Math Chapter Wise

EnglishTGT 2009

Q01.The median of 9 different types of observations is 20.5. If the 4 largest observation are increased by 2, what will be the new median?

AWill increase by 2 BWill decrease by 2 CWill be double of the previous median. DWill remain the same as the previous median.

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EnglishTGT 2005

Q02.Three cards are chosen with sequentially replacement. What will be the probability that the chosen card will contain only 2 aces and 1 king?

A() 1 2 13 17 × B() 1 3 13 C() 3 13 DNone of these

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EnglishTGT 2004

Q03.The median of the following data is Class interval 0-10 10-20 20-30 30-40 40-50 Frequency 5 6 9 12 4

A25 B9 C26.7 D27.3

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EnglishBihar (TRE 2.0)-2023

Q04.Which of the following is a measure of central tendency?

AMode BRange CMedian DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q05.Which of the following sets is countable?

AThe set of all functions from R to {0, 1} BThe set of all functions from N to {0, 1} CThe set of all finite subsets of N DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q06.For α ∈ R, let |α| denotes the greatest integer smaller than or equal to α. Define d: R × R → → [0, ∞ ∞ ∞) by d (x, y) = |x – y|, x, y ∈ R Then which of the following is true?

Ad(x, y) = 0 if and only if x = y, x, y ∈ R Bd (x, y) = d (y, x), x, y ∈ R Cd (x, y) ≤ d(x, z) + d (z, y), x, y, z ∈ R DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q07.Let X be a countable set. Then which of the following is not true?

AThere exists a metric d on X such that (X, d) is complete BThere exists a metric d on X such that (X, d) is not complete CThere exists a metric d on X such that (X, d) is compact DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q08.Let (X, d) be a metric space and let A ⊂ X. For x ∈ X, defined d(x, A) = inf{d(x, a):a ∈A} If d(x, A) = 0 for all x ∈ X, then which of the following assertions must be true?

AA is compact BA is closed CA is dense in X DMore than one of the above ENone of the above

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EnglishRPSC PGT 2022

Q09.If a mapping d: R2 × R2 → R be defined by d (x,y) = |x1 –y1| + |x2 – y2|, where x = (x1, x2), y = (y1,y2)∈R2, then which of the following is true?

Ad is a metric on R2 Bd is not a metric on R2 Cd is not clearly defined Dd is a pseudometric on R2

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EnglishDSSSB PGT 2021

Q10.In a metric space (X, d), A be a metric space, then the largest open subset of AC (complement of A) is

AInterior of A BExterior of A CBoundary of A DClosure of A

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EnglishDSSSB PGT 2021

Q11.If there are two subsets A and B of a metric space (X, d), then which of the following is false?

A(A°)° = A° B(A∩B)° = A° ∩ B° C(A ∪B)° = A° ∪B° DA ⊆B ⇒ A° ⊆B°

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EnglishDSSSB PGT 2021

Q12.In a matrix space (X, d), A be any subset. A point, x ∈ X is called a limit point of A, if for every open ball B (X, r) 1. B (x: r) ∩ (A – {x}) ≠ φ 2. (B (x: r) ∩ A) – {x} ≠ φ 3. (B (x: r) – {x}) ∩ A ≠ φ

AOnly 1 BOnly 2 and 3 COnly 1 and 3 D1, 2 and 3

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EnglishDSSSB PGT 2021

Q13.In metric space (X, d), if A be any subset, then A ⊂ ⊂ ⊂X is closed if and only if- 1. A =A° 2. A = A 3. A ⊂ ⊂ ⊂A° °

AOnly 1 BOnly 2 COnly 3 DOnly 1 and 3

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EnglishDSSSB PGT 2021

Q14.Which of the following is incorrect in (X, 3)?

AA subset A of compact space X is compact BIf X = R and T is usual topology then A = (0, 1) is compact CContinuous image of a compact space is compact DClosed subset and compact space is compact

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EnglishDSSSB PGT 2021

Q15.A one to one continuous map of compact space X onto a Hausdorff space Y is __________ 1. Open map 2. Not an open map 3. Not a homeomorphism

AOnly 1 BOnly 2 COnly 2 and 3 DNeither 1 nor 2 nor 3

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EnglishDSSSB PGT 2021

Q16.Which one of the following is not true?

AEvery co- finite topological space is infinite BA closed and bounded subset of R is compact CAn infinite discrete space is compact DA closed subset of a compact space is compact

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EnglishDSSSB PGT 2021

Q17.Every topological space (X, 3) is compact if ___

AX is not finite B3 is not finite CEvery open cover of X is reducible to finite sub cover DX is not compact at each points

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EnglishDSSSB PGT 2021

Q18.If a sequence converges to a point x0, then the set A consisting of the point xno and xn (n = 1, 2,............) is–

ANot compact BA is not an open cover CCompact DA has infinite sub cover

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EnglishDSSSB PGT 2021

Q19.Let A be the set of rational numbers in the open interval (0, 7) and f: A → R be a uniformly continuous function. Which of the following is true?

Af is necessarily a constant function Bf is bounded Cf is differentiable on (0, 7) Df is differentiable at all the rational points in (0, 7)

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EnglishJSSC PGT 2018

Q20.Let A = {A1, A2, A3...} be an infinite collection of closed sets. Which of the following is true?

AArbitrary intersection of sets from A is open BFinite union of sets from A is closed CNone of the options are true DArbitrary union of sets from A is closed

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