by shivamtripathi22 | Jun 7, 2025 | Uncategorized
1. Permutation & Combination(i) Introduction of Selection/Combination(ii) Number of ways of selecting ‘r’ articles from ‘n’ distinct article(iii) Number of ways of selecting ‘r’ articles from ‘n’ distinct articles if...
by shivamtripathi22 | Jun 7, 2025 | Uncategorized
Races & Circular...
by shivamtripathi22 | Jun 7, 2025 | Uncategorized
Boat and...
by shivamtripathi22 | Jun 7, 2025 | Uncategorized
AP, GP & HP Arithmetic Progression(AP):- AP is a series of numbers where the difference between any two consecutive terms is constant. This constant difference is called the common difference.Ex:-General form: a, a + d, a + 2d, a + 3d, ……..till n...
by shivamtripathi22 | Jun 6, 2025 | Uncategorized
Number of zeroes in an expression:- Zero will be formed when we multiply 2 and 510 = 2×5100 = 2²×5²1000 = 2³×5³10000 = 2⁴×5⁴So we can say that to have ‘n’ zeroes at the end of a product we need exactly ‘n’ combinations of 2 and 5. Number of...
by shivamtripathi22 | Jun 5, 2025 | Uncategorized
Factor Theory Concept ⇒ Consider a composite number n ⇒ n = aᵖbᑫcʳ………..where a, b, c are prime numbers & p, q, r are natural numbers.ThenNumber of factors of n is given...
by shivamtripathi22 | Jun 5, 2025 | Uncategorized
Unit Digit:- The last digit of a number is called unit...
by shivamtripathi22 | Jun 4, 2025 | Uncategorized
Remainder Theorem:...
by shivamtripathi22 | Dec 3, 2024 | Uncategorized
Percentage:- The word ‘per cent’ means per hundred. Thus 9 percent means 9 parts out of 100 parts. This can also be written as (frac{9}{100}).Therefore percentage is a fraction whose denominator is 100, and the numerator of this fraction is called the Rate...
by shivamtripathi22 | Nov 17, 2024 | Uncategorized
1. 15 litres of a mixture of milk and water in the ratio 2:1, the amount of milk added to the mixture so as to have milk and water in the ratio 5:2 ? View Solution 2. 72 litres of a mixture contains milk and water in the ratio of 27:5. How much more water is to be...