# Sample Questions of ISI ME I (Mathematics) 2010 Discussion Classic List Threaded 128 messages 1234 ... 7
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## Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 Administrator Do the following problem: The value of 100[1/(1*2) + 1/(2*3) + ....... 1/(99*100)] is a) 99 b) 100 c) 101 d) (100)*(100)/99
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 99 100(1-1/2+1/2-1/3+1/3-1/4+.....1/99-1/100) 100(1-1/100) 100*99/100 99
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 please explain.. Thank you .. :)
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 1/[n*(n+1)] can be written as [1/n - 1/(n+1)] i.e. 1/(1*2) = 1 - 1/2       1/(2*3) = 1/2 - 1/3       .       .       .       1/(99*100) = 1/99 - 1/100
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 In reply to this post by duck 1/[n*(n+1)] can be written as [1/n - 1/(n+1)]i.e. 1/(1*2) = 1 - 1/2      1/(2*3) = 1/2 - 1/3      .      .      .      1/(99*100) = 1/99 - 1/100On 5 April 2010 00:30, Nidhi Jain [via Discussion forum] wrote: please explain.. Thank you ..Nidhi Jain View message @ http://n2.nabble.com/Sample-Questions-of-ISI-ME-I-Mathematics-2010-Discussion-tp4850019p4850329.html To unsubscribe from Discussion forum, click here.
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 Administrator Very well done Uday. Lets do the next two then: The function f(x) = x(square_root(x) + square_root(x + 9)) is (a) continuously differentiable at x = 0, (b) continuous but not differentiable at x = 0, (c) differentiable but the derivative is not continuous at x = 0, (d) not differentiable at x = 0. Note: square_root(g(x)) stands for square root of g(x) Consider a GP series whose first term is 1 and the common ratio is a positive integer r(> 1). Consider an AP series whose first term is 1 and whose (r+2)th term coincides with the third term of the GP series. Then the common difference of the AP series is (a) r − 1, (b) r, (c) r + 1, (d) r + 2.
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 Thank you.. :) ... :)
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 Ans 2>>> the common difference of the AP series is  (r-1)Ans1>> i think it is continously differentiable at x=0 ... i m not sure about dis answer.. .... :)
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 In reply to this post by Amit Goyal 1) (d) not differentiable at x=0 because left hand limit does not exists so also not continuousOn 4 April 2010 20:41, Amit Goyal [via Discussion forum] wrote: Very well done Uday. Lets do the next two then: The function f(x) = x(square_root(x) + square_root(x + 9)) is (a) continuously differentiable at x = 0, (b) continuous but not differentiable at x = 0, (c) differentiable but the derivative is not continuous at x = 0, (d) not differentiable at x = 0. Note: square_root(g(x)) stands for square root of g(x) Consider a GP series whose first term is 1 and the common ratio is a positive integer r(> 1). Consider an AP series whose first term is 1 and whose (r+2)th term coincides with the third term of the GP series. Then the common difference of the AP series is (a) r − 1, (b) r, (c) r + 1, (d) r + 2. View message @ http://n2.nabble.com/Sample-Questions-of-ISI-ME-I-Mathematics-2010-Discussion-tp4850019p4852132.html To unsubscribe from Discussion forum, click here.
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 1) (d) not differentiable at x=0 because left hand limit does not exists so also not continuous
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 Administrator Definition: Let f be defined (and real valued) on [a, b]. For any x in [a, b] form the quotient g(t) = (f(t) - f(x))/(t - x) (a < t < b, t ≠ x) and define f'(x) = lim (as t → x) g(t) is the derivative of f at x. In particular at end ponits a and b, the derivative if it exists, is a right-hand or left-hand derivative, respectively. Now try this question again. And Nidhi, answer you provided to the problem on AP-GP is correct
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 the answer to that que is>> continuously differentiable at x=0.. :) Thank you sir.. :) .. :)
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 Administrator Good. Lets do the next two. The first three terms of the binomial expansion ((1 + x) to the power n) are 1,−9, 297/8 respectively. What is the value of n? (a) 5 (b) 8 (c) 10 (d) 12 Given log(p)x = a and log(q)x = b , the value of log(p/q)x equals (a) ab/(b - a) (b) (b - a)/ab (c) (a - b)/ab (d) ab/(a - b) log(p)x stands for log of x with base p. And similarly read log(q)x & log(p/q)x.
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 This post was updated on . :)
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 Q1>> its 12 binomial expansion for (1+x)^n = 1+nx+{n (n-1)/2}*x^2 + ........ => first term = 1 ,  second term = nx and  third term = {n (n-1)/2}*x^2 As per given, nx= -9                                    ..(I)   {n (n-1)/2}*x^2= 297/8            ..(II) Now, {n (n-1)/2}*x^2 can be written as nx (nx-x)/2     ....(III) We know, nx= = -9 (from I) substituting in (III) , we have>> -9 (-9-x) ---------   = 297/8     2 => x= -3/4 => n = 12                                                             :)
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 In reply to this post by Amit Goyal 2)Ans.(a)  log(p/q)x = log(x)/log(p/q) = log(x)/[log(p)-log(q)] = 1/[log(x)p-log(x)q] = 1/[(1/a)-(1/b)] = ab/(b-a)
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 Administrator Next three then: Let P = {1, 2, 3, 4, 5} and Q = {1, 2}. The total number of subsets X of P such that X ∩ Q = {2} is (a) 6, (b) 7, (c) 8, (d) 9. An unbiased coin is tossed until a head appears. The expected number of tosses required is (a) 1, (b) 2, (c) 4, (d) ∞ Let X be a random variable with probability density function f(x) = c/sq(x) if x ≥ c, 0 if x < c. Then Expectation of X is (a) 0 (b) ∞ (c) 1/c (d) 1/sq(c) Note: sq(x) stands for square of x.
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## Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

 for Q1 ans is (b) i.e. 7