# Sample Questions of ISI ME I (Mathematics) 2010 Discussion Classic List Threaded 128 messages Open this post in threaded view
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 nidhii...can u give an example..i m still not getting the point thanks
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 Hello. Take f(x)= x whenever x takes any irrational value , f(x) will also take the same. Similarly, f(x) = x^2. When x= 2, F(x) will be an irrational no, and so on.. We can take many examples. Now, suppose f(x)= 2. but its given in the que tht f(1) = 1 therefore, any other constant value apart from 1 cannot be the function. => f(x)=1 hope it was helpful.. :) :)
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 Sorry, for f(x) = x^2 if x takes the values sqrt 22/7 =>f(x)= 22/7 which is an irrational no. :)
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 Sorry for the mistake. 22/7 is a rational number. Hence we cannot use this case to rule out the function ,f(x)= x^2. :) :)
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 In reply to this post by N Uday Hey thanks so much..even my doubt gt cleared and a new concept added too.. :)
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 In reply to this post by Viren Solutions are as follows: Let X be a Normally distributed random variable with mean 0 and variance 1. Let F(.) be the cumulative distribution function of the variable X. Then the expectation of F(X) is (c) 1/2 (Hint: F(X) has uniform distribution on (0, 1)) i could not understand the solution.why do we have to consider limits only from 0 to 1?..please help.
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 In reply to this post by duck hi duck , i got his equation 1/2 +  2 * ( 1/2 ) ^2  +    3 * ( 1/2 ) ^3 +.. but i m nt able to solve it...so pls temme how did u get 2
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 In reply to this post by duck hi duck , i got his equation 1/2 +  2 * ( 1/2 ) ^2  +    3 * ( 1/2 ) ^3 +.. but i m nt able to solve it...so pls temme how did u get 2
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 Set S = 1/2 + 2* (1/2^2) + 3* (1/2^3) .. Now Multiply both sides by 2 and subtract, you'll get S = 3/2 + (infinite GP with a = 1/4 and r = 1/2). Hence ans = 2
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 There is a question : The no. of possible permutations of the integer 1 to 7 such that numbers 1 and 2 always precede 3 and 6 and 7 always succeed the number 3 is?
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 Hi.. :) We need to find no. of permutations such that numbers 1 and 2 always precede 3 and 6 and 7 always succeed the number 3. It means "3" can come only at "third", "fourth" , "fifth" place. Now, fix "3" at "third" position. Number of ways would be : 2!*4! Now, fix "3" at "fourth" position. Number of ways would be : 3!*3! Now, fix "3" at "fifth" position. Number of ways would be 4!*2!. Just add all of them to get total number of ways.   :)
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 Thanks for solving it.  but i have a doubt !  When we fix 3 at the fourth place such that the arrangement is  _ _ _ 3 _ _ _, then for the first place we will have 4 choices i.e. 1,2,4,5 for the next place we will have 3 choices left, and consequently 2 choices for the third place. Moving to the right of 3, we will have 3 choices i.e 6,7 and 4 or 5(depending on which number was put before 3) for the fifth place, 2 choices for the sixth place and the last one will have 1 choice. So wont it be 4*3*2*3*2, which makes the sum 240? However the answer given by sir is however 168 contrary to both our answers!!
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 Hey Sorry, there was a typo in the previous post and a correction.. Fix "3" at "third" position. Number of ways would be : 3!*3!*2 Now, fix "3" at "fourth" position. Number of ways would be : 4!*2! Now, fix "3" at "fifth" position. Number of ways would be 4!*2!. Just add all of them to get total number of ways. :)
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 In reply to this post by duck how is it continuously differentiable?
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 Hi Gagan.. :) First find the derivative of the function. Now, that derivative is also a function.Check for its continuity. You'll find it continuous. Hence, Continuously differentiable. :)
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 In reply to this post by Shweta Singhal how can u solve it??
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 In reply to this post by Shweta Singhal how can u solve it??
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 In reply to this post by anisha pls if anyone can explain me the solutions!!
 This post was updated on . SEE THIS.  Is it sufficient?(Sorry, it is not sufficient. I forgot just taking 2, and in that case you choose none of the 3,4,5 and thus add 3C0=1 to the 7.) Also, many many thanks for leading me to this thread. Will you please link here such informative threads from this site? I will be truly obliged (and it will surely help other aspirants, too. )