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Recent questions tagged p18
Questions
If the curve $ y^{2}=x$ and $xy=k$ are orthogonal than prove that $8k^{2}=1.$
tnstate
class12
bookproblem
ch5
sec-1
exercise5-2
p18
q11
modelpaper
mar-2009
asked
May 3, 2013
by
poojasapani_1
1
answer
Show that the equation of the normal to the curve $x=a\cos^{3}\theta ; y=a\sin^{3}\theta$ at $\;'\theta'$ is$\; x\cos\theta-y\cos\theta=a\cos 2\theta.$
tnstate
class12
bookproblem
ch5
sec-1
exercise5-2
p18
q10
modelpaper
oct-2006
asked
May 3, 2013
by
poojasapani_1
1
answer
At what angle $\theta $ do the curves $y=a^{x}$ and $y=b^{x}$ intersect $(a{\neq}b)$?
tnstate
class12
bookproblem
ch5
sec-1
exercise5-2
p18
q9
asked
May 3, 2013
by
poojasapani_1
1
answer
Prove that the curve $2x^{2}+4y^{2}=1$ and $6x^{2}-12y^{2}=1$ cut each other at right angles.
tnstate
class12
bookproblem
ch5
sec-1
exercise5-2
p18
q8
modelpaper
jun-2008
asked
May 3, 2013
by
poojasapani_1
1
answer
Let $P$ be a point on the curve $y=x^{3}$ and suppose that the tangent line at $P$ intersects the curve again at $Q$. Prove that the slope at $Q$ is four times the slope at $P$.
tnstate
class12
bookproblem
ch5
sec-1
exercise5-2
p18
q7
modelpaper
oct-2007
mar-2010
asked
May 3, 2013
by
poojasapani_1
1
answer
Find the equations of normal to $y=x^{3}-3x$ that is parallel to $2x+18y-9=0.$
tnstate
class12
bookproblem
ch5
sec-1
exercise5-2
p18
q6
asked
May 3, 2013
by
poojasapani_1
1
answer
Find the equations of those tangents to the circle $x^{2}+y^{2}=52,$ which are parallel to the straight line $2x+3y=6$.
tnstate
class12
bookproblem
ch5
sec-1
exercise5-2
p18
q5
asked
May 3, 2013
by
poojasapani_1
1
answer
At what points on the curve $x^{2}+y^{2}-2x-4y+1=0$ the tangent is parallel to $y$- axis.
tnstate
class12
bookproblem
ch5
sec-1
exercise5-2
p18
q4
q4-2
asked
May 3, 2013
by
poojasapani_1
1
answer
At what points on the curve $x^{2}+y^{2}-2x-4y+1=0$ the tangent is parallel to $x$- axis.
tnstate
class12
bookproblem
ch5
sec-1
exercise5-2
p18
q4
q4-1
asked
May 3, 2013
by
poojasapani_1
1
answer
Find at what points on the circle $x^{2}+y^{2}=13$, the tangent is parallel to the line $2x+3y=7$.
