Three consecutive integers are such that when they are taken in increasing order and multiplied by 2,3 and 4 respectively,they add upto 74.Find these numbers.

Three numbers are in G.P. whose sum is 70. If the extremes be each multiplied by 4 and the means by 5, they will be in A.P. Find the numbers.

Find the equation of the plane with the intercept 2,3 and 4 on x,y and z axes respectively.

Find the equation of plane with intercept 2,3 and 4 on x,y and z axis respectively.

Find the number of ways of dividing 15 things in to groups of 8, 4 and 3 respectively.

Out of 3 n consecutive integers, three are selected at random. Find the probability that their sum is divisible by 3 is

A rational number is such that when you multiply it by 5/2 and add 2/3 to the product,you get -7/12 .What is the number?

Take any three consecutive even numbers and find their product , for example, 2xx4xx6=48, 4xx6xx8 = 192 , and so on. Make three conjectures about these products.

Number of electrons transferred in each case when KMnO_4 acts as an oxidising agent to give MnO_2, Mn^(2+), Mn_2(O)_3 and MnO_4^(2-) respectively are :

Statement-1: The smallest positive integer n such that n! can be expressed as a product of n-3 consecutive integers, is 6. Statement-2: Product of three consecutive integers is divisible by 6.