# SET Mathematical Sciences Question Answers

SET Mathematical Sciences Question Answers for competitive exams: This mock test having mcq question each also from Paper II, Paper III Syllabus, with four choices. On each click on answers system will tell you where the answers is correct or incorrect. You can view this SET Mathematical Sciences test question details at the end of the quiz.

## SET Mathematical Sciences Question Answers

State Level Eligibility Test is also know as SET  (State Eligibility TestMathematical Sciences questions answers are applicable for any kind of Higher Mathematical Sciences especially for Lecturer and PHD examination like UGC NET And CSIR NET. . You can practice as much as you can to gather knowledge of how to answers SET Mathematical Sciences critical type papers in short time and this can be a big factor for cracking LS/PHD level exam.

## SET/SLET Mathematical Sciences Paper II - Mock Test

Congratulations - you have completed SET/SLET Mathematical Sciences Paper II - Mock Test.You scored %%SCORE%% out of %%TOTAL%%.Your performance has been rated as %%RATING%%
 Question 1
The function f(x) = sin (1/x), x > 0 is
 A Uniformly continuous on R+ B Uniformly continuous on R C Continuous on R+ D Not continuous on R+
 Question 2
If T: R3→R2 is a linear transformation defined by T (x, y, z) = (x + 2y — z, y + z, x + y — 2z), then the rank of T is equal to
 A 0 B 1 C 2 D 3
 Question 3
Let T: R3→R be a linear transformation defined by T (1, 1, 1) = 3, T (0, 1, — 2) = 1 and T (0, 0, 1) = -2 Then T (x, y, z) =
 A 8x+3y-2z B 3x-8y-2z C 8x-3y-2z D 2x-3y+8z
 Question 4
If f (z)=u (x, y)+iv (x, y)and g (z) = u (x, y)-iv (x, y) are analytic functions defined on the same domain and f (1 + i )=2+3i,then g (4+3i)=
 A 4+3i B 4-3i C 2+3i D 2-3i
 Question 5
If G is a finite abelian group, then G is isomorphic to the direct product of its
 A normal subgroups B abelian subgroups C sylow subgroups D cyclic subgroups
 Question 6
If R is a commutative ring with unit element and M is an ideal of R, then M is a maximal ideal of R if and only if R/M is
 A a quotient ring B a field C a division ring D an ideal
 Question 7
The number of units in the domain of Gaussian integers is
 A 1 B 2 C 3 D 4
 Question 8
The Newton-Raphson method of finding a root of a polynomial or transcendental equation has the rate of convergence
 A 3 B 2 C 1.67 D 1.4
 Question 9
An approximate solution for the system of linear equations l0x+ 2y+ z = 9, 2x +20y-2z = -44; - 2x + 3y + 10z = 22 using Gauss-Seidal method is
 A x = 1.094, y = - 1.908, z = 2.946 B x = 1.082, y = -1.914, z = 2.965 C x=1.108, y=-1.932, z=2.981 D x=1.013, y=-1.996, z=3.001
 Question 10
For any discrete distribution
 A S.D ≥ M.D from mean B S.D=M.D C S.D < M.D from mean D No relation between S.D and M.D
 Question 11
The probability distribution of a random variable X is f (x) = k sin (π x /5), 0 < x <  5, then the ratio between median of X and k is
 A 25: π B 5:2 C 1:2 D 10: π
 Question 12
If you wish to estimate the proportion of engineers and scientists who have studied statistics and you wish your estimate to be correct within 2% with probability 0.95 or more, how large sample would you take if you have no idea what the true proportion is?
 A 1200 B 800 C any number D 95
 Question 13
The Poisson process satisfies the following conditions
 A regularity B homogeneity C independent increments D all the above three (A), (B) and (C)
 Question 14
For a Binomial distribution with p = 0.5 has maximum probability when
 A X = n/2 if n is even B x=1/2(n-1) and x=1/2(n+1) if n is odd C x=n D both A) and B) are correct
 Question 15
The minimum variance bound estimator for ᶿin a Cauchy population with parameter ᶿ is
 A sample mean B sample median C reciprocal of sample median D does not exist
 Question 16
In a Poisson distribution with unit mean the mean deviation about mean is
 A 2/e B e/2 C e D 1
 Question 17
Neyman-Pearson lemma provides
 A An unbiased test B a most powerful test C an admissible test D sufficient test
 Question 18
The information on auxiliary variate is used in the following sampling scheme
 A double sampling B two stage sampling C cluster sampling D quota sampling
 Question 19
The arrival rate and service rates of a M/M/1 queueing system are 3 and 4, then the probability of system emptiness is
 A 0.25 B 0.75 C 0.3 D 0.5
 Question 20
A simplex is a
 A half plane B convex polyhedran C hull D envelop
 Question 21
If f(x) is the p. d. f of a life time distribution then the hazard rate of distribution is
 A f(x)/F(x) B f(x)/(1-F(x)) C F(x)/f(x) D log f(x)/(1-F(x))
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## SET/SLET Mathematical Sciences Paper III - Mock Test

