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Derivatives of tan3θ with respect to sec3θ at θ=π/3 is
(A)` 3/2`
(B) `sqrt3/2`
(C) `1/2`
(D) `-sqrt3/2`
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
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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
If `x = acos^3t`, `y = asin^3 t`,
Show that `(dy)/(dx) =- (y/x)^(1/3)`
Concept: undefined >> undefined
If X = f(t) and Y = g(t) Are Differentiable Functions of t , then prove that y is a differentiable function of x and
`"dy"/"dx" =("dy"/"dt")/("dx"/"dt" ) , "where" "dx"/"dt" ≠ 0`
Hence find `"dy"/"dx"` if x = a cos2 t and y = a sin2 t.
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
If y = sin -1 `((8x)/(1 + 16x^2))`, find `(dy)/(dx)`
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
