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If the coordinates of the sides AB and AC of ∆ABC are (3, 5) and (−3, −3), respectively, then write the length of side BC.
Concept: undefined >> undefined
Write the coordinates of the circumcentre of a triangle whose centroid and orthocentre are at (3, 3) and (−3, 5), respectively.
Concept: undefined >> undefined
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Write the coordinates of the in-centre of the triangle with vertices at (0, 0), (5, 0) and (0, 12).
Concept: undefined >> undefined
If the points (1, −1), (2, −1) and (4, −3) are the mid-points of the sides of a triangle, then write the coordinates of its centroid.
Concept: undefined >> undefined
Write the area of the triangle with vertices at (a, b + c), (b, c + a) and (c, a + b).
Concept: undefined >> undefined
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x is an odd natural number}
Concept: undefined >> undefined
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x is a positive multiple of 3}
Concept: undefined >> undefined
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x is a prime number}
Concept: undefined >> undefined
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x is a natural number divisible by 3 and 5}
Concept: undefined >> undefined
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x is a perfect square}
Concept: undefined >> undefined
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x is perfect cube}
Concept: undefined >> undefined
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x + 5 = 8}
Concept: undefined >> undefined
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : 2x + 5 = 9}
Concept: undefined >> undefined
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x ≥ 7}
Concept: undefined >> undefined
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x ∈ N and 2x + 1 > 10}
Concept: undefined >> undefined
If the latus rectum of an ellipse is equal to half of minor axis, then find its eccentricity.
Concept: undefined >> undefined
Given the ellipse with equation 9x2 + 25y2 = 225, find the eccentricity and foci.
Concept: undefined >> undefined
(3x + 5)(1 + tan x)
Concept: undefined >> undefined
(sec x – 1)(sec x + 1)
Concept: undefined >> undefined
If X and Y are two sets such that n(X) = 17, n(Y) = 23 and n(X ∪ Y) = 38, find n(X ∩Y).
Concept: undefined >> undefined
