Mathematics

Even though it is a GK based blog, we are giving higher priority to getting a job. So we just familiarizing  some important Mathematics questions to freshers.

Mathematics has important role in all competitive exams. Even a single question can change your rank So  we are going to discuss some frequently asking maths questions in all competitive exams like IBPS, Bank Clerk, Postal Assistant, RRB and PSC. Adding more maths question is not so Practical in the case of our blog, so we are posting only One question from a category. Find more and practice regularly.

Some Important Maths Equations

1. a(b+c) = ab + ac

In just FIVE minutes you should learn to quickly multiply up to 20x20

In just FIVE minutes you should learn to quickly multiply up to 20x20 in
your head. With this trick, you will be able to multiply any two numbers
from 11 to 19 in your head quickly, without the use of a calculator.
I will assume that you know your multiplication table reasonably well up to
10x10.
Try this:
Take 15 x 13 for an example.
Always place the larger number of the two on top in your mind.
Then draw the shape of Africa mentally so it covers the 15 and the 3 from
the 13 below. Those covered numbers are all you need.
First add 15 + 3 = 18
Add a zero behind it (multiply by 10) to get 180.
Multiply the covered lower 3 x the single digit above it the "5" (3x5= 15)
Add 180 + 15 = 195.
That is It! Wasn't that easy? Practice it on paper first!

topic in any examination . Problems:

topic in any examination .
Problems:
1) What should come in place of both the question marks?
a) 9/? = ?/16
? 2 = 9 X 16
? = 3 X 4
= 12
In the same way try the below two problems
b)?/29 = 261/? => ?2 = 29 X 29 X 9 => ?= 29 X 3 => ? = 87
c) 13/? = ?/52
Try this question C by yourself
2)Which of the following fraction is the largest?
i) a)2/5 b)1/4 c) 5/8 d) 7/10
Note:If difference between numerator and denominator is same in all the fractions then the highest fraction is the one which has highest numerator or highest denominator . In the same way smallest fraction is the one which has the lowest numerator or lowest denominator.
a) 2/5 difference is 3
b) 1/4 difference is 3
c) 5/8 difference is 3
d) 7/10 difference is 3
So from the above note difference between numerator and denominator is 3 and is same in all four options. Hence the answer is option (d)
3)Which of the following fractions is the smallest?
a)3/5 b)5/7 c)1/3 d)7/9 e) 9/11
From the above note , difference is same in all cases so option d) is the answer.
4)Which of the following fraction is second from the left when they are arranged in ascending (increasing) order from left to right?
a)4/9 b) 5/8 c) 3/5 d) 2/3 e) 3/4
0.4 0.62 0.60 0.66 0.75
Here the difference is not same in all the cases so our note doesn’t work here . So what we have to do is calculate the exact value of all the options. They can be calculated very easily because only easy calculations will be asked in such cases. So below the options you can see the exact values of each fraction. Based on that the answer is option (c)
5)Which of the following fraction third from the right when they are arranged in descending (decreasing) order from left to right?
a)1/3 b)2/5 c)7/9 d)11/15 e) 3/4
0.3 0.4 0.77 0.74 0.75
Here one more important thing to be observed is the order. Even if you miss the order you will be wrong. And you need not calculate the entire value of the fraction, workout only upto 2 decimals and just do this calculation in mind and don’t put these simple calculations in paper as it may waste you a lot of time
So answer is option d)
6) If two – third of one – fifth of three – seventh of a number is four , then what was the number?
Don’t be panic , the solution is very simple that you can do it in your mind once you solve this problem
2/5 x 1/5 x 3/7 x h = 4 ( See that big question was put into just a small equation, so now its simple)
Now cancel the common terms and multiples and multiply the remaining terms
So the answer is h = 70.
7)If three-fifth of two-seventh of a number is 24, then what is its 40%?
3/5 x 2/7 x h = 24
so after cancelling multiples we get h 140
But the question is 40% of h so answer is 40/100 x 140 =56
8)If three-fourth of two-third of a number is 12, then what is the sum of its digits?
3/4 x 2/3 x h = 12
So h = 24
but the question is sum of the digits i.e 2+4 =6
9)If two-third of the first number is same as three – fourth of the second number, then what is their ratio?
2/3 h = 3/4 k =>h/k = 3/4 X 3/2 = 9:8
10)Sum of a two digit number and the number obtained by interchanging the digits is 44. What is the sum of the digits of the number?
Note: If ‘ab’ is a two digit number then sum of two digit number and the number obtained by interchanging the digits ‘ba’ is
= (10a + b) + (10b + a)
= 11(a+b)
Difference between the two digit number and the number obtained by interchanging the digits
= (10a +b ) - (10b + a)
= 9(a-b)
Here in the above problem it is given that
11(a+b) = 44
=> (a+b) = 4
therefore the answer is 4
11) Difference of a two digit number and the number obtained by interchanging the digits is 36. What is the sum of the digits of the number?
From the above note 9(a-b) = 36
therefore the answer is 4

