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Three vertices of a parallelogram, taken in order, are (−1, −6), (2, −5) and (7, 2). Write the coordinates of its fourth vertex.
Concept: undefined >> undefined
If the points (a, 0), (at12, 2at1) and (at22, 2at2) are collinear, write the value of t1 t2.
Concept: undefined >> undefined
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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
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 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
If X and Y are two sets such that X ∪Y has 18 elements, X has 8 elements and Y has 15 elements; how many elements does X ∩Y have?
Concept: undefined >> undefined
In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?
Concept: undefined >> undefined
