Tips and Ticks ഗണിത സൂത്രവാക്യം


Tips and Ticks ഗണിത സൂത്രവാക്യം

  • ആദ്യത്തെ \'n\' എണ്ണൽ സംഖ്യകളുടെ തുക = n(n+1) /2
  • ആദ്യത്തെ \'n\' ഒറ്റ സംഖ്യകളുടെ തുക = n²
  • ആദ്യത്തെ \'n\' ഇരട്ട സംഖ്യകളുടെ തുക = n(n+1)
  • ആദ്യത്തെ \'n\' എണ്ണൽ സംഖ്യകളുടെ വർഗ്ഗങ്ങളുടെ തുക = n(n+1)(2n+1) / 6
  • ആദ്യത്തെ \'n\' എണ്ണൽ സംഖ്യകളുടെ ക്യൂബുകളുടെ തുക = [n(n+1)/ 2]²
  • ആദ്യ പദം \'a\', പൊതു വ്യത്യാസം \'d\' ആയാൽ n-മത്തെ പദം കാണാൻ = a+ (n -1) d
  • ആദ്യ പദം \'a\', പൊതു വ്യത്യാസം \'d\' ആയാൽ, n പദങ്ങളുടെ തുക കാണാൻ = n/2[2a + (n - 1)d]
  • ആദ്യ പദവും (t1), n-മത്തെ പദവും (tn) തന്നാൽ, ശ്രേണിയിലെ പദങ്ങളുടെ എണ്ണവും (n) അറിഞ്ഞാൽ തുക കാണാൻ = n/2[t1 + tn]
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Average calculation

N = the number of terms  .

S = the sum of the numbers in the set.

Average = S/N .


For example.

The marks of a student in five subjects are 96, 94, 92, 87, and 81, then what is the average score of the student?.

N = 5.

S = 96 + 94 + 92 + 87 + 81 = 450.

A = 450/5 = 90.


Another type questions .

1). There are 36 boys and 44 girls in a class. The average score of boys is 40 and girls are 35. Then what will be the average mark? .


Total mark of 36 boys = 36 x 40 = 1440.

Total mark of 44 girls = 35 x 44 = 1540.

Total mark of 80 Students = 1440 + 1540 = 2980 .

Average mark of the class = (2980 / 80).

                 ...

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Combinations and Permutations

Permutation and combination related questions are common in PSC and Bank exams.

Before going to Combinations and Permutations, first lean about factorial. .

If  n  is a positive integer then, factorial of n is denoted as n! . .


4! = (1 x 2 x 3 x 4 ) = 24.


Permutations are for lists of items, whose order matters and combinations are for group of items where order doesn’t matter. in other words, .

When the order of items doesn\\\'t matter, it is called as Combination.
When the order of items does matter it is called as Permutation.


The number of permutations of n objects taken r at a time is determined by using this formula:.

C(n,r)=n!/((n−r)!r!) .

Combination : Picking a team of 3 people from a football coaching group of 10. C(10,3) = 10!(3!(10−3)!) = 120. ....

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BODMAS Rule

BODMAS is an acronym and it stands for Bracket, Of, Division, Multiplication, Addition and Subtraction. .

This explains the order of operations to solve an expression. According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve/simplify the bracket followed by of (powers and roots etc.), then division , multiplication , addition and subtraction from left to right. .

Example :.

7 + (6 × 52 + 3) =   7 + (6 × 25 + 3).

7 + (150 + 3).

7 + (153).

7 + 153 .

Ans: 160. .

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