

Show that the volume of greatest cylinder which can be inscribed in a cone of height h and semi vertical angle $\alpha\;is\;\frac{4}{27}\pi h^3\tan ^2\alpha$

asked Jan 29, 2013 by meena.p

0 answers

Find the absolute maximum and absolute minimum value of $ f(x)=2 \cos x+x \qquad x\in[0,\pi]$

asked Jan 29, 2013 by meena.p

0 answers

Show that the height of a cylinder of maximum volume that can be inscribed in a sphere of radius R is $ \Large\frac{2R}{\sqrt 3}$

asked Jan 29, 2013 by meena.p

0 answers

Show that the right circular cone of least curved surface area and given volume is $\sqrt 2 $ times the radius of the base.

asked Jan 29, 2013 by meena.p

0 answers

Let $f : R - \{ - \frac {4} {3} \} \to R $ be a function defined as $f(x)= \frac {4x} {3x+4} $ .The inverse of $f$ is the map $g$: Range $f \to R - \{ - \frac {4} {3} \} $ given by

asked Nov 19, 2012 by vaishali.a

1 answer

If $f: R\to R$ be given by $f(x)=(3-x^3)^\frac {1}{3} $, then $fof(x)$ is

asked Nov 19, 2012 by vaishali.a

1 answer

Let $f : X \to Y$ be an invertible function. Show that the inverse of $f^{-1}$ is $f$, i.e., $(f^{-1})^{-1} = f$.

asked Nov 16, 2012 by vaishali.a

1 answer

Consider$f:\{1,2,3\} \to\{a,b,c\}$ given by $f(1)=a, \,f(2)=b$ and $f(3)=c$. Find $f^{-1} $ and show that $(f^{-1})^{-1} = f$.

asked Nov 15, 2012 by vaishali.a

1 answer

Let $f : X \to Y$ be an invertible function. Show that $f$ has unique inverse.

asked Nov 15, 2012 by vaishali.a

1 answer

Consider $f:R_+ \to [\;\text{–5}, \infty )$given by $f(x)=9x^2 +6x$-$5$.Show that $f$ is invertible with $ f^{-1} (y) = \bigg(\frac{(\sqrt{y+6}) -1} { 3}\bigg) $

asked Nov 15, 2012 by vaishali.a

1 answer

Ask Questions, Get Answers

Find the rank of the following matrix :$\begin{bmatrix} 1 & -2 & 3 &4 \\-2 & 4 & -1 &-3 \\-1 & 2 & 7 &6 \end{bmatrix}$

Find the rank of the following matrix :$\begin{bmatrix} 1 & 2 & -1 &3 \\2 & 4 & 1 &-2 \\3 & 6 & 3 &-7 \end{bmatrix}$

Find the rank of the following matrix :$\begin{bmatrix} 0 & 1 & 2 &1 \\2 & -3 & 0 &-1 \\1 & 1 & -1 & 0 \end{bmatrix}$

Find the rank of the following matrix :$\begin{bmatrix} 3 & 1 & 2 &0 \\1 & 0 & -1 &0 \\2 & 1 & 3 &0 \end{bmatrix}$

Find the rank of the following matrix :$\begin{bmatrix} 6 & 12 & 6 \\1 & 2 & 1 \\4 & 8 & 4 \end{bmatrix}$

Find the rank of the following matrix :$\begin{bmatrix} 1 & 1 & -1 \\3 & -2 & 3 \\2 & -3 & 4 \end{bmatrix}$

A point on the hypotenuse of a right angled triangle is at distances a and b from the sides. Show that the length of the hypotenuse is at least $ \bigg(a^{2/3}+b^{2/3}\bigg)^{3/2}$

Show that the height of the cone of maximum volume that can be inscribed in a sphere of radius 12 cm is 16 cm.

Find the maximum slope of the curve $ f(x)=2x+3x^2-x^3-27$

Given the sum of the perimeters of a square and a circle show that the sum of their areas is least when the side of the square is equal to the diameter of a circle.

Show that the semi vertical angle of the cone of maximum volume and of given slant height is $ \tan ^{-1} \sqrt 2$

Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is $\Large\frac{8}{27}$ of the volume of the sphere.

Show that the rectangle of maximum area that can be inscribed in a circle of radius 'r' cms is a square of side $\sqrt 2 r$

Of all the rectangles each of which has perimeter 40 metres find one which has maximum area.Find the area also.

Show that the height of the right circular cylinder of maximum volume that can be inscribed in a given right circular cone of height $h\; is\; h/3$

Show that the volume of the greatest cylinder which can be inscribed in a cone of height h and semi vertical angle $ 30^\circ\;is\;\large\frac{4}{81}\pi h^3$

A rectangular window is surmounted by an equilateral triangle. Given that the perimeter is 16 cm. Find the width of the window so that the maximum amount of light may enter.

Find the area of the greatest isoscles triangle that can be inscribed in a given ellipse $ \Large\frac{x^2}{a^2}+\frac{y^2}{b^2}$=1 with its vertex coinciding with one extremity of the major axis.

A window is in the form of a rectangle above which there is a semicircle. If the perimeter of the window is P cm. Show that the window will allow the maximum possible light only when the radius of the semi circle is $\large\frac{p}{\pi+4}cm$

Show that the volume of greatest cylinder which can be inscribed in a cone of height h and semi vertical angle $\alpha\;is\;\frac{4}{27}\pi h^3\tan ^2\alpha$

Find the absolute maximum and absolute minimum value of $ f(x)=2 \cos x+x \qquad x\in[0,\pi]$

Show that the height of a cylinder of maximum volume that can be inscribed in a sphere of radius R is $ \Large\frac{2R}{\sqrt 3}$

Show that the right circular cone of least curved surface area and given volume is $\sqrt 2 $ times the radius of the base.

Let \(f : R - \{ - \frac {4} {3} \} \to R \) be a function defined as \(f(x)= \frac {4x} {3x+4} \) .The inverse of \(f\) is the map \(g\): Range \(f \to R - \{ - \frac {4} {3} \} \) given by

If $f: R\to R$ be given by $f(x)=(3-x^3)^\frac {1}{3} $, then $fof(x)$ is

Let \(f : X \to Y\) be an invertible function. Show that the inverse of $f^{-1}$ is $f$, i.e., $(f^{-1})^{-1} = f$.

Consider\(f:\{1,2,3\} \to\{a,b,c\}\) given by \(f(1)=a, \,f(2)=b\) and \(f(3)=c\). Find \(f^{-1} \) and show that \((f^{-1})^{-1} = f\).

Let \(f : X \to Y\) be an invertible function. Show that \(f\) has unique inverse.

Consider \(f:R_+ \to [\;\text{–5}, \infty )\)given by \(f(x)=9x^2 +6x\)-\(5\).Show that \(f\) is invertible with \( f^{-1} (y) = \bigg(\frac{(\sqrt{y+6}) -1} { 3}\bigg) \)