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Showing posts with label class 12. Show all posts
Showing posts with label class 12. Show all posts

Tuesday, December 27, 2016

index of miscellaneous problems on probablity

index of miscellaneous problems on probablity for cbse xii mathematics

problem 2
A couple has two children, Find the probability that both children are males, if it is known that at least one of the children is male.Also find the probability that both children are females, if it is known that the elder child is a female.
solution to miscellaneous problem 2 on probability of cbse class 12 mathematics

problem 3
Suppose that 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.
solution to miscellaneous problem 3 on probability of cbse class 12 mathematics

problem  4
Suppose that 90% of people are right handed. What is the probability that at most 6 of a random sample of 10 people are right handed?
solution to miscellaneous problem 4 on probability of cbse class 12 mathematics

problem
In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is (5/6). What is the probability that he will knock down fewer than 2 hurdles?

problem
If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive?

problem
An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known
P(A fails) = 0.2 P(B fails alone) = 0.15 P(A and B fail) = 0.15
Evaluate the following probabilities P(A fails|B has failed) ; P(A fails alone)
 answer to electronic assembly question from miscellaneous probability problem in cbse ncert xii mathematics

problem
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?


finding the value of n in binomial distribution given the probability question for cbse ncert 12th mathematics

problem
Assume that the chances of a patient having a heart attack is 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of a certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?
solution to miscellaneous problem  on probability of cbse class 12 mathematics


problem

Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls.One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black
solution to miscellaneous problem  on probability of cbse class 12 mathematics
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index of more problems on baye's theorem for ncert cbse xii mathematics

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Monday, March 11, 2013

integral using manipulation of numerator in terms of denominator

integral of 1/[sin²x cos²x]

 since sin²x + cos²x =1
 rewrite the numerator as sin²x + cos²x
 divide each term with the denominator
simplify and then integrate

 study  integration formulae






free guide on integration  or integral calculus for cbse isc kerala higher secondary class 12 ncert scert students


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index of math problems





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integral using substitution

integral of [√(tanx)] / [sinx cosx]

first introduce [√(tanx)] in the numerator and denominator

then simplify and change the tanx in the numerator in terms of sinx and cosx
simplify in terms of secx and tanx

then use substitution method

study  integration formulae  







 

free guide on integration  or integral calculus for cbse isc kerala higher secondary class 12 ncert scert students


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index of math problems





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Saturday, March 9, 2013

integral using trigonometric manipulation

integral of 1 / [cos(x-a)cos(x-b)]

we will try to write the numerator in terms of the denominator

so introduce sin(a-b) in the numerator and denominator

note that (x-b)-(x-a) =a-b

so write sin(a-b) as sin[ (x-b)-(x-a) ] and expand using sin[A-B] formula

divide the numerator term by term with the denominator

reduce to terms involving sec and then integrate

study  integration formulae a 







 

free guide on integration  or integral calculus for cbse isc kerala higher secondary class 12 ncert scert students


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index of math problems





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integral 5

integral of 1 / [x - √x ]

we have to use substitution method

take √x common in the denominator

put √x =t
study differentiation formulae ands  integration formulae
then take the differential

 (1/[2√x] ) dx = dt

rearrange the integral and rewrite it in terms of t in a single step
and then integrate

note that log x stands for natural logarithm ln x in this question






free guide on integration  or integral calculus for cbse isc kerala higher secondary class 12 ncert scert students


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index of math problems





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integral 4

integral of (log x )² / x
note that log x stands for natural logarithm ln x in this question

since there is no quotient rule in integration and since this is not a standard form you have to try to use substitution method to get to a standard form


so you put log x =t then take the differential

so (1/x) dx = dt

after that arrange the integral so that you can rewrite the integral in terms of t in a single step

then you get a standard integral which can be integrated.
study  integration formulae





free guide on integration  or integral calculus for cbse isc kerala higher secondary class 12 ncert scert students


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index of math problems





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integral 3

integral of sec²x/cosec²x

since there is no quotient rule in integration, change everything in terms of sinx and  cosx simplify to get tan²x
since there is no direct integral for  tan²x change to sec²x-1 using trigonometry formulae and then integrate term by term.
study  integration formulae
and

trigonometry identities formulae etc





free guide on integration  or integral calculus for cbse isc kerala higher secondary class 12 ncert scert students


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index of math problems





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integral 2

integral of [ x^3 - x^2 + x -1] / (x-1)

factorise the numerator

cancel off the common factor

use the integral of x^n to integrate term by term
go through the  integration formulae 







free guide on integration  or integral calculus for cbse isc kerala higher secondary class 12 ncert scert students


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index of math problems





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Friday, March 8, 2013

integral1




integral of (x^3 +3x +4) /sqrt(x)

since quotient rule is not used in integration you divide each term in the numerator with the denominator and
reduce every thing to x^n form and then integrate term by term
go through the  integration formulae 










free guide on integration  or integral calculus for cbse isc kerala higher secondary class 12 ncert scert students


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please leave your comments below

------------------------------------------------------------

index of math problems





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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













Thursday, January 21, 2010

sample question papers and marking scheme for cbse

sample question papers and marking scheme for cbse classX and class XII (10th and 12th) 2010

These seem to be available on the site cbse.nic.in/curric~1/sample2010.htm

The question papers of past years also seem to be available at

cbse.nic.in/curric~1/ms2008.htm

cbse.nic.in/curric~1/qp2009/qp2009.htm

you could also try
cbse.nic.in/student.htm for exam related material




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index of math problems


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Saturday, May 9, 2009

kerala exam results websites

The results of the SSLC exam, TTC, KGTE, VHSE , kerala higher secondary exam SAY exam 2009 etc seem to be available at some of the following sites

results.nic.in

results.kerala.nic.in

sslcexamkerala.gov.in

keralaresults.nic.in

CBSE exam results seem to be available at cbseresults.nic.in

The results , answer key of the kerala engineering , medical entrance exam KEAM may be available at cee-kerala.org

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index of math problems


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SAT Math Probability: Conditional Probability, Two-Way Tables, Formulas and Practice

  SAT Math Probability: Formulas, Conditional Probability, Two-Way Tables and Practice Probability on the SAT Math section is often less abo...