A word (either meaningful or not) is formed of 2 vowels and 4 consonants. One vowel and one consonant revise itself therefore totally 8 letters are used in the word. The difference in the positions of revised consonants in the word is 1 and the difference in the positions of revised vowels in the word is 5. The starting letter of the word comes after 4 places than last letter of the word in English alphabet. The sum of positions in English alphabet of middle two letters in the word and the sum of positions in English alphabet of third letter from start and from end in the word are divisible by the number of days in a week. If the letters used in the word are A, H, M, N, O and R, then which one of the following word is incorrect according to the given condition
The starting letter of the word comes after 4 places than last letter of the word in English alphabet,
This condition is valid only for N and R hence starting letter is R and last is N.
The sum of positions in English alphabet of middle two letters in the word and the sum of positions in English alphabet of third letter from start and from end in the word are divisible by the number of days in a week.
Possible sets of letters which satisfies the condition are (A, M), (H, M), (M, O), (N, N),
The difference in the positions of revised consonants in the word is 1,
Therefore revised consonants have successive positions.
The difference in the positions of revised vowels in the word is 5,
Therefore their definite positions are 2nd and 6th.
Arrange these conditions.
Some birds sit on a tree. Square root of total birds moves away from there. Twice of the remaining birds are equal to the square of sum of birds flown away & square root of birds flown away. How many birds was on tree.
If (x-b) is the HCF of f(x) = x^2 + ax + 1 and g(x) = x^2 - 3x + 2, find the value of a and b.
OPtion
1) a = -2, b = 1
2) a = 2, b = -2
3) a = 1/2, b = 2
4) a = 3, b = 1
5) a = 3, b = -5/2
6) a = 4, b = -2
7) a = 1, b = 1
8) a = 1, b = -1
9) a = 5/2, b = -1
10) None of these
Solution
As (x-b) is the HCF of f(x) and g(x), (x-b) must be a factor of f(x) and g(x)g
Using factor theorem
Solve
Option 1)
Mr. Sonkar says to his son Suresh, " My age was two years more than 7 times of your’s age before 30 and 1/2 a year and after 2 and 1/2 a year, my age will be twice of yours age of 1/2 a year before". What will be the age of Suresh after 12 and 1/2 a year.
Let the present ages of father and son are "x" and "y" respectively.
According to the first condition given
(x - 30.5) = 7 ( y - 30.5 ) + 2 (i)
According to the second condition given
(x + 2.5) = 2 ( y – 0.5) (ii)
On solving these equations we get the solution.
673 is converted as (6+1)|(7+2)|(3+3), on reversing we get 697,
697 is converted as (6+1)|(9+2)|(7+3), on reversing we get 10117,
10117 is converted as (1+1)|(0+2)|(1+3)|(1+4)|(7+5), on reversing we get 125422
Take similar steps for finding answer.
Mathematics has 25%formulas, 25%proofs and apply 25%thinking and 25%efforts.
In real life situations proofs are nothing but already existed stories(we know the solutions from all experienced people).
formulas are nothing but goals. we have so many goals b