Let x = 1! + 2! + 3! + 4! + ... + 100!. Unit's digit ofx^x^x^x..(infinite) is
- 1
- Can't be determined
- 3
- 1 or 3 depending upon the number of times x appears in the power.
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a dies is rolled 6 times . 1,2,3,4,5,6 appears on the consecutive throws of the dies . how many ways are possible of having 1 before 6 ?
the number of permutation of the letters a b c d e f g such that neither the pattern "beg" nor the pattern "acd " occurs ?
Liquid A contains water to milk in 3:5 , B contain 7:8. in what ratio these two liquids should me mixed to get new liquid of 1:2.
* Copied from CGL Thread
in an examination the maximum marks for each of the 3 papers is 50.The max marks for the 4th paper is 100. find the number of ways by which a student can get 60% marks in aggregate?
Vessel 'A' contain liquid 'X' and 'Y' in the ratio of 5:3 and Vessel 'B' contain liquid X and Y in the ratio of 3:5. IN what ratio should the liquid in A and B be mixed in order to have resultant ratio of 2:1 of X and Y??
If X is an positive even integer, what is the probability that X is divisible by 48?
- 1/2
- None of the these
- Cannot be determined
- 1/48
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How many possible 6 digit numbers are there of the form N=abcabd where aā 0,dā 0, d=c+1 and N is a perfect square?
Which of the following is the smallest?
a.(5)^1/2 b.(6)^1/3 c.(8)^1/4 d.(12)^1/5
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In triangle ABC, D is the midpoint of AC and E is the midpoint of AB. BD and CE are perpendicular to each other and intersect at the point G. If AB=7 and AC=9, what is the value of BC^2?
A school is running a raffle for two prizes. 59 tickets were sold for the raffle, numbered 1,ā¦,59. All the tickets are put into a hat and a teacher picks out two tickets which have numbers i and j from the hat. What is the expected value of |iāj|?
Triangle ABC has side lengths BC=13,CA=14,AB=15. A point P is selected at random from the interior of the triangle and the line AP is extended to meet BC at the point Q. What is the expected value of area of ABQ ?
How many triangle of distinct area can be formed such that all the vertices of the triangle should be chosen from the 8 vertices of cube.
Two players play a game starting with a pile of n stones. The players take turns removing stones from the pile. On their turn they are allowed to remove 1 stone from the pile, 2 stones from the pile, or half the stones from the pile, provided the number of stones in the pile is even. The player who wins is the player who makes the last move (i.e. removes the last stone). If the values of n can be any number from 1 to 500 (inclusive), determine for how many of these games the first player can win the game if he plays optimally.
P is a set of all natural numbers wit four factors such that sum of all the factors , excluding the no itself is 31.Find the sum of all the elements in P?
- 495
- 898
- 125
- 716
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Find the largest integer with n ā¤ 4,000,000 such that ā(n + ā(n + ā(n + .... ))) is an integer.
a) 2000
b) 3,999,990
c) 3,998,000
d) None
can someone please answer this question :
If TAYLOR SERIES EXPANSION for f(x) = ln(1+x) is
X - x2/2 + x3/3 - x4/4 + x5/5 - x6/6... =
ā (-1)(n-1) *( x^n/n ) ( for n = 1 to ā)
Then what is the corresponding log function for the taylor series expansion :
((-1)^(n+1)x^2n)/(2n)
can someone please answer this question :
If TAYLOR SERIES EXPANSION for f(x) = ln(1+x) is
X - x2/2 + x3/3 - x4/4 + x5/5 - x6/6... =
ā (-1)^(n-1) *( x^n/n ) ( for n = 1 to ā)
Then what is the corresponding log function for the taylor series expansion :
((-1)^(n+1)x^2n)/(2n)
How many 5 digit numbers are there such that there is at least one digit "1", at least one digit "2", and at least one digit "3".
In triangle ABC right angled at A length BC=15 and its in radius r=4 then sides of triangle is?