Math Chapter Wise

EnglishSection B PGT TIER-I 31.11.2014 UP PCS (Pre) 2006 UP TGT 2021, 2003

Q121.Two finite sets have m and n elements respectively. The number of subsets of the first set is greater than the number of the subsets of the second by 56. Then the value of m2 + n2 is equal to

A40 B38 C42 DNone of the above

Show answer

EnglishUP TGT 2021

Q122.For any two sets A and B, A– (A – B) equals

AA – B BB CA ∪ B DA ∩ B

Show answer

EnglishUP TGT 2021

Q123.If f(x) = tan–1 x and g(x) = sinx, then (gof) (x) is equal to

A2/x 1– x B2 x 1 x + C2 1 x x + D1

Show answer

EnglishUPPSC Ashram Paddhati 2021

Q124.The function f: R→ → →R defined by f(x) = cosx ∀ ∀ x∈R is

Aone-one, but not onto Bonto, but not one-one Cboth one-one and onto Dneither one-one nor onto

Show answer

EnglishUPPSC Ashram Paddhati 2021

Q125.If f: R→ → →R is defined by f(x) = 8x3 and g: R→ → →R is defined by g(x) = x1/3, then the value of (gof) (x) is

A8x B2x C– 2x D4x

Show answer

EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q126.What is the representation of an open disk D(x,y) of radius r centered at origin in R2?

AD ={(x,y)| x2 +y2 < r2 } BD ={(x,y)| x2 +y2 > r2 } CD ={(x,y)| x2 +y2 = r2 } DD ={(x,y)| x2 +y2 < r }

Show answer

EnglishHaryana PGT 2020

Q127.If f(x) = loge (), 2 x + 1+ x then f–1 (x) is equal to:

Ax x e e 2 − Bx x e e 2 − + Cx x e e − + Dx x e e − + −

Show answer

EnglishUKPSC GIC 2018

Q128.A relation R = {(1, 1), (1, 2) (2, 1)} is defined on the set A = {1, 2, 3}, then relation R is

AReflexive BReflexive and transitive CEquivalence relation DSymmetric

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q129.Let f(x) be defined by f(x + y) = f(x) +f(y) for all real numbers x and y, then f(x) is:

Aan odd function Ban even function Can even or an odd function DNone of these

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q130.Which of the following functions is surjective?

Af: R → R defined by f (x) = x2 Bf: R+ → R defined by f (x) = x2 Cf: R+ → R defined by f (x) = x2 Df: R+ → R defined by f (x) = x

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q131.If functions f: R → R and g: R → R are defined as 2 7 8, 1 f() 4 5, 1 7 8 3, 7 + − ≤ = < ≤ + > x x x x x+ x x x and 2 3 g() 0, 3 2 4, 2 − = − ≤ < + ≥ | x |, x < x x then

A(fog) (–3) = 8 B(fog) (9) = 683 C(gof) (9) = – 8 D(gof) (6) = 427

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q132.If f(x) = cos 2 [π ]x + cos[ 2 π − ]x, where [x] stands for the greatest integer function, then π f 2 =

A–1 B1 C0 D2

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q133.The total number of functions f: (1,2..…., m} → {1,2, ….,n} is here m ≠ n): is (here m≠ n)

Am(m–1)....... (m – n + 1) Bn(n–1)....... (n –m + 1) Cmn Dnm

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q134.Let the function f and g be defined by f(x) = 2x + 1 and g(x) = x2 – 2 then the composite function (gof) (x) is given by:

A4x2/+ 4x– 1 Bx2/+ 2x– 1 C4x2/– 3 D2x2/– 3

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q135.If A = {1,2,3} and R= {(1,2),(2,3),(1,3)} is a relation on A, then R is:

Aneither reflexive nor transitive Bneither symmetric nor transitive Ctransitive Dan equivalence relation

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q136.The range of the function 2 x,when x 0 f(x) x,when0 x 1 1,when x 1 x < = ≤ > defined for real numbers is:

A(– ∞,∞) B[0,1] C(– ∞,0) D[0, ∞)

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q137.The maximum number of equivalence relations on the set A = {1,2,3} is:

A1 B2 C9 D5

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q138.The function f: R → R defined by f(x) = 6x + 6|x| is:

Aone-one into Bone-one onto Cmany-one onto Dmany-one into

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q139.Let A,B,C be subsets of the universal set v. If n(v) = 692, n(B) = 230, n(C) = 370, n(B C) 90 ∩ = and n(A B' C') 10 ∩ ∩ =, then n(A' B' C') ∩ ∩ is equal to:

A172 B272 C362 D350

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q140.Let A = {(x, y, z): x, y, z are positive integers and x + y + z = 12}. Then the number of elements in A is:

A122 B78 C55 D36

Show answer