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: 16,066

Thats interesting to note; although its simple arithmetc!

Thanks JaneFairfax!

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#169. What is the value of k if the following equation has equal roots?

#170. What is the value of

if?

#171. What is the value of

if?

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#172. If

, what is the value of?

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#173. What is the solution of the differential equation

(x+y)(dx -dy) = dx + dy?

#174. If p be the length of the perpendicular from the origin to the striaght line x + 2by = 2p, then what is the value of b?

#175. If A, B, and C are the angles of a triangle such that tan A = 1, tan B = 2, then what is the value of tan C?

#176. What is the angle between the lines Ax + By = A + B and

A(x-y) + B(x+y) = 2B?

#177. In what ratio does the line y - x + 2 = 0 cut the line joining the points (3,-1) and (8,9)?

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#178. What is the value of

#179. What is the middle term in the expansion of

#180. If p and q are the roots of the equation ax² + bx + c = 0, then what is the value of

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#181. What is the value of sin(A+B)sin(A-B) + sin(B+C)sin(B-C) + sin(C+A)sin(C-A)?

#182. Given

what is the value of ?

Character is who you are when no one is looking.

Offline

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

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

Answers to #181, and #182:

Both correct, JaneFairfax!!!

#183. What is the value of

#184. What should be the value of k so that the system of linear equations

does not have a unique solution?

#185. What is the value of x if

Character is who you are when no one is looking.

Offline

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

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

Answer to #175:-

Correct, JaneFairfax!

#186. What is the value of

if x>0?

#187. What is the value of

#188. What is the value of

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#189. What is the value of Z if

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#190. The lower 24 meters portion of a 50 meters tower is painted green and the remaining portion is painted red. What is the distance of a point on the ground from the base of the tower where the two different portions of the tower subtend equal angles?

#191. What is the value of

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#192. In a triangle ABC, if cosA = cosB cosC,

what is the value of tanA - tanB - tanC?

#193. What is the angle between the two straight lines

#194. If x = cos t, y = sin t, then what is

equal to?

#195. If

what is equal to?

#196. Given the sphere

A(1, -1, 2) and B(2,-3,4), where do the points A and B lie with respect to the sphere?

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#197. What is the eccentricity of the ellipse whose length of minor axis is equal to the distance between the two foci?

#198. If the tangent to the curve

at its point is also normal to the curve at , then what is the value of mM?#199. What is the value of

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#200. What is the value of

if?

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#201. How many solutions does the following equation have?

#202. What is the value of 1 + abc if

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#203. What is the coefficient of

in the expansion of?

#204. What are the possible values of a and n if

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

#206. What is the relation between w, x, y, and z if

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#207. If three consecutive terms of an Arithmetic Progression and Geometric Progression are a, b, and c, find the value of

#208. If the sum of the first 2n terms of an Arithmetic Progression is equal to the sum of the next n terms, find the sum of the first n+2 terms given that the first term is a.

#209. Find the sum to n terms of the series

#210.Find the sum of the given series upto n terms:

Character is who you are when no one is looking.

Offline

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

*Last edited by JaneFairfax (2009-03-04 07:53:59)*

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

Answer to #209:-

Correct, JaneFairfax!

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#211. Find the sum of the following series to n terms:-

#212. If a[sub]1[/sub], a[sub]2[/sub], a[sub]3[/sub], .... are in Arithmetic Progression and a[sub]1[/sub], a[sub]2[/sub], a[sub]3[/sub], .... are all positive, find the value of

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#213. The p[sup]th[/sup] term of an Arithmetic progression is

. Find the sum to n terms of the Arithmetic Progression.#214. Solve for n if nC[sub]4[/sub], nC[sub]5[/sub], nC[sub]6[/sub] are in Arithmetic Progression.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#215. Find the common area enclosed by the two parabolas 4y² = 9x and 3x² = 16y.

#216. Find the area of the largest rectangle that can be inscribed in a semi-circle of radius r.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#217. What is the value of

#218. What is the value of

#219. If a, b, c, and d are real and

, then what is the value of ?#220. If one of the roots of the equation

is square of the other, then what is equal to?#221. Let

denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. What is the value of n is?

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,066

#222. What is the square root of

?Character is who you are when no one is looking.

Offline