ISI Entrance Exam Syllabus

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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) syllabus

Algebra: 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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M.S.(QE) question paper.pdf (73.8 KB, 34 views)

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:-

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Information Processing and Organization
Information Transfer and Dissemination
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ISI Entrance Exam junior research fellow Syllabus.pdf (200.3 KB, 53 views)

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Hi I want the syllabus of M.S.(QE) of ISI Entrance Exam so can you provide me?

please tell the entrance exam syllabus for ISI.