tnstate
class12
bookproblem
ch5
sec-1
exercise5-2
p18
q3
asked
May 3, 2013
by
poojasapani_1
1
answer
Find the point on curve $x^{2}-y^{2}=2$ at which the slope of the tangent is $2$
tnstate
class12
bookproblem
ch5
sec-1
exercise5-2
p18
q2
asked
May 1, 2013
by
poojasapani_1
1
answer
Find the equation of the tangent and normal to the curves.$ \;y=\large\frac{1+\sin x}{\cos x}$ at $\;x=\large\frac{\pi}{4}$
tnstate
class12
bookproblem
ch5
sec-1
exercise5-2
p18
q1
q1-4
asked
May 1, 2013
by
poojasapani_1
1
answer
Find the equation of the tangent and normal to the curves.$\;y=2\sin^{2} 3x$ at $\;x=\large\frac{\pi}{6}$
tnstate
class12
bookproblem
ch5
sec-1
exercise5-2
p18
q1
q1-3
asked
May 1, 2013
by
poojasapani_1
1
answer
Find the equation of the tangent and normal to the curves.$\;y=x-\sin x\cos x, $at$\;x=\large\frac{\pi}{2}$
tnstate
class12
bookproblem
ch5
sec-1
exercise5-2
p18
q1
q1-2
asked
May 1, 2013
by
poojasapani_1
1
answer
Find the equation of the tangent and normal to the curves. $y=x^{2}-4x-5$ at $\;x=-2$
tnstate
class12
bookproblem
ch5
sec-1
exercise5-2
p18
q1
q1-1
asked
May 1, 2013
by
poojasapani_1
1
answer
State with reason whether following functions have inverse: (ii) \(g: \{ 5,6,7,8\} \to \{1,2,3,4\}\) with \(g= \{(5,4),(6,3),(7,4),(8,2)\}\)
cbse
class12
ch1
sec3
p18
sec-a
bookproblem
q5
q5-2
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
State with reason whether following functions have inverses: (i) \( f: \{ 1,2,3,4,\} \to \{10\}\) with \( f= \{(1,10),(2,10),(3,10), (4,10)\}\)
class12
cbse
ch1
sec3
q5
q5-1
easy
sec-a
p18
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
Find $ gof$ and $fog$, if $f(x) = 8x^3$ and $g(x)=x^\frac{1}{3}$
cbse
class12
bookproblem
ch1
sec3
q3
q3-2
p18
sec-a
easy
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
Find \( gof\) and \(fog\), if (ii) \( f(x) = 8x^3\) and \( g(x) = x ^ \frac { 1} {3} \)
cbse
class12
bookproblem
ch1
sec3
q3
q3-2
p18
math
asked
Mar 7, 2013
by
meena.p
1
answer
Find $ gof$ and $fog$, if $ f(x) = |\;x\;|$ , and $ g(x) = |\;5x-2\;| $
cbse
class12
bookproblem
ch1
sec3
q3
q3-1
p18
sec-a
easy
math
asked
Mar 7, 2013
by
meena.p
1
answer
Show that the semi vertical angle of a right circular cone of given total surface area and maximum volume is $\sin^{-1} \frac{1}{3}$
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q39
p18
math
asked
Jan 29, 2013
by
meena.p
0
answers
Show that the semi vertical angle of a right circular cone of maximum volume and given slant height is $\tan^{-1}\sqrt 2$
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q38
p18
math
asked
Jan 29, 2013
by
meena.p
0
answers
Find the points on the curve $ y=x^3-3x^2+2x$ at which the tangent to the curve is parallel to the line $ y-2x+3=0$
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q37
p18
math
asked
Jan 29, 2013
by
meena.p
0
answers
Prove that the curves $ y^2=4ax\;and\;xy=c^2$ cut at right angles if $ c^4=32a^4$
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q36
p18
math
asked
Jan 29, 2013
by
meena.p
0
answers
Find the equation of all lines having slope -1 and that are tangents to the curve $ y=\Large\frac{1}{x-1}, \normalsize x\neq1$
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q35
p18
math
asked
Jan 29, 2013
by
meena.p
0
answers
Find the point on the curve $ y=x^3-11x+5 $ at which the tangent has equation $y=x-11$
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q34
p18
math
asked
Jan 29, 2013
by
meena.p
0
answers
Find the equation of tangent to the curve $\sqrt x+\sqrt y=\sqrt a $ at the point $(x_1,y_1)$ and show that the sum of its intercepts on the axes is constant.
