meaximum value of Sin^8@ + cos^18 @?
@chillfactor sir,
maximum value of sin^8@ + cos^14@ ?
@chillfactor sir
How many positive integers less than 1998 are relatively prime to 1547?
Mr. Jones has eight children of different ages. On a family trip his oldest child, who is 9, spots a license plate with a 4-digit number in which each of two digits appears two times. "Look, daddy!" she exclaims. "That number is evenly divisible by the age of each of us kids!" "That's right," replies Mr. Jones, "and the last two digits just happen to be my age." Which of the following is not the age of one of Mr. Jones's children?
Mr. Jones has eight children of different ages. On a family trip his oldest child, who is 9, spots a license plate with a 4-digit number in which each of two digits appears two times. "Look, daddy!" she exclaims. "That number is evenly divisible by the age of each of us kids!" "That's right," replies Mr. Jones, "and the last two digits just happen to be my age." Which of the following is not the age of one of Mr. Jones's children?
1)4
2)5
3)6
4)7
5)8
An object in the plane moves from one lattice point to another. At each step, the object may move one unit to the right, one unit to the left, one unit up, or one unit down. If the object starts at the origin and takes a ten-step path, how many different points could be the final point?
A,B,C play a game of rolling die in that order. the person who throws a six is considered to have won the game. after m throws no one has won the game. so the 3 of them took a break after noting down whose turn it was next. if when they resumed the game the probability that A wins the game is the geometric mean of the probability that B wins the game and the probability that C wins the game , then which of the following could be the value of m?
a)6 b)7 c)8 d) none.
Is there any short method of solving this one? I found it in one of the Aimcats
Is there any short method of solving this one? I found it in one of the Aimcats
The number of divisors of every natural number till 1000 is calculated. Which number has the highest number of divisors?
I need to understand the theory behind the solution. Please explain. Thanks π
Find the number of 6-term strictly increasing geometric progressions, such that all terms are positive integers less than 1000.
In a two digit number , the digits differ by 2. 10 times the number exceeds 5 times the sum of the number formed by reversing its digits and the sum of its42 digits by 90. The number is
- 36
- 42
- 46
- 22
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Let x and y be real numbers. Find the smallest possible value of |2 β x| + |x β y| + |y β 2004| .
find the remainder when 2^400 divide by 400 ??
A tournament took place between 5 chess players. Every player played exactly one game with each of the other 4 players. A player gets 1 point for a win and 1/2 a point for a draw. It is known that at the end of the event, no two players had the same number of points, the player in ο¬rst place didn't have a single draw, the one in second place didn't lose a single game, and the one in fourth place didn't win a single game. How many games ended in a draw?
the sum Find the sum of integers c for all triples of integers (a,b,c),aβ€bβ€c, that satisfy the system of equations
β§β©β¨a^2βbc=91 , b^2 β ac = 91 c^2 β ab = 91
Details and assumptions
If a number c appears in several different triples (a,b,c), it must be counted with multiplicity.
please help
P, Q, R, S, T, U, and V are distinct nonnegative integers that are less than 10. We have that
P β Q = R Γ· S = T Γ U = T + V = U.
Find the sum P + Q + R + S + T + U + V.
The number '7abcdefg77' is a 10-digit number (written in base 10) that is equal to the cube of an integer. What is the digit g?
P, Q, R, S, T, U, and V are distinct nonnegative integers that are less than 10. We have that
P β Q = R Γ· S = T Γ U = T + V = U.
Find the sum P + Q + R + S + T + U + V.
22
x and y are positive values satisfying x+y=14. When ln(y2+4xy+7) attains its maximum (subject to the given constraint), what is the value of 1/xy?
Vincenzo makes a sandwich using four kinds of Italian lunch meat: Genoa, prosciutto, Calabrese and capicola and two kinds of Italian cheese: provolone and asiago. Vincenzo's sandwich has a single layer of each type of meat and a single layer of each kind of cheese, but he also wants to make sure that the two types of cheese are not next to each other. How many different ways can Vincenzo arrange the meat and cheese on his sandwich?