wat is d remainder when 34^413 is divided by 9?
"If the number 1735x86y4 is divisible by 11, what is the least value x-y can assume"
The answer is -5
the tens and units alternate sums are 20+y and 14+x.....
What is the remainder when 723^243 + 318^243 is divided by 17?
Given that 2^x^y + x^2^y = 3. What is the total number of integral solutions for the given equation?
0
1
2
3
more than 3
Let a,c (2,4,6,8,10,12) and b (22,24,26), where a, b and c are distinct. Find the number of equations of the form ax^2 + bx + c = 0, that can be formed such that the equation has real roots.
a, b, c are three natural numbers and each of the three natural numbers are multiplied by difference of other two, if sum of these three products is 2008, then find the least possible value of a + b + c.
take a > b > c
a*(b-c) + b*(a-c) + c*(a-b) = 2008
ab - ac + ab - bc + ac - bc = 2008
2b(a-c) = 2008
b(a-c) = 1004 = 251*4
a-c = 251, b = 4 (as a > b > c)
as we need to minimize a b c so
a = 252, b = 4, c = 1
a+b+c = 257
Min value of expression :
(x-5)^2 + (x-7)^2 - (x-4)^2 - (x-8)^2 + (x-3)^2 + (x-9)^2
11
10
12
13
14
S = 5/(1^2 *2^2) + 11/(2^2*3^2) + 19/(3^2*4^2) + 29/(4^2*5^2) ..................infinity
Let A be a subset of T={1,2,…,100} subject to the condition that if 2 distinct elements a and b are in A, then a+b is not in A. What is the maximum value of |A|, which is the number of elements in A?
S = 5/(1^2 *2^2) + 11/(2^2*3^2) + 19/(3^2*4^2) + 29/(4^2*5^2) ..................infinity
2/1^2 - 3/2^2 + 3/2^2 - 4/3^2 + 4/3^2 - 5/4^2 + 5/4^2 - 6/5^2 + . . .
all terms except 1st and last eliminates, taking last term neglisible
=> 2/1^2 = 2
for RAINBOW how many words are there in which A is always before I and I is always before O?
In how mny ways letter of the word RAINBOW can be arranged so that only two vowels always remain together?
In how mny ways letter of the word MOBILE can be arranged so that at least two consonants always remain together?
Find the no of ways in which 12 different books can be arranged on a shelf so that two particular books shall not to be together?
An equilateral triangle with side length 33 is divided into 33^2 smaller unit equilateral triangles each with side 1, forming a triangular lattice. We color each segment of length 1 either Red, Blue or Green, subject to the condition that each small unit equilateral triangle has 3 sides with either 3 different colors or all the same color. If there are N distinct ways to color this triangle, what is the value of ⌊log(base9) N⌋?
Details and assumptions
Two colorings are distinct if at least one segment is colored differently.
Rotations and reflections are considered distinct colorings.
solve the inequality-
x^2 -|5x-3|-x
- b)x<3+2root2
- e)none of these
- c)x>-5
- d)-5<x>&lt;3+2root2</x>
- a)x&gt;3+2root2
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how many arrangement can be made out of letters of the word COMMITTEE taken all at a time such that the four vowels do not come together?
In how mny ways letter of the word MOBILE can be arranged so that at least two consonants always remain together?
explain please
how are you getting 144 discarding cases ?
Pleas Explain with yr answer choice
A Shopkeeper defrauds both the dealer and the customer by measuring weights incorrectly.when he is purchasing items from the dealer ,he takes 20% more than the indicated weight and when he is selling them to the customer,he gives 20% less than the indicated weight.If the price that the shopkeeper charges to the customer is the same as that the dealer charges the shopkeeper,then what profit percentage does the shop keeper make???
- 40%
- 60%
- 44%
- 50%
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