20 August Quantitative Aptitude And Language Proficiency Business Mathematics

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Quantitative Aptitude and Language proficiency

AFTERSCHO☺OL – DEVELOPING CHANGE MAKERS

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Quantitative Aptitude and Language proficiency

Dr. T.K. Jain.

AFTERSCHO☺OLCentre for social entrepreneurship

Bikaner

M: 9414430763

tkjainbkn@yahoo.co.in

www.afterschool.tk

www.afterschoool.tk

I toss a coin twice, what is the probability that I shall get head on both the occasion?

There are two possbility on a coin = either heo ad or a tail.

Head has probability of ½ (because there are two options, and one option out of two has one out of two probability).

To get head again, we need to get the same probability again. Thus probability of two head is ½ * ½ = ¼ answer.

What is the probability that if I draw a card from a card box, it is spade?

There are 52 cards in a card box. There are 13 spades in a card box. Thus the probability of getting a card out of card box is 13/52 or ¼ answer.

(probability = number of expected outcomes of something / total number of outcomes.

What is the probability that if I draw a card from a card box, it is a king?

There are 52 cards in a card box. There are 4 kings in a card box. Thus the probability of getting a card out of card box is 4/52 or 1/13 answer.

What is the probability that if I draw 2 cards from a card box, both are JACKS?

There are 52 cards in a card box. There are 4 JACKS in a card box. Thus the probability of getting a card out of card box is 4/52 or 1/13 answer. Probability that second card is also jack is 3/51 or 1/13 * 3/51 = 1/221 answer.

I throw two dice simultaneously, what is the probabilty that my total score is more than 10?

There are 6 numbers on a dice. I can get score from 0 to 6. the possibility that I get score more than 10 is as under:

6,6 or 6,5 or 5,6. thus there are 3 possibilities. The total number of possibilities are 6^2 = 36

Answer = 3/36 OR 1/12 (answer).

Solution continued . . . . The total possibilites are listed below: 6,1; 6,2; 6,3, ; 6,4, ; 6,5, 6,6 5,1; 5,2 ; 5,3 ‘ 5,4, 5,5 ; 5,6 4,1; 4,2; 4,3; 4,4 4,5,; 4,6; 3,1; 3,2; 3,3; 3,4,; 4,5,; 3,6 2,1; 2,2,; 2,3,; 2,4,; 2,5,; 2,6 1,1; 1,2,; 1,3,; 1,4,;1,5, 1,6 Thus there are 36 possibilities.

Three dice are thrown simultaneously, what is the probability that I get more than 16 points? One dice contains 6 points. Thus the

probabilities are : 6,6,5, or 6,5,6, or 5,6,6, or 6,6,6

Thus there are only 4 possibilities. The total number of possibilities are 6*6*6 -216

=4/216 or 1/54 (answer.)

Three dice are thrown simultaneously, what is the probability that I get more than 4 points?

Let us find out all the possibilities ,when the total of dice is 4 or less.

These are 1,1,1 or 121, or 2,1,1 or 1,1,2 . Thus there are only 4 possibilities. All other possibilities are 216-4 = 212.

Thus required probability is 212/216 answer.

What is the chance that a 2 digit number picked up at random is divisible by 10?

Let us find out number of 2 digit numbers.

WHAT IS A SINGLETON SET?

A SET CONTAINING ONLY ONE ELEMENT IS CALLED SINGLETON SET.

What are equal sets?

When two sets have same elements, they are called equal sets. For example: A = {1,2,3,} and B= {1,2,3,}

A and B are equal sets.

In how many ways can we write set?

Two : 1. roster or Braces form. Example : A = {1,2,3,} 2. set builder or algebraic form or rule

method or property method. N= {X: X is a natural number}

What is Є?

This symbol shows that one element is a part of set. For example,

A = {1,2,3,}, here we can write that 1 ЄA

What is proper subset?

If all the elements of P are also in Q but P is not equal to Q, we can say that P is proper subset of Q. for example,

A = {1,2,3,} and B= {1,2,3,4,5,6,7,} Here A is proper subset of B. A C B

What is union and intersection in sets?

