updates about cbse, university exams, results and other news

 

 Cbse annonces tentative dates for class xii practicals exams 2020-2021

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The IIM CAT 2020 admit cards  can be dowloaded 28th october 2020 evening onwards and the exam may be held on 29th november 2020

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 The online exam application forms for private students appearing  in cbse board 10th and 12th exams in 2021 is available at cbse website

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Anna university has given 75 days to engineering colleges to finish the theory portion of this semester ( using online ? mode.) by October 26 

*CBSE has released Teacher energised manuals for science and maths for 6th to 10th it is available on  http://cbseacademic.nic.in/

* There seems to be a one time exemption this year for students who have cleared only basic math paper in class 10 cbse board exam and who want to take up math in 11th standard in 2020 -2021 session.

*  The dates for application for optional exam for class 12th students who want to better their marks has been announced.The last date seems to be August 22nd .

* The date of application for compartment exams for class 12th students has been announced

* Regular students might have to apply through their schools while  private students may have to apply online. 

* Students can access more details at http://cbse.nic.in/ 

or cbse website 

 

*The exams may be held in September.

* cbse marking schemes for various exams in 10th and 12th is available at

https://www.jagranjosh.com/articles/cbse-marking-scheme-2020-for-10th-12th-released-download-pdf-1596814891-1

 

 

chapter 8 binomial theorem miscellaneous exercise

 1.Find a , b and n in the expansion of (a+b)^n if the first three terms in the expansion are 729, 7290, 30375

solution

 

2.  Find a if the coefficients of (x^2)  & (x^3) in the expansion of {(3+ax)^9} are equal 

solution

  3.find the coefficient of {x^5} in the expansion of{(1+2x)^6}{(1-x)^7}

solution

 

5.evaluate { (sqrt(3) + sqrt(2))^6 } - { (sqrt(3) - sqrt(2))^6 }

solution 

 6.find the value of [(a^2)+sqrt{(a^2)-1}]^4 + [(a^2)-sqrt{(a^2)-1}]^4 

solution

 

7.find an approximate value of (0.99^5) using the first three terms of its expansion

solution  

 

8.find n if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of [(fourth root of 2) + {1/(fourth root of 3)}]^n is (sqrt6):1 

solution

 

exercise 8.2

 

 5. find the 4th term in the expansion of (x-2y)^12

solution

7. Find the middle terms in the expansion of [3 - ((x^3) / 6)]^7

solution

Q8) Find the  middle terms in the expansion of [(x/3)+9y)]^10

solution

 

 10.The coefficients of the (r-1)th, rth, (r+1)th  terms in the expansion of [(x+1)^n] is in the ratio 1:3:5. Find n and r.

solution

 

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problem 12 and problem 13 of bayes theorem

 problem 12

A card from a pack of 52 cards is lost. From the remaining cards of the pack,two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.

Let E1 be the event that the lost card is a diamond.

let E2 be the event that the lost card is not a diamond.

let A be the event that the two cards selected from the remaining 51 cards are both diamonds .


P( E1 ) = ( 13 / 52 )  { 13 diamonds in a pack of 52 cards }

P( E2 ) = ( 39 / 52 )  { 52 - 13 = 39 non-diamonds in a pack of 52 cards }

P( A / E1 ) = ( C (12,2) / C(51,2) ) { If E1 occurs, there are only 12 more diamonds among the remaining 51 cards}

P( A / E2 ) = (  C (13,2) / C(51,2) ) { If E2 occurs, there are  13 diamonds among the remaining 51 cards}

where C(n,r) = number of combinations of n things taken r at a time.



Required probability = P [ lost card is a diamond given that the two cards drawn from the remaining 51 cards are both diamonds ]

Required probability = P [ E1 / A ]




P(E1 / A)=[( 13/52 )( C (12,2)/C(51,2))] / {[( 13/52 )( C (12,2)/C(51,2))]+[( 39/52)( C (13,2)/C(51,2))]  }


P ( E1 / A ) =  [(13) * C (12,2) ] / { [(13) * C (12,2) ] + [(39) * C (13,2) ] }

P ( E1 / A ) =  [ C (12,2) ] / { [ C (12,2) ] + [(3) * C (13,2) ] }  = ( 11 / 50 )

index of more problems on baye's theorem for ncert cbse mathematics

problem 13

 Probability that a man speaks truth is (  4 / 5 ). A coin is tossed and the man reports that a head appeared.Find the probability that actually there was a head.

Let E1 be the event that the coin toss actually resulted in a head.

let E2 be the event that the coin toss did not result in a head.

let A be the event that the man reports that a head appeared in the toss.


P( E1 ) = ( 1 / 2 ) 

P( E2 ) = ( 1 / 2 ) 

P( A / E1 ) = ( 4 / 5 ) { If E1 occurs, head has occured and the man is speaking the truth }

P( A / E2 ) = (  1 / 5 ) { If E2 occurs, head has not occured and the man is lying  hence [ 1 - (1/5)] }


Required probability = P [ the coin toss actually resulted in a head given that the man reports a head ]

Required probability = P [ E1 / A ]


 


P(E1 / A)=[( 1 / 2 )( 4 / 5 ) ] / {[( 1 / 2 )( 4 / 5 ) ] + [( 1 / 2 )( 1 / 5 ) ]  }


P ( E1 / A ) =  [4] / { [4] + [1] } = ( 4 / 5 )

index of more problems on baye's theorem for ncert cbse mathematics


disclaimer:
There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work