TRICK Probability

TRICK

Probability = Occurrence of event/Total possible events
Simple probability problemSimplest questions asked in bank exams are asked about deck of cards, dice and coins. There is no co-occurrence of events.
Lets take an example :-
Question -One card is drawn from a deck of 52 cards. Find the probability that it is a black queen or king.
Simple solution to this problem is 2/52 = 1/26
Venn Diagram
Question - One card is drawn from a deck of 52 cards. Each card is equally likely to be drawn. Find the probability that card drawn is either black or queen.
In this question we are going to use a simple formula
P(AB) = A ∪ B ∩ AB
Don't be confused with the formula.
In a deck of cards there are 26 black cards and 4 queens. But 2 black cards are queen. These cards are part of grey and brown circles in above diagram. As pink region is added twice, we need to deduct it once.
So the solution is 26 + 4 - 2 = 28
Probability (AB) = 28/52 = 7/13
Independent Events
In case you need to find probability of happening of two independent events we use multiplication theorem.
P(AB) = P(A) * P(B)
Lets understand this theorem with help of an example
Question -An unbiased coin is tossed twice. Find the probability of getting 1,2,3 or in the first toss and 4,5 or 6 in second attempt ?
Solution -Probability of getting 1,2,3 or 4 in first toss = 4/6 = 2/3
Probability of getting 4,5 or 6 in second toss = 3/6 = 1/2
Now both events are independent and we will use multiplication theorem
1/2 * 2/3 = 1/3

Trick to Find Cube Root of a number without Calculator

Trick to Find Cube Root of a number without Calculator

Cube Root.Number
CubeLast Digit of Cube
0 0 0
1 1 1
2 8 8
3 27 7
4 64 4
5 125 5
6 216 6
7 343 3
8 512 2
9 729 9
Trick Used:
We will follow these steps to find the cube root of a number:
1.Ignore the last3 digitsof the number. Let remaining number be“I”.
2.From the above table check which number’s cube is less than or equal to‘I’. It will be left part of our answer. Let it be“L”.
3.Let Right part of our answer be“R”. It will be determined from the above table. For Ex. If last digit of question is7, then last digit of our answer will be3.
4.Our answer will beL|R.

Example 1
Suppose we want to find the cube root of21952.
Step 1:Ignore last three digits of 21952. Remaining number left is’21′.
Step 2:From the above table cube of’2′is less than’21′. Therefore left part(L)of our answer will be’2′.
Step 3:Since last digit of‘21952‘is‘2‘. Therefore right part(R)of our answer will be’8′. (Because Last digit of ‘cube of 8′ is 2. see table above.)
Step 4:Our Answer will beL|R. Therefore Answer will be 2|8 =28.
Example 2
Suppose we want to find the cube root of148877.
Step 1:Ignore last three digits of 148877. Remaining number left is’148′.
Step 2:From the above table cube of’5′is less than’148′. Therefore left part(L)of our answer will be’5′.
Step 3:Since last digit of‘148877‘is‘7‘. Therefore right part(R)of our answer will be’3′. (Because Last digit of ‘cube of 3′ is 7. see table above.)
Step 4:Our Answer will beL|R. Therefore Answer will be 5|3 =53.
Example 3
Suppose we want to find the cube root of636056.
Step 1:Ignore last three digits of 636056. Remaining number left is’636′.
Step 2:From the above table cube of’8′is less than’636′. Therefore left part(L)of our answer will be’8′.
Step 3:Since last digit of‘636056‘is‘6‘. Therefore right part(R)of our answer will be’6′. (Because Last digit of ‘cube of 6′ is 6. see table above.)
Step 4:Our Answer will beL|R. Therefore Answer will be 8|6 =86.