Commerce (English Medium) Class 11 - CBSE Question Bank Solutions

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))`

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.

Write the negation of the following statements:

Chennai is the capital of Tamil Nadu.

Write the negation of the following statements:

`sqrt2` is not a complex number.

Write the negation of the following statements:

All triangles are not equilateral triangle.

Write the negation of the following statements:

The number 2 is greater than 7.

Write the negation of the following statements:

Every natural number is an integer.

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.

Are the following pairs of statements negations of each other?

The number x is a rational number.

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.

Find the component statements of the following compound statements and check whether they are true or false.

All integers are positive or negative.

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.

Write the negation of the following statements:

p: For every positive real number x, the number x – 1 is also positive.

Write the negation of the following statements:

q: All cats scratch.

Write the negation of the following statements:

r: For every real number x, either x > 1 or x < 1.

Write the negation of the following statements:

s: There exists a number x such that 0 < x < 1.

Which of the following are examples of empty set? 

Set of all even natural numbers divisible by 5

Which of the following are examples of empty set? 

Set of all even prime numbers

Which of the following are examples of empty set? 

 {x : x² −2 = 0 and x is rational}

Which of the following are examples of empty set? 

{x : x is a natural number, x < 8 and simultaneously x > 12};