Maths Questions 19 May

Mathematics for competitive examination Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk

www.afterschoool.tk

Mention smallest prime number? • 2

www.afterschoool.tk

How many prime numbers are there till 100? • 2,3,5,7,11,13,17,19,23,29,31,37,41,43, 47,53,59,61,67,71,73,79,83,89,97. • Count these: • Total 25

www.afterschoool.tk

Is 1027 a prime number? • Step 1. – take square root of 1027 – to nearest place – lets say 33. • Take all prime numbers till 33 • Divide 1027 by each of these numbers and see – what remainder do you get - if 1027 is not divisible by any one of these – it is prime number. • 2,3,5,7,11,13,17,19,23,29,31 – try with these • Since none of these words divide 1027, so it is a prime no.

www.afterschoool.tk

How many numbers are there till 1000, which are divisible by 7 and 11? • • • • • •

Steps : Divide 1000 by 7= 142 (ignore decimals) Divide 1000 by 11=90 (ignore decimals) Divide 1000 by 77 =12(ignore decimals) Add 142+90 and deduct 12 142+90-12 = 220 Ans.

www.afterschoool.tk

Find the average of first 12 prime numbers? • Step 1: take first 12 prime numbers. 2,3,5,7,11,13,17,19,23,29,31,37 • Step 2: add these numbers: =197 • Step 3: divide 197 by 12 (as there are 12 digits) • You get 16.41 Ans.

www.afterschoool.tk

Which of the following is coprime: (23:46),(49:210),(18:25) • Find the two numbers which don’t have even one number common among them. • Obviously, 18 and 25 don’t have any common factor – as the factors of 18 are 2*3*3, and factors of 25 are 5*5– so this is the answer. www.afterschoool.tk

How many four digit numbers can you make with 1,2,3,4 (repeatition not allowed)? • There are four digits – so you can make 4! (factorials) numbers i.e. • 4*3*2*1 = 24 Ans.

www.afterschoool.tk

How many numbers can you make with 1,2,3,4 (repeatition not allowed)? • Four digit numbers: 24 (as per previous solution) • Three digit numbers: • For first digit, you have four choices, and for second digit you have three choice and for third digit you have 2 choice so ans is : 4*3*2 = 24 • For two digit numbers : • For first digit you have 4 choice and for second digit you have 3 choices so : 4*3 = 12 • For one digit number – you have 4 choice only. • Total them up: 24+24+12+4 = 64 Ans.

www.afterschoool.tk

How many four digit numbers can you make with 1,2,3,4 (repetition allowed)? • There are four choices for you for each digit, so the answer is 4*4*4*4=256 Ans. www.afterschoool.tk

How many four numbers can you make with 1,2,3,4 (repetition allowed)?

• • • • •

Four digit numbers : 256 Three digit numbers: 4*4*4 =64 Two digit numbers: 4*4=16 One digit numbers: 4 Total: 256+64+16+4= 340

www.afterschoool.tk

How many four digit numbers can you make with 1,2,3,4 (repetition not allowed) which are exactly divisible by 4? • Any number will be divisible by four only if its last two

digits are divisible by 4, so find out all the possibilities for last two digits. These are : 24,12,32 (3 only), for the first two digits, you have remaining two choices. Thus total possibilities are: • 3*2 =6 ans.

www.afterschoool.tk

How many numbers can you make with 1,2,3,4 (repetition not allowed) which are exactly divisible by 4? • Four digit numbers = 6 (previous solution) • Three digit numbers = 6 (we have two choices for first digit and three choices for last two digits, so 2*3=6) • Two digit numbers = 3 • One digit number =1 • Total = 16

www.afterschoool.tk

In how many ways, can 4 person sit on a round table? • The formulae is (n-1)! • So solution is (4-1)! = 3! • =3*2*1 =6 Ans.

www.afterschoool.tk

In how many ways can we make a necklace from 4 diamonds? • • • • •

Here the formulae is :1/2 (n-1)! =1/2(4-1)! =1/2(3)! =1/2*(3*2*1) =3 Ans.

www.afterschoool.tk

What is the average speed of an airplane which traveled by 200 km per hour once and 300 Km. per hour next time (same distance)?

• For all such questions (speed) use harmonic mean. • Take harmonic mean of 200 and 300, you will get 240: formulae is ( inverse of ½(1/200+1/300) ) Ans.

www.afterschoool.tk

www.afterschoool.tk

Thanks Afterschoool conducts three year integrated PGPSE (after class 12 along with CA & CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.

www.afterschoool.tk

www.afterschoool.tk social entrepreneurship for better society

www.afterschoool.tk