26
Which one among the following is the first of the major Environmental Protection Act promulgated in India?
Answer
A. Water Act
27
In order to be eligible for gratuity under the Payment of Gratuity Act, 1972, an employee should have a minimum continuous service of:
Answer
B. 5 years
28
Under the provisions of prevention of sexual harassment (at work place) Act, the term aggrieved woman means:
Answer
D. all of the above
29
According to Right to Information Act, within what time should the information be provided to an applicant in normal cases:
Answer
D. 30 days
30
Who is an adolescent as per Factories Act 1948?
Answer
C. who has completed 15 years but less than 18 years
31
If `A_n={(A if n "is odd"),(B if n "is even"):}`
then lim inf `A_n=`` `
then lim inf `A_n=`` `
Answer
B. `quadAnnB`
32
Which of the following statement(s) is/are wrong?
I: A monotone field in not a sigma field
II: A sigma field is a monotone field
I: A monotone field in not a sigma field
II: A sigma field is a monotone field
Answer
A. I alone
33
If `quadmu_1` is a measure defined on a sigma field `quadfrA_1` and `quadmu_2` is a measure defined on a sigma field `quadfrA_2` , then `quadmu_1+mu_2` is a measure only when
Answer
C. `quadfrA_1=frA_2`
34
Which of the following statement(s) is/are true?
A : Every subsets of are Borel sets
B : Every Borel set in measurable
A : Every subsets of are Borel sets
B : Every Borel set in measurable
Answer
B. B alone
35
Let `quadI = (0, 1)` , be the Borel field of subsets of `quadI` and `mu` is the Lebesgue measure on. For `quadn = 1, 2,....,` if `quadA_n=(0,1/n), mu(lim "sup" A_n)=`
Answer
A. 0
36
Let `quadW` be the subspace of generated by the vectors (1, -2, 5, -3), (2, 3, 1, -4) and (3, 8, -3, -5). Then the dimension of `quadW` is
Answer
C. 2
37
For any arbitrary matrices `quadA` and `quadB` , the sum of ranks of `quadA` and `quadB` is always
Answer
D. greater than or equal to rank`quad(A+B)`
38
Let `quadA` and `quadB` are `quadnxxn` square matrices. Then the eigen values of `quadAB` are same as the eigen values of
Answer
D. `quadBA`
39
The quadratic polynomial corresponds to the matrix `quadA=((1,0,1/2),(0,0,-1),(1/2,-1,0))` ` ` is
Answer
B. `quadx^2-2yz+xz`
40
Let `quadP` be an `quadmxxm` orthogonal matrix, `quadQ` be an `quadnxxn` orthogonal matrix and `quadA` any `quadmxxn` matrix. If `quadA^T` denote the transpose of `quadA` and `quadA^-` denote the generalized inverse of `A` , then the generalized inverse of `quadPAQ` is
Answer
B. `quadQ^TA^{-}P^T`
41
If `quad{A_n}` is a sequence of events on a probability space (Ω,`quadA,P)` such that `quadA_n->A` as `quadn->oo` , then what is the value of lim`quadP(A_n)` ?
Answer
C. `quadP(A)`
42
If `quadA` and `quadB` are mutually exclusive events, each with positive probabilities, then they are
Answer
B. dependent events
43
If `quad{A_n}` is a sequence of events such that `quadsum_(k=1)^ooP(A_k)=oo` , then `quadP(lim"sup"A_n)=1` provided events are
Answer
C. independent
44
Let `quad{A_n}` be a sequence of events such that `quadB_1=A_1` and `quadB_k=A^c_1 A^c_2...` `A_{k-1}^c A_k` for `quadk>=2` , in which `quadA^c` is the complement of `quadA` . Then the sequence of events `quad{B_n}` are
Answer
D. Pair-wise mutually exclusive
45
If `quadX` is a random variable with finite expectation, then the value of `quadxP(X<-x)` as `quadx->oo` is
Answer
C. zero
46
If `quadX` is a symmetric random variable with distribution function `quadF` and real valued characteristic function Φ, then for any `quadx` in ,`quadF(x)=`
Answer
D. `quad1-F(-x-0)`
47
If the characteristic function Φ of distribution function `quadF` is absolutely integrable on , then for any`quadx` in , `quad f'={dF(x)}/dx` is
Answer
C. both (A) and (B)
48
Let `quadX` and `quadX_n` be independent standard normal variables on a probability space (Ω,`quadfrA,P)` ` `, for `quadn>=1` . Then which of the following is not true?
Answer
A. `X_nstackrel(P)(->)X`
49
The sequence `quad{X_n}` of independent random variables, each with finite second moment, obeys SLLN if
Answer
D. `quadsum_(k=1)^oo{Var(X_k)}/k^2<oo`
50
Let `quad{X_n}` sequence of independent random variables with
`quadP(X_k=+-k)=1/2k^-Lambda` and `quadP(X_k=0)=1-k^-Lambda` , for `quadk>=1`
Then the sequence does not obey CLT if
`quadP(X_k=+-k)=1/2k^-Lambda` and `quadP(X_k=0)=1-k^-Lambda` , for `quadk>=1`
Then the sequence does not obey CLT if
Answer
B. `quadLambda=1`
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