Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,375

#103. NO!

#104. What is the number of factors (including 1 and the number itself) of

#105. What is the sum of all the proper divisors of 9900 (other than 1 and the number itself)?

#106. What is the sum of all the divisors of

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,375

Answers to #102, and #103:-

Both the answers are correct, JaneFairfax!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,375

#107. What is the value of

#108. If x = a cos²M sin N and y = a sin²M cos N, what is the value of

#109. If sin x + sin² x = 1, then what is the value of

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,375

Answer to #109:-

Perfect, JaneFairfax!

#110. Let n (>1) be a positive integer. What is the largest integer m such that

is divisible by ?

#111. If S be the sum, P the product, and R, the sum of reciprocals of n terms of a Geometric Progression, what is

#112. If

where |b|<1, then what is

equal to?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,375

#113. What is the value of

#114. If

, then what is the value of?

#115. What is the largest number of four digits exactly divisible by 88?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,375

Answers to #113, #114, and #115 :-

All correct, JaneFairfax!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,375

#116. If xy + yz + xz = 0, then, what is the value of

#117. If the sum of the first 11 terms of an Arithmetic Progression is equal to that of the first 19 terms, then what is the sum of the first 30 terms of the Arithmetic Progression?

#118. Two boats travelling at speeds of 5 km/hour and 10 km/hour, head directly towards each other. They begin at a distance of 20 kilometers from each other. How far apart would they be (in kilometers) one minute before they meet each other?

#119. Two new societies, P and Q, are formed on the 1st of January, 2009, each with n members. On the first day of each subsequent month, society P adds b members while society Q multiplies its number of members at that point of time by a constant factor r. Both the scieties P, and Q would have the same number of members on July 2, 2009. If b = 10.5(n), what is the value of r?

#120. What is/are the value(s) of r if

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,375

Answers to #116, #117, #118, #119 and #120:-

All correct, JaneFairfax!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,375

#121. If

are the roots of the equation , what is the value of?

#122. If p and q are the roots of the equation

, then what is/are the value(s) of p?Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,375

#123. If x, y, z are the

terms respectively of an Arithmetic Progression and also of a Geometric Progression, then what is the value of?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,375

Answers to #121, and #122:

Both correct, JaneFairfax!!!

#124. For the equation

where p>0, if one of the roots is the square of the other, what is p equal to?#125. How many quadratic equations are there which are unchanged by squaring their roots?

#126. How many real roots does the following quadratic equation have:

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,375

Answers to #124, and #126:-

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,375

Answers to #124, and #126:-

Both correct, JaneFairfax!**Excellent!!!**

#127. Which is the term independent of x in the expansion of

#128. If the fourth term of the following expansion is

, then what are the values of a and n?Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,375

Answers to #127, and #128:-

#128 is correct.**Excellent!!!**

#127: But for a minor calculation mistake, you would've got the right answer. Please check your answer.

#129. What is the sum of the coefficients of the odd powers of x in the expansion of

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

I had an inkling I had made a careless mistake somewhere.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,375

#130. If the coefficients of

and are 3 and -6 respectively in the expansion of,

then what is the value of m?

(i) 6 (ii) 9 (iii) 12 (iv) 24

#131. In the exapnsion of

, the sum of the fifth and sixth terms is zero. Then, what is equal to?#132. If the coefficients of the

and terms in the expansion of are equal, then what is r equal to?Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,375

#133. What is the value of

#134. What is tanA + tanB if in the triangle ABC, C is equal to 90°?

#135. If

,then what is the value of

?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,375

#136. If

, then what is equal to?Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline