Consider N=20132013…2013, where N consists of the number 2013 repeated 2013 times. What is the remainder of N when divided by 1001?
For how many odd positive integers n
what is the value of log [(p(p(p........infinity)^1/2)^1/2)^1/2 divide by (q(q(q...infinity)^1/2)^1/2)^1/2 ] ?
a 1/2 log p to the base q
b 1/4 log p to the base q
c log p to the base q
d infinity
2. if the mantisaas of the common logarithm of 2548 and 6732 are 4062 and 8282 respectively, what is the common logarithm of 9th root of (.002548/.6732) ?
a -1.3976 b .3976 c -1.7309 d .7309 d none
please tell the approach @chillfactor @AvishekAdhvaryu @anantn @scrabbler
Tetrahedron ABCD has side lengths AB=CD=12, and these edges are perpendicular to each other. Let Eand F be the midpoints of AB and CD respectively. We are given that EF=10 and is perpendicular to both AB and CD. What is the volume of ABCD?
What is the largest 3 digit divisor of N=1024^3−639^3−385^3?
Find the smallest prime number N such that the following is true:
The largest prime factor of N−1 is A; The largest prime factor of A−1 is B; The largest prime factor of B−1 is 7.
5 distinct numbers are chosen out of first 8 natural numbers. The probability that the sum of these numbers is at least 20 is
- 45/56
- 17/28
- 2/7
- 11/16
0 voters
The function f from the real numbers to the real numbers satisfies f(1)=4, and
f(x+y)=(1+y/(x+1))f(x)+(1+x/(y+1))f(y)+x^2y+xy+xy^2, for x,y≠−1, x,y real numbers. If f(5/3)=a/b, where a and b are coprime positive integers, what is the value of a+b?
How many 5 digit numbers N are there, such that the digit sum of N is 43, and N is divisible by 11?
3 men and 5 women together can finish a job in 3 days.. working on the same job 3 women takes 5 days more than the time required by 2 men. what is ratio of efficiency of a man to a woman?
A five digit number is formed using digits 1,3 ,5,7 and 9 without repeating any one of them. wht is the sum of all such possible numbers.
1.6666600
2.6666660
3.6666666
4. None
Consider the function on the integers given by f(x,y)=x^2y. How many ordered pairs of integers satisfying −10≤x,y≤10 is f(x,y)=f(y,x)?
For the set of integers Z, an arithmetic operation $ is defined as a$b=a+b+2ab. How many elements of Z have an inverse element for $?
How many ordered triples of rational numbers (a,b,c) are there such that the cubic polynomials f(x)=x^3+ax^2+bx+c has roots a,b and c?
note :
repeated roots is allowed
last two digits of 4^1997?
please solve the question
a large solid sphere of diameter 15 m is melted and recast into several small spheres of diameter 3m. what % increase in surface area of smaller spheres over that of large sphere?
a blacksmith has a rectangular iron sheet 10 feet long. he has to cut out 7 circular discs from this sheet. what is the minimum possible iron sheet width if radius of each disc = 1 feet?
10000!=[(100!)^k]*P, where k,p are integers. find max value of k:
a. 105
b. 102
c. 103
d. 104
Amit has a pencil box of volume 60 cm cubic. what can be the maximum possible length of pencil that can be accommodated in the box. given all sides are integral (in cm) and different from each other?