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Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0, 4, 0) and (6, 0, 0).
Concept: undefined >> undefined
Find the coordinates of a point on y-axis which are at a distance of `5sqrt2` from the point P (3, –2, 5).
Concept: undefined >> undefined
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A point R with x-coordinate 4 lies on the line segment joining the pointsP (2, –3, 4) and Q (8, 0, 10). Find the coordinates of the point R.
[Hint suppose R divides PQ in the ratio k: 1. The coordinates of the point R are given by `((8k + 2)/(k+1), (-3)/(k+1), (10k + 4)/(k+1))`
Concept: undefined >> undefined
If A and B be the points (3, 4, 5) and (–1, 3, –7), respectively, find the equation of the set of points P such that PA2 + PB2 = k2, where k is a constant.
Concept: undefined >> undefined
Write the negation of the following statements:
Chennai is the capital of Tamil Nadu.
Concept: undefined >> undefined
Write the negation of the following statements:
`sqrt2` is not a complex number.
Concept: undefined >> undefined
Write the negation of the following statements:
All triangles are not equilateral triangle.
Concept: undefined >> undefined
Write the negation of the following statements:
The number 2 is greater than 7.
Concept: undefined >> undefined
Write the negation of the following statements:
Every natural number is an integer.
Concept: undefined >> undefined
Are the following pairs of statements negations of each other?
The number x is not a rational number.
The number x is not an irrational number.
Concept: undefined >> undefined
Are the following pairs of statements negations of each other?
The number x is a rational number.
The number x is an irrational number.\
Concept: undefined >> undefined
Find the component statements of the following compound statements and check whether they are true or false.
Number 3 is prime or it is odd.
Concept: undefined >> undefined
Find the component statements of the following compound statements and check whether they are true or false.
All integers are positive or negative.
Concept: undefined >> undefined
Find the component statements of the following compound statements and check whether they are true or false.
100 is divisible by 3, 11 and 5.
Concept: undefined >> undefined
Write the negation of the following statements:
p: For every positive real number x, the number x – 1 is also positive.
Concept: undefined >> undefined
Write the negation of the following statements:
q: All cats scratch.
Concept: undefined >> undefined
Write the negation of the following statements:
r: For every real number x, either x > 1 or x < 1.
Concept: undefined >> undefined
Write the negation of the following statements:
s: There exists a number x such that 0 < x < 1.
Concept: undefined >> undefined
Which of the following are examples of empty set?
Set of all even natural numbers divisible by 5
Concept: undefined >> undefined
Which of the following are examples of empty set?
Set of all even prime numbers
Concept: undefined >> undefined
