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Questions asked by thanvigandhi_1
Questions
5837
questions
1
answer selected
Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B(4, 5) and C(6, 3).
cbse
class12
bookproblem
ch8
misc
q13
p376
sec-b
medium
math
asked
Dec 4, 2012
1
answer
Using the method of integration find the area of the region bounded by lines: \(2x + y = 4, 3x - 2y = 6\) and \(x - 3y + 5 = 0\)
cbse
class12
bookproblem
ch8
misc
q14
p376
sec-c
medium
math
asked
Dec 4, 2012
1
answer
Find the area of the region ${(x, y) : y^2\: \leq \: 4x, 4x^2 + 4y^2\: \leq\: 9}$
cbse
class12
bookproblem
ch8
misc
q15
p376
sec-c
difficult
modelpaper
2012
q26
math
asked
Dec 4, 2012
1
answer
Choose the correct answer in the area bounded by the curve $ y = x^3$, the $x$ - axis and the ordinates $x = -2$ and $x = 1$ is
cbse
class12
bookproblem
ch8
misc
q16
p376
sec-a
easy
math
asked
Dec 4, 2012
1
answer
Choose the correct answer in the the area bounded by the curve $y = x |\; x\; | ,\; x$ - axis and the ordinates $x = -1$ and $x = 1$ is given by [Hint : $y = x^2$ if $x > 0$ and $y = -x^2$ if $x < 0$].
cbse
class12
bookproblem
ch8
misc
q17
p376
sec-a
medium
math
asked
Dec 4, 2012
1
answer
Choose the correct answer in the the area of the circle \(x^2 + y^2 = 16\) exterior to the parabola \(y^2 = 6x\) is \[\begin{array} (A) \frac{4}{3} (4\pi - \sqrt 3) \quad &(B) \frac{4}{3} (4\pi + \sqrt 3) \quad & (C) \frac{4}{3} (8\pi - \sqrt 3) \quad & (D) \frac{4}{3} (8\pi + \sqrt 3) \end{array}\]
cbse
class12
bookproblem
ch8
misc
q18
p376
sec-b
medium
math
asked
Dec 4, 2012
1
answer
Choose the correct answer in the the area bounded by the \(y\) - axis, \(y = \cos\: x\) and \(y = \sin\: x\) when \(0 \leq x \leq \frac{\large \pi}{2}\) is
cbse
class12
bookproblem
ch8
misc
q19
p376
sec-c
difficult
math
asked
Dec 4, 2012
1
answer
Choose the correct answer in the area of the region bounded by the curve $y^2 = 4x,\; y$ - axis and the line $y = 3$ is
cbse
class12
bookproblem
ch8
sec1
q13
p366
sec-a
easy
math
asked
Dec 4, 2012
1
answer
Choose the correct answer in area lying in the first quadrant and bounded by the circle $x^2 + y^2 = 4 $ and the lines $x = 0$ and $x = 2$ is
cbse
class12
bookproblem
ch8
sec1
q12
p366
sec-a
easy
math
aims-12-math
asked
Dec 4, 2012
1
answer
Find the area of the region bounded by the curve $y^2 = 4x$ and the line $x = 3$.
cbse
class12
bookproblem
ch8
sec1
q11
p366
sec-b
easy
math
asked
Dec 4, 2012
1
answer
Find the area bounded by the curve $x^2 = 4y$ and the line $x = 4y - 2$.
cbse
class12
bookproblem
ch8
sec1
q10
p366
sec-c
medium
math
asked
Dec 4, 2012
1
answer
Find the area of the region bounded by the parabola $y = x^2$ and $y = \left | x \right | $.
cbse
class12
bookproblem
ch8
sec1
q9
p366
sec-a
easy
math
aims-12-math
asked
Dec 4, 2012
1
answer
The area between $x = y^2$ and $x = 4$ is divided into two equal parts by the line $x = a$, find the value of $a$.
cbse
class12
bookproblem
ch8
sec1
q8
p366
sec-b
medium
math
asked
Dec 4, 2012
1
answer
Find the area of the smaller part of the circle $x^2 + y^2 = a^2$ cut off by the line $x =\Large { \frac{a}{\sqrt 2}}$.
cbse
class12
bookproblem
ch8
sec1
q7
p366
sec-b
easy
math
asked
Dec 4, 2012
1
answer
Find the area of the region in the first quadrant enclosed by $x$ - axis, line $x = \sqrt {3}\: y$ and the circle $x^2 + y^2 = 4$.
cbse
class12
bookproblem
ch8
sec1
q6
p366
sec-c
medium
math
asked
Dec 4, 2012
1
answer
Find the area of the region bounded by the ellipse $\frac{\Large x^2}{\Large 4 } + \frac{\Large y^2}{\Large 9} = 1$
cbse
class12
bookproblem
ch8
sec1
q5
p366
sec-a
easy
math
asked
Dec 4, 2012
1
answer
Find the area of the region bounded by the ellipse $\frac{\Large x^2}{\Large 16} + \frac{\Large y^2}{\Large 9} = 1$
cbse
class12
bookproblem
ch8
sec1
q4
p366
sec-a
medium
math
asked
Dec 4, 2012
1
answer
Find the area of the region bounded by $x^2 = 4y, y = 2, y = 4$ and the $y$ - axis in the first quadrant.
cbse
class12
bookproblem
ch8
sec1
q3
p366
sec-a
medium
math
asked
Dec 4, 2012
1
answer
Find the area of the region bounded by $y^2 = 9x,\; x = 2,\; x = 4$ and the $x$ - axis in the first quadrant.
cbse
class12
bookproblem
ch8
sec1
q2
p365
sec-a
easy
math
aims-12-math
asked
Dec 4, 2012
1
answer
Find the area of the region bounded by the curve $y^2 = x$ and the lines $x = 1, x = 4$ and the $x$ - axis.
cbse
class12
bookproblem
ch8
sec1
q1
p365
sec-b
easy
math
aims-12-math
asked
Dec 4, 2012
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
1
answer
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
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
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
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
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
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
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
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
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
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
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
1
answer
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