Union means to unite two sets (to add two sets). Intersection means to find common elements in two sets.

Exmple: A = {1,2,3,} and B= {3,5,7,8,9} AUB is called A union B. = {1,2,3,5,7,8,9} A∩B is called A intersection B. ={3}

If A = {1,2,3,} How many subsets can you make from set A.

There are 3 elements in A, so formulae is 2^n subsets can be made. Thus we can make 2^3 = 8 subsets out of this set.

A null set is represented by which symbol?

Ф answer.

What is cardinal number in AUB, if A = {1,2,3,} and B= {11,12,13,14}

AUB = {1,2,3,11,12,13,14} Thus cardinal number is 7. answer.

What is cartesian product of A & B, if A = {1,2} and B= {5,6}

A * B = { (1,5), (1,6), (2,5),(2,6)} Here first element is from A and second

element is from B. the way it is written is called ordered pair, because here we have one element from A and another element from B.

What is AUA?

What is A U Ф

What is A ∩ Ф

Ф answer.

If A is a set of squares of all natural numbers, then what is domain of A?

Set of all natural numbers is domain of A.

If A is a set of squares of all natural numbers, then what is co-domain of A?

Set of squares of all natural numbers is co-domain of A.

If A is a set of squares of all natural numbers, then can we call it one - one function?

Yes - because there is distinct image in A for each natural number, thus it is One – one function.

If A is a set of squares of all natural numbers, then can we call it ONTO function?

Yes – because for each element in A, we have a preimage in the set of natural numbers. That means, if we take any number in A, (for example, 25), we will find its preimage in set of natural number (5 in this case). Answer.

If A is a set of squares of all natural numbers, then is it one to one correspondence (Bijective function)?

Yes, it is both one-one and ONTO therefore we call it One to one correspondence or Bijective function.

If A ={1,2,3}, and B {X: X is power Zero raised to each element of A}, what kind of function is it?

It is a constant function, because each element in A will have only one element in B, if you raise power zero to any element, it will be one. Thus each element in A will have only one answer in B (1). Thus this is a constant function.

When is a function invertible?

Only when it is one-one and ONTO (both the conditions must be fulfilled).

If A is a set of squares of all natural numbers, then can we call invertible function?

Yes, because function can be inverted. Instead of defining A is set of squares, we can define the other set as a set of square roots.

What may be the relation in the form of function between A & B, if A = {1,2} and B= {5,6} where A→B

(1,5), (2,6)

Or (1,5), (2,5) Or (1,6), (2,6).

What may not be the relation in the form of function between A & B, if A = {1,2} and B= {5,6}, where A→B

(1,5), (1,6)

Or (2,5), (2,6).

What is the domain of : (1,3) (2,4)?

Domain is (1,2)

What is the range of : (1,3) (2,4)?

If f(X) = 2^x, then is it one-one mapping?

Yes, because for each element in domain, we have a distinct element in range. Thus it is one-one mapping.

If F(X) = 2X, what is inverse function of this function?

1/2x answer.

If A has 32 elements and B has 24 element, and AUB have 40 elements, then how many elements are there in their intersection?

Add 32 and 24, we get 56. however, AUB has only 40, so we have 16 elements in intersection of A and B. answer.

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Components Pedagogy curriculum and approach based on IIM Ahmedabad and ISB

Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad) Meditation, spiritualisation, and self development Essential softwares for business Business plan, Research projects Participation in conferences / seminars Workshops on leadership, team building etc. Written submissions of research projects/articles / papers Interview of entrepreneurs, writing biographies of entrepreneurs Editing of journals / newsletters Consultancy / research projects Assignments, communication skill workshops Participation in conferences and seminars Group discussions, mock interviews, self development diaryng Mind Power Training & writing workshop (by Dr. T.K.Jain)

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Case Studies

We want to write case studies on social entrepreneurs, first generation entrepreneurs, ethical entrepreneurs. Please help us in this process. Help us to be in touch with entrepreneurs, so that we may develop entrepreneurs.

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