Math Chapter Wise

EnglishUKPSC Lecturer (Mains) 2020

Q101.The kind of discontinuity, the function f(x)=[x]+[–x] has for integral values of x, is:

Aremovable Bfirst kind Csecond kind Dmixed

Show answer

EnglishUKPSC Lecturer (Mains) 2020 JDD 75PGT TIER -II-X 2015

Q102.If e sin(+ y) = log (+ y), x x then dy = dx

A–1 B1 C–2 D2

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q103.If 2 1 2f() – 3f =, 0 x x x x ≠ then f(2) is equal to:

A5/2 B−7/4 C1 D−5/2

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q104.If f: → R R be a positive increasing function such that x f(3x) lim = 1 f(x) → ∞ → ∞ → ∞ → ∞, then x f(2x) lim f(x) → ∞ → ∞ → ∞ → ∞ is

A2/3 B3/2 C3 D1

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q105.Let f(x+ y) = f(x) f(y) for all real values of x and y. If f(5) = 2, f'(0) = 3 then f'(5) =

A1 B3 C6 D9

Show answer

EnglishHaryana PGT 2019

Q106.2 x 1, 0 x 2 f (x), 2x 3, 2 x 3 − < < = + ≤ < then the quadratic equation whose roots are x 2 lim f (x) − → and x 2 lim f (x) + → is:

Ax2 – 6x + 9 = 0 Bx2 – 7x + 8 = 0 Cx2 – 14x + 49 = 0 Dx2 – 10x + 21 = 0

Show answer

EnglishHaryana PGT 2019

Q107.If k x +1,0 x 3 f(x) = mx + 2, 3x 5 ≤≤≤≤ is differentiable. then k+m =

A2 B16/5 C10/3 D4

Show answer

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

Q108.At what value or values of x this function is discontinuous: f (x) = x + 4 if x ≤ – 1 & x2 if –1 < < x 1; 2 – x if x ≥ 1?

A2 B–1 C0 D1

Show answer

EnglishUK SSSC LT 2020

Q109.The function ((())) [ [ [ ] ] f | x 1| | x 2|,x 0,3 x = − + − ∈ = − + − ∈ = − + − ∈ = − + − ∈ is not differentiable at point:

Ax = 0 Bx = 2 Cx = 3 DNone of the above

Show answer

EnglishUK SSSC LT 2020

Q110.If f(x) = x sin x, then f' 2 π is equal to:

A0 B1 C–1 D1/2

Show answer

EnglishUK SSSC LT 2020

Q111.The value of x logx lim x →∞ is:

A0 B∞ C–∞ D1

Show answer

EnglishUK SSSC LT 2020

Q112.If y = log [log(log x)], then the value of dy dx will be:

A() 1 log logx B() 1 xlog x.log log x C() 1 xlog log x DNone of the above

Show answer

EnglishUK SSSC LT 2020

Q113.The function f(x) = |x| at x = 0 is:

ADifferentiable BDiscontinuous CContinuous but not differentiable DNone of the above

Show answer

EnglishHaryana PGT 2020

Q114.If f(x) = xx, x > 0 is strictly increasing, then:

A1 x e > Bx > e Cx > e + 1 Dx >1 1 e +

Show answer

EnglishHaryana PGT 2020

Q115.If x = a(1 + cos 2θ) sin 2θ; y = b(1 – cos2θ) cos 2θ, then dy = dx

Ab cot a θ Bb tan a θ Cb sin 2 cos2. a cos θ − θ Da sin b θ

Show answer

EnglishHaryana PGT 2020

Q116.If sin y = (1 + x) sin (1 + y), then dy = dx

Asin (1 + y) B() 2 sin 1 y sin1 + C() sin 1 y sin y + D() sin y sin 1 y +

Show answer

EnglishHaryana PGT 2018

Q117.Let f: () ∞ → 0, R be a differentiable function, such that f'(x2) = 1 – x3 for all x > 0 and f(1) = 0, then f(4) =

A−5/8 B−8/5 C−47/5 D−5/47

Show answer

EnglishHaryana PGT 2018

Q118.→ ∫ + x -1 2 x 0 x 2 1 lim sin t dt = sin x

A1/4 B1/8 C3/8 D0

Show answer

EnglishHaryana PGT 2018

Q119.If f and g are twice differentiable function and f(p) = 3, f'(p) = –2, g(p) = –1, g'(p) = 4, then: () () () () → − x p g x f p g p f x lim = x p

A5 B–5 C–10 D10

Show answer

EnglishHaryana PGT 2018

Q120.→∞ n x lim = 0, e (n integer), for:

ANo value of n BOnly positive values of n COnly negative values of n DAll values of n

Show answer