Math Chapter Wise

EnglishBihar (TRE 1.0) -2023

Q01.The function f(x, y) = 3x2 y + 4y3 – 3x2 – 12y2 + 1 has a saddle point at.

A(0, 0) B(0, 2) C(–2, 1) DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q02.Let f(x, y) = 2 2 2 x y x + y for (x, y) ≠ (0, 0) then

Af x ∂ and f are bounded Bf x ∂ is bounded and f is unbounded Cf is continuous DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q03.Let α = ∞ ∫ 2 0 1 1+ t at Which of the following is true?

A2 d 1 dt 1 t α = + Bα is a rational number Csin (α) = 1 DMore than one of the above ENone of the above

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EnglishEMRS TGT-2023

Q04.∫ 2 2 dx sin x.cos x equals

Atanx.cotx + c Btanx – cotx + c Ctanx – cot2x + c Dtanx + cotx + c

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EnglishJSSC PGT 2018

Q05.Find the directional derivation of Du f(x, y) at the point (x, y) = (1, 2), where f (x, y) = x3 – 3xy + 4y2 and u is the unit vector in the direction θ = π/6.

A13 – 3 3/2 B10 C3 3 D0

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EnglishJSSC PGT 2018

Q06.Evaluate lim(x,y,z)→ → →(3,0,1)exp–xy sin(xy/z):

Aπ B1 C0 DDoes not exist

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EnglishUPPSC GDC 2021

Q07.() () → 3 3 x,y 0,0 x + y lim x – y

AExists and equals to zero BExists but not equal to zero CExists but not unique DDoes not exist

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q08.If 2 xy z = e,x = tcost,y = tsint, then the value of dz π at,t = is - dt 2

A2 4 π B2 – 8 π C3 – 8 π D3 8 π

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EnglishUPPSC Ashram Paddhati 2021

Q09.If u = () 2 2 2 3 3 2 2 x (x – y) x + y, the value of ∂ ∂ ∂ u u x + y y x is

A6 B2u C6u D2

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EnglishUPPSC Ashram Paddhati 2021

Q10.If u is a homogeneous function of x and y of degree n, the value of ∂ ∂ ∂ ∂ ∂ 2 2 2 2 2 u u u x + 2xy + y x y is

Anu B(n – 1)u Cn(n – 1)u Dn(n – 2)u

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EnglishUP PGT 2021

Q11.If V = (x2 + y2 + z2)–1/2, then ∂ ∂ ∂ ∂ ∂ ∂ V V V x + y + z x y z is equal to

AV B1 V 2 C–V D0

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EnglishUPPSC GIC 2021

Q12.If u = x y +, then the value of 2 2 2 2 2 2 u u u x xy y, x y ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ + + ∂ ∂ is -

Au/4 B4u C−u/4 D2 u 4

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EnglishUPPSC GIC 2021

Q13.If u = f (y/x), then the value of u u x y ∂ ∂ + ∂ ∂ is –

A0 Bu C2u Dx + y

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EnglishUP PGT 2021 UP PCS (Pre) 1994 Rajsthan TGT 2011

Q14.If u = sin–1 2 2 + y x, then x ∂ ∂ u u + y y x is equal to –

Acos 2u Btan u Ctan 2u Dcot u

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q15.If L= → 2 2 (x,y) (0,0) sin(x + y) lim x + y and () → 2 2 (x,y) (0,0) x – y M = lim,then - x + y

AL does not exist but M exists BL exists but M does not exist Cboth L and M exist Dboth L and M do not exist

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EnglishUP PGT 2021

Q16.() () () –1 x,y 2,1 sin xy – 2 lim tan 3xy – 6 → is equal to –

A1/3 B1/2 C1 D2

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EnglishUP Higher Asst. Prof. 2021

Q17.For the function f(x,y) defined as () 2 2 4 xy,if x,y 0 x y f(x,y) 0,if x,y 0 ≠ + = at the origin directional derivative

Aexists and f(x) is continuous. Bexists and f(x) is not continuous. Cdose not exists and f(x) is continuous. Ddose not exists and f(x) is not continuous.

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

Q18.Find the maximum value from the extreme values of this function: u = x2 y2 – 5x2 –8xy–5y2

A(–1,1) B(0,0) C(3,3) D(1,–1)

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EnglishHaryana PGT 2018

Q19.If z = f(x + ay) + φ(x – ay), then.

AFormula option A (see source) BFormula option B (see source) C2 2 2 2 2 z 1 z x a y ∂ − ∂ = ∂ ∂ D2 2 2 2 2 z z 2a x y ∂ ∂ = ∂ ∂

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EnglishHaryana PGT 2018

Q20.→ y x x y x - y lim x - y =

Ae 1 log y 1 log y + − Be 1 log y 1 log y − + Ce 1 log y 1 log y − + + De 1 log y 1 log y − − −

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