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Recent questions tagged q24
Questions
A curve passing through the point (1,1) has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of p from the x-axis. Determine the equation of the curve.
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q24
p34
sec-b
math
asked
Feb 4, 2013
by
meena.p
0
answers
Show that of all the rectangles of given area, the square has the smallest perimeter.
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Feb 4, 2013
by
thanvigandhi_1
1
answer
Draw the rough sketch of $ y=\sin 2x $ and determine the area enclosed by the lines $ x=\pi/4\; and\;x=\Large\frac{3\pi}{4}$
cbse
class12
additionalproblem
kvquestionbank2012
ch8
q24
p32
math
asked
Feb 4, 2013
by
meena.p
0
answers
Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Feb 4, 2013
by
thanvigandhi_1
0
answers
Show that the volume of the greatest cylinder that can be inscribed in a cone of height 'h' and semi-vertical angle \( \alpha \) is \( \large\frac{4}{27}\pi h^3\tan^2 \alpha \).
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Feb 4, 2013
by
thanvigandhi_1
1
answer
Show that the volume of the greatest cylinder which can be inscribed in a cone of height h and semivertical angle $ \alpha, \: is \: \large\frac{4}{27}$$ \pi \: h^3\: tan^2\: \alpha $
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Feb 3, 2013
by
thanvigandhi_1
1
answer
Show that the normal at any point \( \theta \) to the curve \( x=a\cos\theta+a\theta\: \sin\theta\) and \( y=a\sin\theta-a\theta \cos\theta\) is at a constant distance from the origin.
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Feb 3, 2013
by
thanvigandhi_1
0
answers
Show that semi vertical angle of right circular cone of given surface area and maximum volume is $ \sin^{-1} \bigg( \large\frac{1}{3} \bigg). $
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Feb 2, 2013
by
thanvigandhi_1
0
answers
A wire of length 36 cm is cut into two pieces. One of the pieces is turned in the form of a square and the other in the form of an equilateral triangle. Find the length of each piece so that the sum of the areas of the two be minimum.
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Feb 2, 2013
by
thanvigandhi_1
1
answer
If $\Large \int \normalsize \tan^4 xdx = a\tan^3x+b\tan x+cx,then $\[(a)\;a=\frac{1}{3} \qquad (b)\;b=-1 \qquad(c)a=1\qquad(d)\;c=1\]
cbse
class12
additionalproblem
kvquestionbank2012
ch7
q24
p25
math
asked
Feb 1, 2013
by
meena.p
0
answers
Show that volume of the greatest cylinder which can inscribed in a cone of height h and semi-vertical angle $ 30^{\circ} \: is \: \large\frac{4}{81} $$\: \pi h^3.$
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 31, 2013
by
thanvigandhi_1
1
answer
Find the area of greatest rectangle which can be inscribed in a circle of radius 10 cm.
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 31, 2013
by
thanvigandhi_1
0
answers
Find the equation of the plane passing through the intersection of planes \( 4x-y+z=10\: and \: x+y-z=4\) and parallel to the line with direction ratios < 2, 1, 1>. Find also the perpendicular distance of (1, 1, 1) from the plane.
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 30, 2013
by
thanvigandhi_1
1
answer
Find point on the curve \( y^2=4x\) which is nearest to point (2, -8).
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 30, 2013
by
thanvigandhi_1
0
answers
Show that the semi-vertical angle of the right circular cone of given slant height and maximum volume is \( tan^{-1}\sqrt 2 \)
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 30, 2013
by
thanvigandhi_1
0
answers
Find the area of the smaller region bounded by the ellipse $\large\frac{x^2}{a^2}+\large\frac{y^2}{b^2}$$=1$ and the straight line $\large\frac{x}{a}+\frac{y}{b}$$=1$.
