Please select a subject first
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Write of the statement in the form "if p, then q".
Whenever it rains it is cold.
Concept: undefined >> undefined
Write of the statement in the form "if p, then q".
It never rains when it is cold.
Concept: undefined >> undefined
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Check the validity of the statement:
p : 100 is a multiple of 4 and 5.
Concept: undefined >> undefined
Check the validity of the statement:
q : 125 is a multiple of 5 and 7.
Concept: undefined >> undefined
Check the validity of the statement:
r : 60 is a multiple of 3 or 5.
Concept: undefined >> undefined
If a is the G.M. of 2 and \[\frac{1}{4}\] , find a.
Concept: undefined >> undefined
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.
Concept: undefined >> undefined
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.
Concept: undefined >> undefined
statement are true and false? In each case give a valid reason for saying so
r : Circle is a particular case of an ellipse.
Concept: undefined >> undefined
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.
Concept: undefined >> undefined
statement are true and false? In each case give a valid reason for saying so
t : \[\sqrt{11}\] is a rational number.
Concept: undefined >> undefined
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.
Concept: undefined >> undefined
Find the two numbers whose A.M. is 25 and GM is 20.
Concept: undefined >> undefined
Construct a quadratic in x such that A.M. of its roots is A and G.M. is G.
Concept: undefined >> undefined
If AM and GM of roots of a quadratic equation are 8 and 5 respectively, then obtain the quadratic equation.
Concept: undefined >> undefined
If AM and GM of two positive numbers a and b are 10 and 8 respectively, find the numbers.
Concept: undefined >> undefined
Prove that the product of n geometric means between two quantities is equal to the nth power of a geometric mean of those two quantities.
Concept: undefined >> undefined
If the A.M. of two positive numbers a and b (a > b) is twice their geometric mean. Prove that:
\[a : b = (2 + \sqrt{3}) : (2 - \sqrt{3}) .\]
Concept: undefined >> undefined
If one A.M., A and two geometric means G1 and G2 inserted between any two positive numbers, show that \[\frac{G_1^2}{G_2} + \frac{G_2^2}{G_1} = 2A\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{\sqrt{1 + x + x^2} - 1}{x}\]
Concept: undefined >> undefined
