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Recent questions tagged ch6
Questions
Show that the normal at any point \(\theta\) to the curve $ x = a \cos\theta + a \: \theta \sin\: \theta, y = a\sin\theta - a\theta \cos\theta$ is at a constant distance from the origin.
cbse
class12
bookproblem
ch6
misc
q5
p242
sec-b
easy
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Find the equation of the normal to curve \(y^2 = 4x\) which passes through the point \((1, 2).\)
cbse
class12
bookproblem
ch6
misc
q4
p242
sec-a
easy
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
The two equal sides of an isosceles triangle with fixed base $b$ are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base ?
cbse
class12
bookproblem
ch6
misc
q3
p242
sec-b
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Show that the function given by \( f(x) =\large \frac{\log \: x}{x}\) has maximum at \(x = e.\)
cbse
class12
bookproblem
ch6
misc
q2
p242
sec-b
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Using differentials, find the approximate value of each of the following: $(33)^{-\large\frac{1}{5}}$
cbse
class12
bookproblem
ch6
misc
q1b
p242
sec-a
easy
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Using differentials, find the approximate value of each of the following: $ \left(\large\frac{17}{81}\right)^{\frac{1}{4}}$
cbse
class12
bookproblem
ch6
misc
q1a
p242
sec-b
easy
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
The maximum value of $ [ x(x-1) +1]^{\frac{1}{3}}, 0 \leq \: x \leq$ is
cbse
class12
bookproblem
ch6
sec5
q29
p234
sec-a
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
For all real values of \(x\), the minimum value of \( \large\frac{1-x+x^2}{1+x+x^2}\) is
cbse
class12
bookproblem
ch6
sec5
q28
p234
sec-b
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the point on the curve \( x^2 = 2y\) which is nearest to the point \((0, 5)\) is
cbse
class12
bookproblem
ch6
sec5
q27
p234
sec-b
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Show that semi-vertical angle of right circular cone of given surface area and maximum volume is \( \sin^{-1} \left(\frac{1}{3}\right)\)
cbse
class12
bookproblem
ch6
sec5
q26
p233
sec-c
medium
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is \(\tan^{-1} \sqrt {2}\).
cbse
class12
bookproblem
ch6
sec5
q25
p233
sec-c
medium
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Show that the right circular cone of least curved surface and given volume has an altitude equal to \(\sqrt 2\) time the radius of the base.
cbse
class12
bookproblem
ch6
sec5
q24
p233
sec-c
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
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.
cbse
class12
bookproblem
ch6
sec5
q23
p233
sec-c
difficult
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?
cbse
class12
bookproblem
ch6
sec5
q22
p233
sec-b
medium
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Of all the closed cylindrical cans (right circular), of a given volume of 100 cubic centimetres, find the dimensions of the can which has the minimum surface area?
cbse
class12
bookproblem
ch6
sec5
q21
p233
sec-b
medium
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base.
cbse
class12
bookproblem
ch6
sec5
q20
p233
sec-c
medium
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.
cbse
class12
bookproblem
ch6
sec5
q19
p233
sec-c
medium
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps. What should be the side of the square in cms to be cut off so that the volume of the box is maximum ?
cbse
class12
bookproblem
ch6
sec5
q18
p233
sec-b
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible.
cbse
class12
bookproblem
ch6
sec5
q17
p233
sec-c
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.
cbse
class12
bookproblem
ch6
sec5
q16
p233
sec-a
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Find two positive numbers \(x\) and \(y\) such that their sum is 35 and the product \(x^2 y^5\) is a maximum.
cbse
class12
bookproblem
ch6
sec5
q15
p233
sec-b
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Find two positive numbers $x$ and $y$ such that $x + y = 60$ and $xy^3$ is maximum.
cbse
class12
bookproblem
ch6
sec5
q14
p233
sec-b
medium
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Find two numbers whose sum is 24 and whose product is as large as possible.
cbse
class12
bookproblem
ch6
sec5
q13
p233
sec-b
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Find the maximum and minimum values of \( x + \sin\: 2x\) on \([0, 2\pi].\)
cbse
class12
bookproblem
ch6
sec5
q12
p233
sec-b
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
It is given that at $x = 1$, the function $x^4 – 62x^2 + ax + 9$ attains its maximum value, on the interval $[0, 2].$ Find the value of $a.$
cbse
class12
bookproblem
ch6
sec5
q11
p233
sec-a
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Find the maximum value of \(2x^3 – 24x + 107\) in the interval \([1, 3]\).
cbse
class12
bookproblem
ch6
sec5
q10
q10-1
p232
sec-b
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
What is the maximum value of the function $\sin \: x + \cos x$?