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 29, 2013
by
thanvigandhi_1
0
answers
The least value of 'a' such that the function $ f(x)=x^2+ax+1 $ is strictly increasing on (1,2) is \[(a)\;-2\qquad(b)\;2\qquad(c)\;\frac{1}{2}\qquad(d)\;-\frac{1}{2}\]
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q24
p17
math
asked
Jan 29, 2013
by
meena.p
0
answers
Find the area of the region $ \{(x,y); x^2+y^2 \leq 1 \leq x+y \}.$
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 28, 2013
by
thanvigandhi_1
0
answers
Prove that the area of a right-angled triangle of given hypotenuse is maximum when it is isosceles.
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 27, 2013
by
thanvigandhi_1
0
answers
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
modelpaper
2012
sec-c
q24
math
asked
Jan 27, 2013
by
thanvigandhi_1
0
answers
A point on the hypotenuse of a right-angled triangle is at distances a and b from the sides. Show that length of the hypotenuse is at least \( (a^{\large\frac{2}{3}}+b^{\large\frac{2}{3}})^{\large\frac{3}{2}} \)
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 26, 2013
by
thanvigandhi_1
0
answers
Show that semi-vertical angle of the right circular cone of given total surface area and maximum volume is \( sin^{-1}\frac{1}{3} \)
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 26, 2013
by
thanvigandhi_1
0
answers
Let $f(x) = \left\{ \begin{array}{l l} \Large\frac{1-sin^3x}{3cos^2x}, & \quad if\; { x < \Large\frac{\pi}{2}}\\ a, & \quad if\; { x = \Large\frac{\pi}{2}} \\ \Large\frac{b(1-sin x)}{(\pi - 2x)^2}, & \quad if \;{ x > \Large\frac{\pi}{2}} \end{array}. \right.$ If f(x) is continuous function at x \( x = \Large\frac{\pi}{2} \), find a and b.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q24
p13
medium
math
sec-b
asked
Jan 25, 2013
by
meena.p
1
answer
A wire of length 30 cm 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 could be the lengths of two peices, so that the combined area of the square and the circle is minimum?
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 25, 2013
by
thanvigandhi_1
0
answers
An open box with a square base is to be made out of given quantity of sheet of area \( a^2 \). Show that maximum volume of the box is \( \large\frac{a^3}{6\sqrt3}.\)
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 25, 2013
by
thanvigandhi_1
0
answers
If $ A=\begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix},$ show that $ A^2-5A+7I=0,$ use the result to find $A^4$.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q24
p8
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
A window is in the form of rectangle above which there is a semi circle. If the perimeter of window is p units, show that the window will allow maximum light, when radius of the semicircle is \( \large\frac{p}{\pi + 4} \) units.
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 24, 2013
by
thanvigandhi_1
0
answers
Find the present worth of an ordinary annuity of Rs. 1,200 per annum for 10 years at 12% per annum, compounded annually. [Use (1.12) -10 =0.3221]
cbse
class12
modelpaper
2005
sec-c
q24
math
asked
Jan 24, 2013
by
fingeazy
1
answer
Solve: $\sin\lfloor2\cos^{-1}\{\cot(2\tan^{-1}x)\}\rfloor=0$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q24
p6
difficult
sec-b
math
asked
Jan 24, 2013
by
meena.p
1
answer
A toy company manufactures two types of dolls, A and B. Each doll of type B takes twice as long as to produce as one of type A. If the company produces only type A. It can make a maximum of 2000 dolls per day. The supply of plastic is sufficient to produce 1500 dolls per day. Type B requires a fancy dress which cannot be available for more than 600 per day. If the company makes profit of Rs.3 and Rs.5 per doll respectively on doll A and doll B, how many of each should be produced per day in order to maximise the profit?
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 23, 2013
by
thanvigandhi_1
1
answer
Let f and g be real valued functions, such that $(fog)(x)=\cos x^3\; and\;(gof)(x)=\cos^3x,$ find the functions f and g.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q24
p4
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the minimum length of hypotenuse is \( \bigg[ a^{\large\frac{2}{3}} + b^{\large\frac{2}{3}} \bigg]^{\large\frac{3}{2}} \).
