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Show that the height of the cylinder of maximum volume, that can be inscribed in a sphere of radius R is `(2R)/sqrt3.` Also, find the maximum volume.
Concept: undefined >> undefined
Find the equation of the planes parallel to the plane x + 2y+ 2z + 8 =0 which are at the distance of 2 units from the point (1,1, 2)
Concept: undefined >> undefined
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An open box is to be made out of a piece of a square card board of sides 18 cms by cutting off equal squares from the comers and turning up the sides. Find the maximum volume of the box.
Concept: undefined >> undefined
Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is `(4r)/3`. Also find maximum volume in terms of volume of the sphere
Concept: undefined >> undefined
A telephone company in a town has 5000 subscribers on its list and collects fixed rent charges of Rs.3,000 per year from each subscriber. The company proposes to increase annual rent and it is believed that for every increase of one rupee in the rent, one subscriber will be discontinued. Find what increased annual rent will bring the maximum annual income to the company.
Concept: undefined >> undefined
Show that the points (1, –1, 3) and (3, 4, 3) are equidistant from the plane 5x + 2y – 7z + 8 = 0
Concept: undefined >> undefined
Find the distance of the point (1, 2, –1) from the plane x - 2y + 4z - 10 = 0 .
Concept: undefined >> undefined
A rod of 108 meters long is bent to form a rectangle. Find its dimensions if the area is maximum. Let x be the length and y be the breadth of the rectangle.
Concept: undefined >> undefined
Write the negation of the following.
Tirupati is in Andhra Pradesh.
Concept: undefined >> undefined
Write the negation of the following.
3 is not a root of the equation x2 + 3x – 18 = 0
Concept: undefined >> undefined
Write the negation of the following.
`sqrt2` is a rational number.
Concept: undefined >> undefined
Write the negation of the following.
Polygon ABCDE is a pentagon.
Concept: undefined >> undefined
Write the negation of the following.
Concept: undefined >> undefined
Write the negation of the following.
x + 8 > 11 or y – 3 = 6
Concept: undefined >> undefined
Write the negation of the following.
11 < 15 and 25 > 20
Concept: undefined >> undefined
Write the negation of the following.
Quadrilateral is a square if and only if it is a rhombus.
Concept: undefined >> undefined
Write the negation of the following.
It is cold and raining.
Concept: undefined >> undefined
Write the negation of the following.
If it is raining then we will go and play football.
Concept: undefined >> undefined
Write the negation of the following.
All-natural numbers are whole numbers.
Concept: undefined >> undefined
Write the negation of the following.
∀ n ∈ N, n2 + n + 2 is divisible by 4.
Concept: undefined >> undefined
