Math Chapter Wise

EnglishJSSC PGT 2018

Q121.Suppose (X, Y) jointly distributed with the following density function: () 2 2 1/xif s + t 1 f s,t = 0 otherwise ≤ Find Cov (X, Y).

A–1 B1 C0 Dπ

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EnglishJSSC PGT 2018

Q122.Which one of the following gives a pair of independent random variables?

A10 coins are thrown at random. X denotes the total number of heads that appear and Y denotes the total number of tails that appear. B10 coins are tossed at random. X denotes the total number of heads appeared on even tosses i.e., on 2; 4,.., 10th toss whereas Y denotes the total number tails appeared on odd tosses i.e., 1st, 3rd,...9th toss. CFor 1 ≤ i ≤ 6, let Xi denote the number of times digit 'i' appears in 10 tosses of a dice. Consider (X1, X2). DTwo dice are thrown at random and X denote the maximum of the digits appeared and Y denote the minimum of the digits appeared.

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EnglishJSSC PGT 2018

Q123.Which one of the following statements is true?

AFor two random variables X and Y, if Cov (X, Y) = 0 (covariance) then the two random variables are independent. BIf V(X) = 0 (variance) then ⇒ P (X = 0) = 1 CLet F be the distribution function of a random variable. Then limn→∞ F (x + 1/n) always exists. DIf P (X ≤ 100) = 1, then E (X) (expectation) always exists.

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EnglishJSSC PGT 2018

Q124.What is the probability that in a random arrangement of English alphabets, the word "MOTHER" will appear?

A(1/6)3 B(20!)/(26!) C(21!/(26!) D(22!)/(26!)

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EnglishJSSC PGT 2018

Q125.Let X and Y be two independent N (0, 1) random variables. Find Cov (X + 3Y, 5X – 2Y).

A1 B–1 C0 D11

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EnglishJSSC PGT 2018

Q126.Which one of the following statements is false?

ATwo independent events cannot be disjoint. BFor a probability density function f, we always have |f(x)| ≤ 1 for all x ∈ ℝ. CFor N (0, 2) random variable, we have mean = median = mode. DAny continuous non-negative function with () – f x dx 1 ∞ = ∫ gives a density function.

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EnglishOAVS TGT 2017

Q127.Two cards are drawn from a pack of cards one after the other. Find the probability that the first card is king and the second card is queen. If the first card is not replaced

A4/663 B1/13 C1/169 D4/51

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EnglishOAVS TGT 2017

Q128.If A and B are mutually exclusive events with P(B) ≠1, then P () A/B =?

A() 1 P B B() P A P B C() 1 1– P B D() P A 1– P B

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EnglishOAVS TGT 2017

Q129.According to Chebyshev's Inequality, which of following is true?

A() 2 Pr X – k 1/ k µ ≤ σ = B() 2 Pr X – k 1/ k µ ≥ σ ≥ C() 2 Pr X – k 1/ k µ ≥ σ ≤ D() 2 Pr X – k 1/ k µ ≥ σ =

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EnglishOAVS TGT 2017

Q130.A cumulative frequency graph is a:

ABar graph BCurve CStraight line DParabola

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EnglishOAVS TGT 2017

Q131.Age Frequency 18 12 19 5 20 3 21 9 22 1 23 8 24 12 25 12 26 5 27 3 Total 71 For the given data set what is the mode?

A19, 26 are modes BNo mode C20, 27 are modes D18, 24, 25 are modes

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EnglishOAVS TGT 2017

Q132.Let x1, x2 be the means of two samples of size n1, n2, then the mean X of combined sample of size n1 + n2 is:

A() 1 1 2 2 1 2 n x n x X n n × = × B() 1 1 2 2 1 2 n x n x X n – n + = C1 1 2 2 X n x n x = × D() 1 1 2 2 1 2 n x n x X n n × = +

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EnglishOAVS TGT 2017

Q133.A box contains cards numbered from 1 to 17. If one card is drawn at random from the box, find the probability that it bears a prime number.

A7/17 B9/17 C2/17 D11/17

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EnglishOAVS TGT 2017

Q134.A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls, if one ball is drawn at random, find the probability that it is black.

A7/24 B7/17 C8/24 D5/24

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EnglishOAVS TGT 2017

Q135.Let A & B be two events with P(A)=1/2, P(B) = 1/3 and ∩ P(A B) = 1/4, then P(A/B) = _____.

A3/8 B4/7 C7/12 D3/4

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EnglishOAVS TGT 2017

Q136.In a survey conducted on 250 persons it was found that 180 drink tea and 70 drink coffee and 50 take both tea and coffee. How many drink neither?

A200 B60 C50 D110

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EnglishKVS TGT 2017

Q137.The standard deviation of the first n natural numbers is–

An 1/2 Bn(n 1)/2 C2 n 1 12 D(2n 1)(n 1)/6

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EnglishKVS TGT 2017

Q138.The mean and S.D. of 1, 2, 3, 4, 5, 6 is–

A7 35, 2 12 B3,3 C7, 3 2 D35 3, 12

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EnglishKVS TGT 2017

Q139.The mean of 100 observations is 50 and their standard deviation is 5. The sum of squares of all observations is–

A50,000 B2,50,000 C2,52,500 D2,55,000

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EnglishKVS TGT 2017

Q140.The mean of first three terms is 14 and the mean of next two terms is 18. The mean of all the five terms is–

A14.5 B15.0 C15.2 D15.6

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