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Recent questions tagged ch6
Questions
Find the dimentions of the rectangle of perimeter 36cm which will sweep out a volume as large as possible,when revolved about one of its sides.Also find the maximum volume.
cbse
class12
ch6
q30
p137
exemplar
sec-c
medium
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
An open box with square base is to be made of a given quantity of card board of area $ c^2$.Show that the maximum volume of the box is $\Large \frac{c^3}{6\sqrt 3}$ cubic units.
cbse
class12
ch6
q29
p137
exemplar
medium
sec-c
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
If the straight line $x\cos\alpha+y\sin\alpha=p$ touches the curve $\Large\frac{x^2}{a^2}\;\;\frac{y^2}{b^2}=\normalsize 1$,then prove that $a^2\cos^2\alpha+b^2\sin^2\alpha=p^2$.
cbse
class12
ch6
q28
p137
exemplar
math
sec-b
asked
Jan 11, 2013
by
sreemathi.v
0
answers
A telephone company in a town has 500 subscribers on its list and collects fixed charges of Rs300/- per subscriber per year.The company proposes to increase the annual subscription and it is believed that for every increase of Re1/- one subscriber will discontinue the service.Find what increase will bring maximum profit?
cbse
class12
ch6
q27
p137
exemplar
math
sec-b
asked
Jan 11, 2013
by
sreemathi.v
0
answers
Find the points of local maxima,local minima and the points of inflection of the function $f(x)=x^5-5x^4+5x^3-1$. Also find the corresponding local maximum and local minimum values.
cbse
class12
ch6
q26
p137
exemplar
medium
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
If the sum of the lengths of the hypotenuse and a side of a right angled triangle is given,show that the area of the triangle is maximum when the angle between them is $\Large \frac{1}{3}$
cbse
class12
ch6
q25
p137
exemplar
medium
sec-c
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Prove that $f(x)=\sin x+\sqrt 3\cos x$ has maximum value at $x=\Large\frac{1}{6}$.
cbse
class12
ch6
q24
p137
short-answer
exemplar
easy
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
At what point,the slope of the curve $y=-x^3+3x^2+9x-27$ is maximum?Also find the maximum slope.
cbse
class12
ch6
q23
p137
short-answer
exemplar
easy
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Show that $f(x)=\tan^{-1}(\sin x+\cos x)$ is an increasing function in$\bigg(0,\Large \frac{1}{4}\normalsize \bigg).$
cbse
class12
ch6
q22
p137
short-answer
exemplar
medium
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Show that for a$\quad 1,f(x)=\sqrt 3\sin x-\cos x-2ax+b$ is decreasing in R.
cbse
class12
ch6
q21
p137
short-answer
exemplar
medium
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Show that $f(x)=2x+\cot^{-1}x+log\bigg(\sqrt {(1+x^2)}-x\bigg)$ is increasing in R.
cbse
class12
ch6
q20
p136
short-answer
exemplar
difficult
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Show that the line $\Large \frac{x}{a}+\frac{y}{b}\normalsize=1$,touches the curve $y=b.e^{\Large \frac{-x}{a}}$ at the point where the curve intersects the axis of y.
cbse
class12
ch6
q19
p136
short-answer
exemplar
medium
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
At what points on the curve $x^2+y^2-2x+4y+1=0$,the tangents are parallel to the y-axis?
cbse
class12
ch6
q18
p136
short-answer
exemplar
easy
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Find the equation of the normal lines to the curve $3x^2-y^2=8$ which are parallel to the line x+3y=4.
cbse
class12
ch6
q17
p136
short-answer
exemplar
difficult
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Prove that the curves $y^2=4x$ and $x^2+y^2-6x+1=0$ touch each other at the point (1,2).
cbse
class12
ch6
q16
p136
short-answer
exemplar
difficult
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Find the angle of intersection of the curves $y=4-x^2$ and $y=x^2$.