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 22, 2013
by
thanvigandhi_1
0
answers
Show that the right circular cone of least curved surface and given volume has an altitude equal to \( \sqrt 2\) times the radius of the base.
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 22, 2013
by
thanvigandhi_1
0
answers
Show that semi-vertical angle of the cone of maximum volume and of given slant height is \( \tan^{-1} \sqrt 2\).
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 21, 2013
by
thanvigandhi_1
1
answer
Prove that the area of right angled triangle of given hypotenuse is maximum when the triangle is isoceles.
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 21, 2013
by
thanvigandhi_1
0
answers
Find the differential equation of system of concentric circles with centre(1,2).
cbse
class12
ch9
sec-a
q24
p194
short-answer
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
The value of $\lambda$ for which the vectors $3\hat i+6\hat j+\hat k $ and $ 2\hat i+4\hat j+\lambda\hat k$ are parallel is
cbse
class12
ch10
q24
p217
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Show that the semi-vertical angle of rightcircular of given surface area and maximum volume is \( \sin^{-1} \bigg( \large\frac{1}{3} \bigg).\)
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 16, 2013
by
thanvigandhi_1
0
answers
The area of the region bounded by the y-axis ,$y=\cos x$ and $y=\sin x,0\leq x\leq \large\frac{\pi}{2}$ is\begin{array}{1 1}(A)\;1\sqrt 2sq.units & (B)\;(\sqrt 2+1)sq.units\\(C)\;(\sqrt 2-1)sq.units & (D)\;(2\sqrt 2-1)sq.units \end{array}
cbse
class12
ch8
q24
p177
objective
exemplar
sec-b
difficult
math
asked
Jan 16, 2013
by
sreemathi.v
1
answer
A square piece of tin of side 24 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. What should be the side of the square to be cut off so that volume of the box is maximum?
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 15, 2013
by
thanvigandhi_1
1
answer
An open box with a square base is to be made out of given quantity of sheet of area \( a^2\). Show that maximum volume of the box is \( \large\frac{a^3}{6\sqrt 3}. \)
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 15, 2013
by
thanvigandhi_1
0
answers
Evaluate the following $\int\frac{\sqrt x}{\sqrt{a^3-x^3}}dx$
cbse
class12
ch7
q24
p165
short-answer
exemplar
sec-b
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
(i) If a young lady drives her scooty at 30 km/hour, she had to spend Rs. 2.00 per km on petrol. If she drives at speed 50 km/h the petrol cost is Rs. 4.00 per km. She has Rs. 150 to spend on petrol and wants to describe the maximum distance she can travel within 2 hours. Express this as L.P.P and solve it graphically. (ii) Which mode of transport you suggest to a student and why?
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 13, 2013
by
thanvigandhi_1
0
answers
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
Solve, using matrices : $ 2x-y+3z=5;3x+2y-z=7 ; 4x+5y-5z = 9$
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 11, 2013
by
thanvigandhi_1
1
answer
Using matrix solve the following system of linear equations : $ 2x+y+z=3 ; 3x-y+z=0 ;x-2y+3z = -6$
cbse
class12
modelpaper
2012
sec-c
q24
medium
math
asked
Jan 11, 2013
by
thanvigandhi_1
0
answers
Show that the height of the cylinder of maximum volume that can be inscribed in a cone of height h is \( \large\frac{1}{3}h.\)
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 10, 2013
by
thanvigandhi_1
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.
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Find the equations of the tangent and normal to the curve \( 16x^2+9y^2 = 144\) at \( (x_1, y_1)\) where \( x_1=2\: and \: y_1 > 0.\) Also, find the points of intersection where both tangent and normal cut the \( x\) - axis.
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Consider the probability distribution of a random variable X.
cbse
class12
ch13
q24
p274
short-answer
exemplar
sec-a
easy
math
asked
Jan 9, 2013
by
sreemathi.v
1
answer
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