Congratulations - you have completed SET/SLET Mathematical Sciences Paper III - Mock Test.You scored %%SCORE%% out of %%TOTAL%%.Your performance has been rated as %%RATING%%
 Question 1
Compact subsets of metric spaces are
 A convex B open C closed D connected
 Question 2
The Cayley Hamilton theorem states that
 A The characteristic roots of a non-singular matrix are distinct B The characteristic equation of a matrix admits a non-zero solution C Every matrix satisfies its own characteristic equation D The eigen values of any matrix are linearly independent
 Question 3
If ɑ and ß are two eigen values of a matrix A, then the corresponding eigen vectors of A are
 A linearly dependent B orthogonal C orthonormal D linearly independent
 Question 4
If w is a subspace of V4(R) generated by the vectors (1,-2, 5, -3), (2, 3, 1, -4), (3, 8, -3, -5), then dim (w) =
 A 1 B 2 C 3 D 4
 Question 5
If u(x, y) = 2x — x2 + ky2 is to be harmonic function, then k should be equal to
 A 0 B 1 C 2 D 3
 Question 6
If w = logz, then w is not analytic
 A On real axis B on negative real axis C at z=0 only D for complex z
 Question 7
If H and K are two subgroups of a group G, then HK is a subgroup of G if and only if
 A O (HK) = O (KH) B HK=KH C O (H)=O (K) D either O(H) or O(K) is a prime number
 Question 8
If H is a subgroup of G and N (H) = {aɛG | a Ha-1 =H} then N(H) is
 A a normal subgroup of G B a subgroup of G C an abelian group D a cyclic group
 Question 9
Let O(G) = Pq with p, q primes, p > q where G is a group. Then which one of the following statements is NOT true?
 A If q | p — 1, then there exists a non-abelian group of order pq B If q | p — 1, then G is cyclic C G has a subgroup of order p and a subgroup of order q D Any two non-abelian groups of order Pq are isomorphic
 Question 10
Let G be a group of order 112.132. Then the number of 13 —   Sylow subgroups in G are
 A 1 B 2 C 3 D 4
 Question 11
If p is a prime number, then the splitting field over F, the field of rational numbers, of the polynomials xp — 1 is of degree
 A 2p+1 B P+1 C p -1 D 2p-1
 Question 12
The singular solution of the equation xp2-2yp + 4x =0 is
 A x B 2x C 3x D 4x
 Question 13
Consider the boundary value problem: y”+λy = 0, y(-π) = y(π), y’(-π) = y’(π) then to each eigen value λ there corresponds
 A a unique eigen function B two eigen functions C two linearly independent eigen functions D two mutually dependent eigen functions
 Question 14
A real root of the equation x log10x = 1.2 correct to 3 decimal places obtained by Newton’s iteration method, is
 A 2.74 B 2.752 C 2.758 D 2.762
 Question 15
Given that y’= — x2y, y(0) =2, then the value of y (0.2) obtained by modified Eulers method with h = 0.1 is
 A 1.912 B 1.918 C 1.923 D 1.932
 Question 16
The approximate value of y(0.2) obtained upto 3 decimal Places by solving y’= x+y, y(0) =1 with h= 0.2 using the fourth order Runge-Kutta method, is
 A 1.216 B 1.232 C 1.243 D 1.263
 Question 17
The shortest curve joining two fixed points on a given surface and lying entirely on that surface is called a
 A cycloid B geodesic C catenary D helix
 Question 18
A triangle enclosing the greatest area for a given perimeter, is
 A an isosceles triangle B an equilateral triangle C a right angled triangle D a scalene triangle
 Question 19
The number of degrees of freedom of a particle moving in space, is
 A 4 B 2 C 1 D 6
 Question 20
The mean absolute deviation is minimum when it is measured from
 A mean B median C mode D standard deviation
 Question 21
For a negatively skewed distribution, the correct relation between mean, median and mode is
 A mean=median= mode B mean C median< mean D mode< mean< median
 Question 22
If a random variable U is uniformly distributed over the interval (0, 1), then the distribution of Y = tan (π (U — 0.2)) is
 A Normal B Laplace C Cauchy D Exponential
 Question 23
The domain of a probability measure is
 A the sample space B the interval [0, 1] C the sigma field of subsets of the sample space D the real line
 Question 24
Identify in the following, a stochastic process that is an example of discrete time, discrete state space stochastic process
 A Yule process B renewal process C Wiener process D Branching process
 Question 25
If the mean of a binomial distribution is 3, then its variance could be
 A 7.5 B 5.5 C 3.5 D 1.5
 Question 26
If X and Y are two i.i.d standard normal variates then E(X/Y) =
 A 1 B 0 C does not exist D 1/2
 Question 27
An example of a distribution which does not possess monotone likelihood ratio property is
 A Normal B Cauchy C exponential D Gamma
 Question 28
Neyman-Pearson most powerful test with power 1-ß and size ɑ satisfies
 A ɑ<1-ß B ß<1-ɑ C 1-ß<ɑ D ɑ<ß
 Question 29
The non-parametric test used for testing equality of more than two means of the population is
 A Kruskal Wallis B Median test C Run test D Rank test
 Question 30
Confounding is a technique used for
 A reducing the block size B increasing the block size C reducing the number of factors D reducing the number of blocks
 Question 31
For the linear programming problem, maximize z = x + 2y subject: x + y >1, x+2y<10, y<4, x>0, y>0
 A Optimum solution is unique B optimum solution exists but not unique C optimum solution is unbounded D optimum solution does not exist
 Question 32
The bath-tup curve type of hazard function is associated with
 A Weibull distribution B exponential distribution C two component mixture of Weibull distributions D Pareto distribution
 Question 33
For economic order quantity models i) the demand rate is constant always ii) the replenishment rate is either finite or infinite iii) the items are non-deteriorating only Then
 A i) is correct B i) is not correct but ii) and iii) are correct C ii) is correct D i), ii) and iii) are correct
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