cbse
class12
ch6
q15
p136
short-answer
exemplar
medium
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Find the co-ordinates of the point on the curve $\sqrt x\quad \sqrt y=4$ at which tangent is equally inclined to the axes.
cbse
class12
ch6
q14
p136
short-answer
exemplar
medium
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Prove that the curves $xy=4$ and $x^2+y^2=8$ touch each other.
cbse
class12
ch6
q13
p136
short-answer
exemplar
medium
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Find the condition that the curves $2x=y^2$ and $2xy=k$ intersect orthogonally.
cbse
class12
ch6
q12
p136
short-answer
exemplar
difficult
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
x and y are the sides of two squares such that $y=x-x^2$.Find the rate of change of the area of second square with respect to the area of first square.
cbse
class12
ch6
q11
p136
short-answer
exemplar
easy
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
The volume of a cube increases at a constant rate.Prove that the increase in its surface area varies inversely as the length of the side.
cbse
class12
ch6
q10
p136
short-answer
exemplar
medium
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
A swimming pool is to be drained for cleaning .If L represents the number of litres of water in the pool seconds after the pool has been plugged off to drain and $L=200(10-t)^2$.How fast is the water running out at the end of 5 seconds?What is the average rate at which the water flows out during the first 5 seconds?
cbse
class12
ch6
q9
p136
short-answer
exemplar
medium
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
A man, 2m tall, walks at the rate of $1\frac{2}{3}m/s$ towards a street light which is $5\frac{1}{3}m$ above the ground.At what rate is the tip of his shadow moving?At what rate is the length of the shadow changing when he is $3\frac{1}{3}m$ from the base of the light?
cbse
class12
ch6
q8
p135
short-answer
exemplar
difficult
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Find the approximate volume of metal in a hollow spherical shell whose internal and external radii are 3cm and 3.0005cm,respectively.
cbse
class12
ch6
q7
p135
short-answer
exemplar
easy
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
FInd the approximate value of $(1.999)^5$.
cbse
class12
ch6
q6
p135
short-answer
exemplar
easy
sec-a
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Find an angle $\theta$,$0$ <$\;\theta<\Large \frac{1}{2}$,which increases twice as fast as its sine.
cbse
class12
ch6
q5
p135
short-answer
exemplar
easy
sec-a
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Two men A and B start with velocities v at the same time from the junction of two roads inclined at $45^\circ$ to each other.If they travel by different roads,find the rate at which they are being separated.
cbse
class12
ch6
q4
p135
short-answer
exemplar
difficult
sec-b
math
asked
Jan 10, 2013
by
sreemathi.v
1
answer
A kite is moving horizontally at a height of 151.5 meters If the speed of kite is 10m/s,how fast is the string being let out,when the kite is 250m away from the boy who is flying the kite?The height of boy is 1.5m
cbse
class12
ch6
q3
p135
short-answer
exemplar
medium
sec-b
math
asked
Jan 10, 2013
by
sreemathi.v
1
answer
If the area of a circle increases at a uniform rate,then prove that perimeter varies inversely as the radius.
cbse
class12
ch6
q2
p135
short-answer
exemplar
easy
sec-a
math
asked
Jan 10, 2013
by
sreemathi.v
1
answer
A spherical ball of salt is dissolving in water in such a manner that the rate of decrease of the surface.Prove that the radius is decreasing at a constant rate.
cbse
class12
ch6
q1
p135
short-answer
exemplar
easy
sec-a
math
asked
Jan 10, 2013
by
sreemathi.v
1
answer
The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rate of change of (a) the perimeter, (b) the area of the rectangle.
