Find the number of factors of 13! + 14! + 15! which are one more than multiple of 4 !
Team BV--Pratik Gauri
ABC is a triangle with circumcenter O, obtuse angle BAC and AB is less than AC. M and N are the midpoints of BC and AO respectively. Let D be the intersection of MN with AC. If 2AD=(AB+AC), what is the measure (in degrees) of ∠BAC?
A bin contains 11 blue chips, 4 red chips, 7 green chips, and 16 yellow chips. The probability of drawing a red chip, putting it back in the bin, then drawing a green chip can be written as ab, where a and b are positive, coprime integers. What is the value of a+b?
Hi All,
Please Address the question.
Q. A fraction is such that if double the numerator and tripple the denominator is changed by +10% and -30% respectively, then we get 11% of 16/21
I am getting -- 8/99
(2p*11)/(3q*7) = (1/9) * (16/21)
OA = 2/25
There is a remainder computing algorithm that takes input only in the form of 2^k and then returns the remainder when this number is divided by k. What is the absolute difference between the outputs, for k=1990 and k=1001?
N and M are positive integers such that N+M=21. The largest possible value of 1/N+1/M is a/b, where a and b are positive co-prime integers. What is the value of a+b?
is the largest possible value of a/b = N+M/NM = 21/(21-M)M = 21/(21M - M^2)
i don't know what must i do next
Let f be a function from the positive integers to the positive integers satisfying
f(1)=2, f(2)=1, f(3n)=3f(n)
f(3n+1)=3f(n)+2, f(3n+2)=3f(n)+1.
How many positive integers N≤1000 satisfy f(N)=2N?
Determine the leftmost three digits of the number 1^1 + 2^2 + 3^3 + … + 999^999 + 1000^1000
Given that the equation x^3 + ax2 + bx + c = 0 has three real roots α, beta and gamma. If [α] = [beta] = [gamma] =1, then which of the following cannot be a combination of the values of the constants 'c' and 'a'? {Here, [x] denotes the greatest integer less than or equal to x.}
a) a = –3.3 and c = –1.25 c) a = –5.7 and c = –6.75
b) a = –4.8 and c = –3.75 (d) a = –4.2 and c = –2.85
1. The sequence 1, 3, 4, 9, 10, 12, ... includes all numbers that are a sum of one or more distinct powers of 3. Then the 50th term of the sequence is.
Let S(n) be the set of the numbers 2 ± √(2 ± √(2 ± √2 ± · · · ± √2)))· · ·) having n square root symbols and (n + 1) 2's. Evaluate the product of all elements of S(n).
Find the GCD of all the terms we can get by the expression a^4 - 10a^2 + 9, where a is a prime number greater than 5
1. Delegates from 9 countries including A, B ,C, D are to be seated in a row. How many different seating arrangements are possible if the delegates of the countries A and B are to be seated next to each other and the delegates of C and D are not be seated next to each other?
ls5 �fi1. We define the number 's' as
(1to infinity ) Σ 1 / ((10^i) - 1) = 1/9 + 1/99 + 1/999 + 1/9999 + 1/99999 + ....... = 0.12232424....
Determine the smallest prime number 'p' for which the pth digit right of the decimal point of 's' is greater than 2.
A right angled triangle have lengths 10,8,6. A circle with center P and radius 1 rolls around the inside it, always remaining tangent to at least one side of the triangle. When P first returns to its original position, through what distance has P traveled?
(A) 10 (B) 12 (C) 14 (D) 15 (E) 17
Which of the following could represent the exact number of zeroes that n! could end with, for any natural value of n.
answer - 32
How would you go about it?
Please solve this
(sinA+cosecA)^2+(cosA+secA)^2 will be equal to
Tan^2A+cot^2A+4
Tan^2A-cot^2A+5
Tan^2A-cot^2A
Tan^2A+cot^2A+7
please explain
A boy has 121 rupees with him in 1 rupee coins.He must fill it in piggy banks so that he can hand out any amount without breaking open the piggy bank.what r th min number of piggy banks required
What is the units digit of 1^4+2^4+3^4+4^4+...+120^4