#### Frequently Asked Questions

Which one of the following statement is true

A: Only one line can pass through a single point.

B: There are an infinite number of lines which pass through two distinct points.

C: Two distinct lines cannot have more than one point in common.

D: If two circles are equal, then their radii are not equal.

**Solution:**

**Explanation: **

From one point there is an uncountable number of lines that can pass through.

Hence, the statement “ Only one line can pass through a single point” is false.

We can draw only one unique line passing through two distinct points.

Hence, the statement “There are an infinite number of lines which pass through two distinct points” is false.

Given two distinct points, there is a unique line that passes through them.

Hence, the statement “Two distinct lines cannot have more than one point in common” is true.

If circles are equal, which means the circles are congruent. This means that circumferences are equal and so the radii of two circles are also equal.

Hence, the statement “If two circles are equal, then their radii are not equal” is false.

**Final Answer:**

The correct option is (C) Two distinct lines cannot have more than one point in common.

The class mark of the class 90-120 is

A: 90

B: 105

C: 115

D: 120

**Solution:**

**Explanation: **

To find the class mark of a class interval, we find the sum of the upper limit and lower limit of a class and divide it by 2 Thus,

Class -mark=Upper limit + Lower limit/2

Here, the lower limit of 90-120=90

And the upper limit of 90-120=120

So,

Class -mark=120+90/2

=210/2

=105

Hence, the class mark of the class 90-120 is 105

That is, option (B) is correct.

**Final Answer: **

Option (B) 105 is correct.

ABCD is a parallelogram and AP

and CQ are perpendiculars from vertices A and C on diagonal BD Show that i)ΔAPB**≅**ΔCQD ii) AP = CQ

**Solution:**

Find the roots of the following equation

A: - 1, - 2

B: - 1, - 3

C: 1,3

D: 1,2

**Solution:**

**Explanation:-**

**Final answer:-**

Hence the correct option is (D) i.e. 1,2.

The product of any two irrational numbers

A: Is always an irrational number

B: Is always a rational number

C: Is always an integer

D: Can be rational or irrational

**Solution:**

**Explanation: **

The set of irrational numbers is formed by all numbers that cannot be expressed as the ratio between two integers.

The product of two irrational numbers can be rational or irrational depending on the two numbers.

For example, √3 ×√3=3 where √3 is irrational and their product 3 is rational.

Also, √2 ×√3= √6 where √2 and √3 is irrational and their product √6 is irrational.

**Final Answer: **

Hence, the correct option is (D) can be rational or irrational.