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ISI Entrance Exam Syllabus |

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Re: ISI Entrance Exam Syllabus
As you are looking for the syllabus of ISI entrance result, hereby I am providing you a PDF file with the complete syllabus. It contains the following:- Foundations of information Science Information Sources, communication Media, Information Systems and Programmes. Information Processing and Organization Information Transfer and Dissemination Information Technology and its Applications Information System/Centre Planning and Management Research Methods, Bibliometrics / Informetrics and Scientometrics
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Re: ISI Entrance Exam Syllabus
Ok, as you want the syllabus of M.S.(QE) of ISI Entrance Exam so here I am providing you. ISI Entrance Exam M.S.(QE) syllabusAlgebra: Binomial Theorem, AP, GP, HP, Exponential, Logarithmic Series, Sequence, Permutations and Combinations, Theory of Polynomial Equations (up to third degree). Matrix Algebra: Vectors and Matrices, Matrix Operations, Determinants. Calculus: Functions, Limits, Continuity, Differentiation of functions of one or more variables. Unconstrained Optimization, Definite and Indefinite Integrals: Integration by parts and integration by substitution, Constrained optimization of functions of not more than two variables. Elementary Statistics: Elementary probability theory, measures of central tendency; dispersion, correlation and regression, probability distributions, standard distributions - Binomial and Normal. 1. Let f(x) = 1−x 1+x, x 6= −1. Then f(f( 1 x)), x 6= 0 and x 6= −1, is (A) 1, (B) x, (C) x2, (D) 1 x. 2. The limiting value of 1.2+2.3+...+n(n+1) n3 as n → ∞ is, (A) 0, (B) 1, (C) 1/3, (D) 1/2. 3. Suppose a1, a2, . . . , an are n positive real numbers with a1a2 . . . an = 1. Then the minimum value of (1 + a1)(1 + a2) . . . (1 + an) is (A) 2n, (B) 22n, (C) 1, (D)None of the above. 4. Let the random variable X follow a Binomial distribution with parameters n and p where n(> 1) is an integer and 0 < p < 1. Suppose further that the probability of X = 0 is the same as the probability of X = 1. Then the value of p is (A) 1 n, (B) 1 n+1 , (C) n n+1 , (D) n−1 n+1. 5. Let X be a random variable such that E(X2) = E(X) = 1. Then E(X100) is (A) 1, (B) 2100, 2 (C) 0, (D) None of the above. 6. If _ and _ are the roots of the equation x2 − ax + b = 0, then the quadratic equation whose roots are _ + _ + __ and __ − _ − _ is (A) x2 − 2ax + a2 − b2 = 0, (B) x2 − 2ax − a2 + b2 = 0, (C) x2 − 2bx − a2 + b2 = 0, (D) x2 − 2bx + a2 − b2 = 0. 7. Suppose f(x) = 2(x2 + 1 x2 ) − 3(x + 1 x) − 1 where x is real and x 6= 0. Then the solutions of f(x) = 0 are such that their product is (A) 1, (B) 2, (C) -1, (D) -2. 8. Toss a fair coin 43 times. What is the number of cases where number of ‘Head’> number of ‘Tail’? (A) 243, (B) 243 − 43, (C) 242, (D) None of the above. 9. The minimum number of real roots of f(x) = |x|3 + a|x|2 + b|x| + c, where a, b and c are real, is (A) 0, (B) 2, (C) 3, (D) 6. 10. Suppose f(x, y) where x and y are real, is a differentiable function satisfying the following properties: 3 (i) f(x + k, y) = f(x, y) + ky; (ii) f(x, y + k) = f(x, y) + kx; and (iii) f(x, 0) = m, where m is a constant. Then f(x, y) is given by (A) m + xy, (B) m + x + y , (C) mxy, (D) None of the above. 11. Let I = 343 R2 {x − [x]}2dx where [x] denotes the largest integer less than or equal to x. Then the value of I is (A) 343 3 , (B) 343 2 , (C) 341 3 , (D) None of the above. 12. The coefficients of three consecutive terms in the expression of (1+x)n are 165, 330 and 462. Then the value of n is (A) 10, (B) 11, (C) 12, (D) 13. 13. If a2 + b2 + c2 = 1, then ab + bc + ca lies in (A) [ 1 2 , 1], (B) [−1, 1], (C) [−1 2 , 1 2 ], (D) [−1 2 , 1] . 14. Let the function f(x) be defined as f(x) = |x−4|+|x−5|. Then which of the following statements is true? (A) f(x) is differentiable at all points, 4 (B) f(x) is differentiable at x = 4, but not at x = 5, (C) f(x) is differentiable at x = 5 but not at x = 4, (D) None of the above. 15. The value of the integral 1 R0 x R0 x2exydxdy is (A) e, (B) e 2 , (C) 1 2 (e − 1), (D) 1 2 (e − 2). 16. Let N = {1, 2, . . .} be a set of natural numbers. For each x ∈ N, define An = {(n + 1)k, k ∈ N}. Then A1 ∩ A2 equals (A) A2, (B) A4, (C) A5, (D) A6. 17. lim x→0{1 x (√1 + x + x2 − 1)} is (A) 0, (B) 1, (C) 1 2 , (D) Non-existent. 18. The value of _n 0_ + 2_n 1_ + 3_n 2_ + . . . + (n + 1)_n n_ equals (A) 2n + n2n−1, (B) 2n − n2n−1, (C) 2n, (D) 2n+2. Here I am attaching a pdf file of M.S.(QE) question paper.
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