Math Chapter Wise

EnglishEMRS PGT-2023

Q01.If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is:

A30 B51 C31 D50

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EnglishEMRS PGT-2023

Q02.All the students of a class performed poorly in Mathematics. The teacher decided to give 10 grace marks to each of the students. Which of the following statistical measure will not change even after the grace marks were given?

AMedian BMode CVariance DMean

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EnglishEMRS PGT-2023

Q03.Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse, is:

A3/5 B1/5 C2/5 D4/5

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EnglishEMRS PGT-2023

Q04.A random variable χ χ χ has the probability distribution χ χ 1 2 3 4 5 6 7 8 P(χ χ χ) 0.15 0.23 0.12 0.10 0.20 0.08 0.07 0.05 For the events, E = {χ χ χ is a prime number} and { }. F = χ < 4 The probability of () E F ∪∪∪∪ is:

A0.77 B0.35 C0.50 D0.87

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EnglishEMRS PGT-2023

Q05.If the probability of hitting a target by a shooter in any shot is 1 3, then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than 5 6, is:

A5 B4 C3 D6

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EnglishEMRS PGT-2023

Q06.Two integers are selected at random from the set {1, 2, 3, 4,..., 11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even, is:

A1/2 B7/10 C3/5 D2/5

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EnglishEMRS PGT-2023

Q07.If the standard deviation of the numbers 2, 3, a and 11 is 3.5 then which of the following is true?

A3a2 –32a+84=0 B3a2 –34a+91=0 C3a2 –23a+44=0 D3a2 –26a+55=0

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EnglishEMRS PGT-2023

Q08.If the mean deviations about the median of the numbers a, 2a, 3a,..., 50a is 50, then |a| equals:

A4 B5 C2 D3

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EnglishBihar (TRE 2.0)-2023

Q09.If E1 and E2 are independent events, then

AP (E1 ∩ E2) = P (E1) | P (E2) BP (E1 ∩ E2) = P (E1). P (E2) CP (E1 ∩ E2) = P (E1) + P (E2) DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q10.The probability of landing exactly three tails when three coins are tossed simultaneously is

A1/4 B1/8 C1/2 DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q11.If E1 and E2 are two events such that P (E1) ≠ 0 and P (E2|E1) = 1, then

AE1 ⊂ E2 BE2 ⊂ E1 CE2 = φ DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q12.The mode of the following data 4, 6, 5, 9, 3, 2, 7, 7, 6, 5, 4, 9, 10, 3, 4, 7, 6, 9, 9, 10 is

A4 B9 C20 DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q13.Let X has probability density function f(x) = () [ ] ∈ 2 0.75 1- x, x -1,1 0, otherwise What is the probability of ≤ 1 1 P - X 2 2

A0.68 B0.60 C0.65 DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q14.For a given probability distribution f(x) = 3 1,x = 0,1,2,3 x 8 for a random variable X, the moment generating function of this is

A(1 + et/)2 Bt 1 e 4 C() 3 t 1 1 e 8 + DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q15.What is the second moment about the origin for a random variable X with probability density? f(x) = x, 0 < x < 2 2 0, otherwise

A2 B3 C4 DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q16.If X is a real valued random variable, then which of the following values cannot be attained by E(X) and E[X2 ] respectively?

A0 and 1 B2 and 5 C2 and 3 DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q17.A and B are two independent events with equal probabilities such that P(A∪ ∪ ∪B) = 0.75, then

AP(B) = 0.25 BP(A) = 0.75 CP(B) = 0.5 DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q18.A box contains 10 mangoes out of which 4 are rotten, 2 mangoes are taken out together. If one of them is found to be good, then probability that the other is also good is

A1/3 B8/15 C5/13 DMore than one of the above ENone of the above

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EnglishEMRS TGT-2023

Q19.The median of a set of 9 distinct observations is 20.5 If each of the largest four observations of the set is increased by 2, then the median of the new set:

Ais now times the original median. Bremains the same as that of the original median. Cis increased by 2. Dis decreased by 2.

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EnglishEMRS TGT-2023

Q20.The mean of the probability distribution of the number obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is:

A2 B5 C8/3 D1

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