A farmer has 12 plots of land, arranged in a row. To ensure viability of the soil, the farmer never uses two adjacent plots at the same time. This season, the farmer wishes to plant one plot of each of the following: corn, wheat, soybeans, and rice. Each crop is assigned its own plot of land. How many ways can the farmer allocate plots of land for these crops?

(a) 1680 (b) 3024 (c) 5040 (d) 7920 (e) 11880

Let Pn be the set of all subsets of the set [n]={1,2,…,n}. If two distinct elements of P5 are chosen at random, the expected number of elements (of [n]) that they have in common can be expressed as a/b where a and b are coprime positive integers. What is the value of a+b?

Details and assumptions

As an explicit example, P2={∅,{1},{2},{1,2}}. {1} and {1,2} are 2 elements of P2, which have 1 element in common.

N! is completely divisible by 13^52 . What is sum of the digits of the smallest such number N? (a) 11 (b) 15 (c) 16 (d) 19

Smallest integer K is a perfect square when divided by 2 and a perfect cube when divided by 3. Find K

For how many integral values of x is (x^2-8x+24)/(x^2-8x+16) is a prime no?

A,B,C play a game of rolling die in that order. the person who throws a six is considered to have won the game. after m throws no one has won the game. so the 3 of them took a break after noting down whose turn it was next. if when they resumed the game the probability that A wins the game is the geometric mean of the probability that B wins the game and the probability that C wins the game , then which of the following could be the value of m?

How many integral values of (x, y) will satisfy the following inequality:-
√(x² - 6x + 25) + √(y² - 8y + 25) ≤ 7

a) 0
b) 1

c) 2
d) 3
e) more than 3

In how many different way a fruit basket can be filled with at least one fruit if we have 7 different apples, 5 different mangoes and 10 identical oranges?

Don't have the answer...

find the no of odd natural nos less than or equal to 1200 which are divisible by neither 3 or 5??

320

640

300

280