PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions for Mathematics

Write of the statement in the form "if p, then q". 

There is traffic jam whenever it rains.

Write of the statement in the form "if p, then q". 

 It is necessary to have a passport to log on to the server.

Write of the statement in the form "if p, then q". 

 It is necessary to be rich in order to be happy.

Write of the statement in the form "if p, then q". 

 The game is cancelled only if it is raining.

Write of the statement in the form "if p, then q". 

 It rains only if it is cold.

Write of the statement in the form "if p, then q". 

 Whenever it rains it is cold.

Write of the statement in the form "if p, then q". 

Check the validity of the statement:

 p : 100 is a multiple of 4 and 5.

Check the validity of the statement:

q : 125 is a multiple of 5 and 7.

Check the validity of the statement:

If a is the G.M. of 2 and \[\frac{1}{4}\] , find a.

 statement are true and false? In each case give a valid reason for saying so

 p : Each radius of a circle is a chord of the circle.

 statement are true and false? In each case give a valid reason for saying so

q : The centre of a circle bisects each chord of the circle.

 statement are true and false? In each case give a valid reason for saying so

r : Circle is a particular case of an ellipse.

 statement are true and false? In each case give a valid reason for saying so

 s : If x and y are integers such that x > y, then − x < − y.

 statement are true and false? In each case give a valid reason for saying so

 t :  \[\sqrt{11}\]  is a rational number. 

Determine whether the argument used to check the validity of the following statement is correct:
p : "If x² is irrational, then x is rational"
The statement is true because the number x² = π² is irrational, therefore x = π is irrational.