cbse
class12
modelpaper
2012
sec-b
q15
difficult
ch6
math
asked
Jan 4, 2013
by
thanvigandhi_1
1
answer
Choose the correct answer in the points on the curve \(9y^2 = x^3\), where the normal to the curve makes equal intercepts with the axes are
cbse
class12
bookproblem
ch6
misc
q24
p244
sec-b
easy
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the normal to the curve \(x^2 = 4y\) passing \((1,2)\) is
cbse
class12
bookproblem
ch6
misc
q23
p244
sec-c
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the normal at the point \((1,1)\) on the curve \(2y + x^2 = 3\) is
cbse
class12
bookproblem
ch6
misc
q22
p244
sec-a
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the line \(y = mx + 1\) is a tangent to the curve \(y^2 = 4x\) if the value of \(m\) is
cbse
class12
bookproblem
ch6
misc
q21
p244
sec-b
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the slope of the tangent to the curve \(x = t^2 + 3t – 8, y = 2t^2 – 2t – 5\) at the point \((2,– 1)\) is
cbse
class12
bookproblem
ch6
misc
q20
p243
sec-b
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in a cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of
cbse
class12
bookproblem
ch6
misc
q19
p243
sec-a
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height \(h\) and semi vertical angle $\alpha$ is one-third that of the cone and the greatest volume of cylinder is $\large \frac{4}{27}$$\pi h^3 \: tan^2 \: \alpha $
cbse
class12
bookproblem
ch6
misc
q18
p243
sec-c
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is \(\large\frac{2R}{\sqrt 3}\) . Also find the maximum volume.
cbse
class12
bookproblem
ch6
misc
q17
p243
sec-c
difficult
math
asked
Nov 28, 2012
by
thanvigandhi_1
2
answers
Let \(f\) be a function defined on \([a, b]\) such that \(f' (x) > 0\), for all \(x \: \in (a, b)\). Then prove that \(f\) is an increasing function on \((a, b).\)
cbse
class12
bookproblem
ch6
misc
q16
p243
sec-b
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius \(r\) is \( \large\frac{4r}{3}\)
cbse
class12
bookproblem
ch6
misc
q15
p243
sec-b
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Find the absolute maximum and minimum values of the function $(f)$ given by $ f (x) = cos^2 x + sin\: x, x\: \in [0, \pi]$
cbse
class12
bookproblem
ch6
misc
q14
p243
sec-b
easy
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Find the points at which the function \(f\) given by \(f (x) = (x – 2)^4 (x + 1)^3\) has a (i) local maxima, (ii) local minima and the (iii) point of inflexion.
cbse
class12
bookproblem
ch6
misc
q13
p243
sec-b
easy
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
A point on the hypotenuse of a triangle is at distance \(a\) and \(b\) from the sides of the triangle.Show that the maximum length of the hypotenuse is $ (a^{\large\frac{2}{3}} + $$b^{\large\frac{2}{3}})^{\Large\frac{3}{2}}$
cbse
class12
bookproblem
ch6
misc
q12
p243
sec-c
difficult
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.
cbse
class12
bookproblem
ch6
misc
q11
p243
sec-c
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
The sum of the perimeter of a circle and square is \(k\), where \(k\) is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.
cbse
class12
bookproblem
ch6
misc
q10
242
sec-b
easy
modelpaper-2014
modelpaper-2012
q28
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is $2 m$ and volume is $8 m^3$. If building of tank costs Rs 70 per sq metres for the base and Rs 45 per square metre for sides. What is the cost of least expensive tank?
cbse
class12
bookproblem
ch6
misc
q9
p242
sec-c
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Find the maximum area of an isosceles triangle inscribed in the ellipse $\large\frac{x^2}{a^2} + \frac{y^2}{b^2} $$= 1 $ with its vertex at one end of the major axis.
cbse
class12
bookproblem
ch6
misc
q8
p242
sec-b
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
2
answers
Find the intervals in which the function \(f\) given by $f(x) = x^3 + \large\frac{1}{x^3}$$, x \neq 0$ is $(i) \;increasing\qquad (ii) \;decreasing.$
cbse
class12
bookproblem
ch6
misc
q7
p242
sec-b
easy
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Find the intervals in which the function \(f\) given by $ f(x) =\large \frac{4sin\: x - 2x - xcos \: x}{2+cos\:x}$ is (i) increasing (ii) decreasing.
cbse
class12
bookproblem
ch6
misc
q6
p242
sec-b
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
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