Please Address the Question.
Find the smallest positive integer that leaves a remainder of 1, 2, 3 and 4 when divided by 3, 5, 7 and 9 respectively.
What will be the minimum value of n for which 36!/12ⁿ is not divisible by 12 ?
a) 35
b) 34
c) 18
d) 17
e) 4
Find the value of x for which the below expression is a perfect square:
2^84+2^(53+x)+2^100
Consider a convex polygon with 11 sides. What is the least number of interior angles that are obtuse or right (i.e. ≥90∘)?
How often does the factor 2 occur in the product (n + 1)(n + 2)...(2n - 1)2n ?
A teacher asked 4 students to think of 4-digit numbers, then she asked them to shift the first digit to the end and add the new number to the old one. Then asked for their results:
A: 8612
B: 4322
C: 9867
D: 13859
Only one of them is correct, can you tell which one ??
Consider a convex polygon with 11 sides. What is the least number of interior angles that are obtuse or right (i.e. ≥90∘)?
For how many prime numbers 'p', the number 'p^2 + 11' has exactly six distinct positive integral divisors?
What can be said about the number N, if A, B, C, D, E, F denotes distinct digits from 0 to 9 in some order
N = ABCDEF x A x B x C x D x E x F
i) N is not a multiple of 3
ii) N is always a multiple of 3 but not of 9
iii) N is always a multiple of 9
iv) None of the above
How many of the first 242 positive integers are expressible as sum of three or fewer members of the set {1, 3, 9, 27, 81} if we are allowed to use same member more than once. For example, 19 = 9 + 9 + 1 can be represented but 20 cannot.
Aman: I'm thinking of a two digit number. Bet you can't guess it.
Naveen: Bet I can.
Aman: Well, I'll tell you remainder of my number with anything from 1 to 10, whichever you say, one at a time. How many questions do you think you will have to ask?
Naveen: That depends on how lucky I am. But I'll take my chances. I'm sure that I can guess your number with exactly _____ questions.
101 digits are selected randomly and two numbers a, b are formed using all digits exactly once. What is the probability that a^4 = b?
Set P is defined as follows
P = {4, 9, 15, 22, 30, …}
What is the sum of first 100 terms of P?
Sets A, B, C, D and S are defined as follows:
A = {3k + 1|k E W, k B = {4k + 2|k E W, k C = {6k + 3|k E W, k D = {8k + 4|k E W, k
S = {A ∩ B ∩ C ∩ D}
What is the number of elements in set S?
A survey was conducted among 200 people, where they were asked if they had watched first 3 games of recent T-20 tournament. 50 said they watched only the first game, 25 watched only the second game, and some people watched only the third game. 40 said they watched the second and the third games only, and 20 said they watched all the games. Also total number of people who have not watched any game is 25. Then what will be the maximum number of people who watched only the third game?
sultan took a loan from the bank at 8% p.a and was supposed to pay a sum of rs 2240 at the end of 4 years.If the same sum is cleared off in four equal annual installments at the same rate.the amount of each installments will be ?(simple interest)
how many 4 digits numbers are there whose decimal notation contains not more than 2 distinct digits?
In a test consisting of 15 questions, 3 marks are awarded for a correct answer, 1 mark is deductedfor an incorrect answer and no mark is awarded for an unattempted question. If a student attemptsat least one question in the paper, what is the number of distinct scores that he can get?
(a) 57 (b) 58 (c) 59 (d) None of these