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q33
p18
math
asked
Jan 29, 2013
by
meena.p
0
answers
Find the interval in which the function f(x) is increasing or decreasing $ f(x)=x^3-12 x^2+36x+17 $
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q32
p18
math
asked
Jan 29, 2013
by
meena.p
0
answers
A cone is circumscribed about a sphere of radius r. Show that the volume of the cone is maximum when its semi vertical angle is $\sin^{-1}\bigg(\Large\frac{1}{3}\bigg)$
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q31
p18
math
asked
Jan 29, 2013
by
meena.p
0
answers
What angle is formed by the y-axis and the tangent to the parabola $ y=x^2+4x-17$ at the point $ p(5/2,-3/4)?$
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q30
p18
math
asked
Jan 29, 2013
by
meena.p
0
answers
If $ P_1\;and\; P_2 $are the lengths of the perpendiculars from origin on the tangent and normal to the curve $ x^{2/3}+y^{2/3}=a^{2/3} $respectively Prove that $ 4P_1^2+P_2^2=a^2$
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q29
p18
math
asked
Jan 29, 2013
by
meena.p
0
answers
Find the equation of normal to the curve $ y=(1+x)^y+\sin^{-1}(\sin^2x)$ at x=0
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q28
p18
math
asked
Jan 29, 2013
by
meena.p
0
answers
Find the interval in which the following functions are increasing or decreasing\[(a)\;y=log \bigg(x+\sqrt{1+x^2}\bigg)\qquad(b)\;y=\frac{10}{4x^3-9x^2+6x}\]
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q27
p18
math
asked
Jan 29, 2013
by
meena.p
0
answers
Determine the points of maxima and minima of the function $ f(x)= \frac{1}{8}log x-bx+cx^2\; where\; b \geq 0$
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q26
p18
math
asked
Jan 29, 2013
by
meena.p
0
answers
The least value of $ f(x)=\tan -1(\sin x+cos x)$ strictly increasing is \[(a)\;\bigg(\frac{\pi}{4},\frac{\pi}{2}\bigg)\qquad(b)\;\bigg(0,\frac{\pi}{2}\bigg)\qquad(c)\;0\qquad(d)\;none\; of\; these.\]
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q25
p18
math
asked
Jan 29, 2013
by
meena.p
0
answers
Consider \( f:R_+ \to [4,\infty)\)given by \(f(x)=x^2 +4\). Show that \(f\) is invertible with the inverse \(f^{-1}\)of \(f\) given by \(f^{-1}(y) = \sqrt {y-4}\),where $R_+$ is the set of all non-negative real numbers.
cbse
class12
bookproblem
ch1
sec3
q8
p18
medium
sec-b
math
asked
Nov 14, 2012
by
vaishali.a
1
answer
Consider $f:R \to R$ given by $f(x)=4x+3$. Show that $f$ is invertible. Find the inverse of $ f$
cbse
class12
bookproblem
ch1
sec3
q7
p18
medium
sec-b
math
asked
Nov 14, 2012
by
vaishali.a
1
answer
Show that $f : [-1,1]$ $ \rightarrow R$, given by $f(x) =\frac {x } { (x+2)}$ is one-one. Find the inverse of of the $f : [-1,1] \rightarrow $ Range $ f$.
cbse
class12
bookproblem
ch1
sec3
q6
p18
medium
sec-b
math
asked
Nov 14, 2012
by
vaishali.a
1
answer
State with reason whether following functions have inverse: (iii) \(h: \{2,3,4,5,\} \to \{7,9,11,13\}\) with \(h=\{(2,7),(3,9),(4,11),(5,13) \} \)
cbse
class12
bookproblem
ch1
sec3
q5
p18
q5-3
sec-a
easy
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
If $f(x) = \frac { (4x+3) } { (6x-4) }, x \neq \frac {2} {3}$, show that $ f(x) =x $, for all $ x \neq \frac {2} {3}$. What is the inverse of $f$
cbse
class12
bookproblem
ch1
sec3
q4
p18
medium
sec-b
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
Find \( gof\) and \(fog\), if (i) \( f(x) = |\;x\;| \, and \, g(x) = |\;5x-2\;| \)
cbse
class12
bookproblem
ch1
sec3
q3
q3-1
p18
easy
sec-a
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
Let \(f,\, g\, and\, h\) be functions from \(R\, to\, R.\) Show that \[ (f+g) oh = foh + goh\]
cbse
class12
bookproblem
ch1
sec3
q2
p18
easy
sec-a
q2-1
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
Let $f:\{1,3,4\} \to \{1,2,5\} $ and $g:\{1,2,5\}\to\{1,3\}$ be given by $f = \{(1, 2), (3, 5), (4, 1)\}$ and $ g = \{(1, 3), (2, 3), (5, 1)\}$. Write down $gof$.
cbse
class12
bookproblem
ch1
sec3
q1
p18
easy
sec-a
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
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