Math Chapter Wise

EnglishUP PCS (Pre) 1994

Q41.3.If y z xy x f then z z x y is equal to–

Az B2z Cxz Dyz

Show answer

EnglishUP PCS (Pre) 1994

Q42.If u f(x y,y z,z x) then u u u x y z is equal to–

A3 B0 C1 DNone of these

Show answer

EnglishUP PCS (Pre) 1994

Q43.If 4 2 2 4 f(x,y) x x y y then 2 f x y is equal to-

A4xy B12x2/+ 2y2 C2x2/+ 12y2 D4x2/+2xy2

Show answer

EnglishUP PCS (Pre) 1995

Q44.If 2 3 4 u 3x yz 2yz 6x then u u u x y z x y z is equal to–

A2 3 4/6x yz 4yz 12x B2 3 4/3x yz 4yz 6x C2 3 4/12x yz 6yz 12x D2 3 4/12x yz 8yz 24x

Show answer

EnglishUP PCS (Pre) 1996

Q45.Let x y (x,y) x y − = + f with x y 0 Then:

Ax 0 x 0 lim lim (x, y) 1 f Bx 0 y 0 lim lim (x,y) 1 → → = f Cx 0 y 0 lim lim (x, y) 1 f DNone of these

Show answer

EnglishUP PCS (Pre) 1996

Q46.If x y z x y z c, where c, is a constant, then at 2 z x y z, x y ∂ = ∂ ∂ is equal to:

A1 e (x log x)− − B1 e (x log x)− C−e/(x log x) DNone of these

Show answer

EnglishUP PCS (Pre) 1996

Q47.If 2 2 2 r x y, then 2 2 r r x y is equal to–

A2 1 r r x y r B2 r r x y C2 1 r r x y r DNone of these

Show answer

EnglishUP PCS (Pre) 1999

Q48.If x = r cos θ, y = r sin θ, then the value of ∂ (x, y) (r, θ) is:

Ar B1/2 r C3/2 r D0

Show answer

EnglishUP PCS (Pre) 1999

Q49.If u =2(ax+by)2 –(x2 +y2) and a2 +b2 = 1, then the value of 2 2 u u x y ∂ ∂ + ∂ ∂ is:

A1 Ba Cb D0

Show answer

EnglishUP PCS (Pre) 1999

Q50.If u = log(x3 +y3 +z3 –3xyz), then the value of 2 + u x y z ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ + ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ is:

A()2 3 x y z + + B()2 9 x y z − + + C()2 9 x y z + + D()2 3 x y z − + +

Show answer

EnglishUP PCS (Pre) 2000

Q51.If x = r cos θ, y = r sin θ, then 2 x y ∂ θ ∂ ∂ is:

A2 cos r θ B2 sin r θ C2 sin 2 r θ − D2 cos2 r θ −

Show answer

EnglishUP PCS (Pre) 2000

Q52.If 3 3 1 x y u tan x y − + = − then u u x y ∂ ∂ + ∂ ∂ is equal to:

Asin 2u Bcos 2u Ctan 2u Dcot 2u

Show answer

EnglishUP PCS (Pre) 2001

Q53.If y x u = sin + tan x y then ∂ ∂ u u x + y x y is equal to:

A3u B2u Cu Dzero

Show answer

EnglishUP PCS (Pre) 2001

Q54.If f(x,y,z = 3x2 yz+5xy2 z+4z4 then the value of y f f f x z x y z ∂ ∂ ∂ + + ∂ ∂ ∂ is:

Af B2f C4f D3f

Show answer

EnglishUP PCS (Pre) 2001

Q55.If 2 2 -1 y u= x y sin, x then at x=y=1 the value of ∂ u y is:

A1 Bπ C0 DNone of these

Show answer

EnglishUP PCS (Pre) 2003

Q56.If 2 2 u log x y, then 2 2 u u x y

A2 2/x y B2 2 1 x y C2 2/x y D0

Show answer

EnglishUP PCS (Pre) 2007

Q57.If 4 4 x y u log x y then the value of u u x y is equal to –

A3 B4 C1 D2

Show answer

EnglishUP PCS (Pre) 2008

Q58.If 2 2 2 1 u = x +y +z then ∂ ∂ ∂ + + ∂ ∂ ∂ 2 2 2 2 2 2 u u u x y z is equal to

A3u3 B0 C–3u3 Du3

Show answer

EnglishUP PCS (Pre) 2008

Q59.If u = loge(x3 +y3 +z3) than ∂ ∂ ∂ + + ∂ ∂ ∂ u u u x y z is equal to

A1 x y z + + B2 x y z + + C3 x y z + + D()2 3 x y z + +

Show answer

EnglishUP PCS (Pre) 2009

Q60.If f(x, y) is a homogeneous function of x and y of degree n, then ∂ ∂ + ∂ ∂ f f x y is equal to

A0 Bm Cn f(x, y) D(f(x, y))n

Show answer