cbse
class12
bookproblem
ch6
sec5
q9
p232
sec-b
medium
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
At what points in the interval \([0, 2\pi]\), does the function \(\sin\: 2x\) attain its maximum value?
cbse
class12
bookproblem
ch6
sec5
q8
p232
sec-b
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Find both the maximum value and the minimum value of $3x^4 - 8x^3 + 12x^2 - 48x + 25$ on the interval $[0, 3].$
cbse
class12
bookproblem
ch6
sec5
q7
p232
sec-b
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Find the maximum profit that a company can make, if the profit function is given by $ p(x) = 41 - 72x - 18x^2$
cbse
class12
bookproblem
ch6
sec5
q6
p232
sec-b
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: $\: f (x) = x^3, x \in [– 2, 2] $
cbse
class12
bookproblem
ch6
sec5
q5
q5-1
p232
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Prove that the following functions do not have maxima or minima: $ (i)\: f (x) = e^x $
cbse
class12
bookproblem
ch6
sec5
q4
q4-1
p232
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: $ (i)\: f (x) = x^2 $
cbse
class12
bookproblem
ch6
sec5
q3
q3-1
p232
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Find the maximum and minimum values, if any, of the following functions given by $ f (x) = |x + 2| - 1$
cbse
class12
bookproblem
ch6
sec5
q2
q2-1
p232
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Find the maximum and minimum values, if any, of the following functions given by?$\;f(x)=(2x-1)^2+3$
cbse
class12
bookproblem
ch6
sec5
q1
q1-1
p231
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
The approximate change in the volume of a cube of side $x$ metres caused by increasing the side by $3\%$ is
cbse
class12
bookproblem
ch6
sec4
q9
p216
sec-a
medium
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
If $f(x) = 3x^2 + 15x + 5$, then the approximate value of $f (3.02)$ is
cbse
class12
bookproblem
ch6
sec4
q8
p216
sec-b
medium
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
If the radius of a sphere is measured as $9 \: m$ with an error of $0.03 \: m$, then find the approximate error in calculating its surface area.
cbse
class12
bookproblem
ch6
sec4
q7
p216
sec-a
easy
modelpaper
q15
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
If the radius of a sphere is measured as $7 \: m$ with an error of $0.02 \: m$, then find the approximate error in calculating its volume.
cbse
class12
bookproblem
ch6
sec4
q6
p216
sec-a
medium
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Find the approximate change in the surface area of a cube of side $x$ metres caused by decreasing the side by $1\%$.
cbse
class12
bookproblem
ch6
sec4
q5
p216
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Find the approximate change in the volume V of a cube of side $x$ metres caused by increasing the side by $1\%$.
cbse
class12
bookproblem
ch6
sec4
q4
p216
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Find the approximate value of \(f (5.001)\), where $f (x) = x^3 – 7x^2 + 15.$
cbse
class12
bookproblem
ch6
sec4
q3
p216
sec-a
medium
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Find the approximate value of $ f (2.01)$, where $f (x) = 4x^2 + 5x + 2$.
cbse
class12
bookproblem
ch6
sec4
q2
p216
sec-a
medium
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Using differentials, find the approximate value of each of the following up to $3$ places of decimal. $(i)\;\sqrt{25.3}$
cbse
class12
bookproblem
ch6
sec4
q1
q1-1
p216
sec-b
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the line $y = x + 1$ is a tangent to the curve $y^2 = 4x$ at the point
cbse
class12
bookproblem
ch6
sec3
q27
p213
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the slope of the normal to the curve $ y = 2x^2 + 3 \sin\: x$ at $x = 0$ is
cbse
class12
bookproblem
ch6
sec3
q26
p213
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Find the equation of the tangent to the curve $y = \sqrt {3x - 2}$ which is parallel to the line $4x - 2y + 5 = 0 $.
cbse
class12
bookproblem
ch6
sec3
q25
p213
sec-c
medium
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Find the equations of the tangent and normal to the hyperbola $\large {\frac{x^2}{a^2}} -\large { \frac{y^2}{b^2}} =\normalsize 1$ at the $ (x_0, \: y_0)$.
cbse
class12
bookproblem
ch6
sec3
q24
p213
sec-b
medium
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Prove that the curves \(x = y^2\) and \(xy = k\) cut at right angles* if \(8k^2 = 1.\)
cbse
class12
bookproblem
ch6
sec3
q23
p213
sec-b
medium
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Find the equations of the tangent and normal to the parabola $y^2 = 4ax$ at the point $(at^2, 2at)$.
cbse
class12
bookproblem
ch6
sec3
q22
p213
sec-b
medium
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
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