Math Chapter Wise

EnglishHaryana PGT 2018

Q21.If u = sin-1 1 1 1 2 3 3 1 1 2 2 x + y x + y then ∂ ∂ u u x + y x y is:

A12/tan u B−12/tan u C1 tan u 12 D1 tan u 12 −

Show answer

EnglishPGT 2011

Q22.If ((())) ((()) u y ax y ax = φ + + ψ − = φ + + ψ − = φ + + ψ − = φ + + ψ − then 2 2 2 2 2 u u a x y ∂ ∂ − ∂ ∂ equal to:

Au B0 Ca DNone of these

Show answer

EnglishPGT 2011

Q23.If 2 2 1 2 2 x y u sin x y − = + then u u x y ∂ ∂ + ∂ ∂ equal to

A0 B2 C3 DNone of these

Show answer

EnglishPGT 2013

Q24.If 3 3 1 tan x y u x y − + = + then du du x y dx dy + + equal to.

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

Show answer

EnglishPGT 2013

Q25.If ((())) ((()) f x cos logx = then (((()))) + × x f f x y y equal to.

A( ) ( )/f x f y B() () 2 / f x f y C() () / f x f y D( ) ( )/2 f x f y

Show answer

EnglishPGT 2010

Q26.The complete integral of the equation p q 1 + = + =, where z z P,q x y ∂ ∂ = ∂ ∂ is

A() 2 1 z ax a y c = + − + B() 2 1 z ax a y c = + − + C() 2 1 z ax a y c = + − + D() 2 2 2 1 z ax a y c = + − +

Show answer

EnglishPGT 2009

Q27.If u=x3 +y3 + z3 + 3xyz, then x u u u y z x y z ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ + + ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ is equal to

A2u B3u C4u DNone of these

Show answer

EnglishPGT 2005

Q28.If F is a differentiable point vector function and its second order partial derivative exists, then () (.) ∇ × ∇ × = ∇ × ∇ − ∇ × ∇ × = ∇ × ∇ − ∇ × ∇ × = ∇ × ∇ − ∇ × ∇ × = ∇ × ∇ − F F T. What is T?

A∇F B2 ∇ −∇ F F C2/2∇ F DNone of these

Show answer

EnglishPGT 2005

Q29.If 1 x/ y u xytan (e), − = then u u x y ∂ ∂ + ∂ ∂ is equal to

A0 Bu C3u D2u

Show answer

EnglishPGT 2005

Q30.z = φ (x + iy) + ψ ψ ψ (x – iy) is a solution of partial differential equation:

A2 2 z z 0 x y ∂ ∂ − = ∂ ∂ B2 2 z z 0 x y ∂ ∂ + = ∂ ∂ C2 2 2 2 2 z z z 0 x y ∂ ∂ ∂ + + = ∂ ∂ DNone of these

Show answer

EnglishPGT 2004

Q31.If u=xn-1 y f(y/x), then 2 2 2 u u x y x ∂ ∂ + ∂ ∂ ∂ is equal to?

Anu Bn(n - 1) u C(1) ∂ − ∂ u n x D(1) ∂ − ∂ u n y

Show answer

EnglishPGT 2003

Q32.Determine the general integral of the partial differential equation (())) () () y z p z x q x y + + + = + + + + = + + + + = + + + + = +

A()() ()() 2 2, 0 + + − + + − = x y z x y x y z x z φ B()()2 0 + + − = x y z x y φ C()() 2 0 + + − = x y z x z φ DNone of the above

Show answer

EnglishPGT 2003

Q33.Solve the partial differential equation (()) 2 2 2 1 p y x qx + =

A() 2 2 2 1 2 = + + + z a x a y β B1 2 2 2 1 2 z a x a y β = + + + C() 2 2 2 1 = + + + z a x a y β DNone of the above [Where α, β are any constant]

Show answer

EnglishPGT 2000

Q34.If x = rcosθ, y = rsinθ, Then the value of 2 2 x y ∂ θ ∂ θ ∂ θ ∂ θ ∂ θ ∂ θ ∂ θ ∂ θ + ∂ ∂ is:

A1 B0 Cz x ∂ Dx y ∂

Show answer

EnglishRajasthan TGT 2016

Q35.For the function 1 y z tan x − = consider the following statements: 1 z z S x y 0 x y ∂ ∂ ≡ + = ≡ + = ≡ + = ≡ + = ∂ ∂ 2 2 2 2 2 2 2 z z z S x 2xy y 0 x x y y ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ≡ + + = ≡ + + = ≡ + + = ≡ + + = ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ 2 2 3 2 2 z z S 0 x y ∂ ∂ ≡ + = ≡ + = ≡ + = ≡ + = ∂ ∂ Which of the following is true?

Aonly S1 Bonly S1 and S2 CAll S1, S2, S3 DNone of these

Show answer

EnglishRajasthan TGT 2015

Q36.If 1 y u tan, x − = then the value of u u x y ∂ ∂ + ∂ ∂ is

A0 Bu Ctan u Dsec2/u

Show answer

EnglishRajasthan TGT 2013

Q37.If F(u) = f(x,y,z) is the homogeneous function of degree n in x,y,z and ux= u x ∂ etc, then, xux+yuy+zuz=

AnF(u) BF'(u) n F(u) CF(u) n F'(u) DF(u)/F'(u)

Show answer

EnglishRajasthan TGT 2011 UP PCS (Pre) -1994

Q38.If 2 2 1 x y f sin x y − + = + then f f x x y ∂ ∂ + ∂ ∂ is equal to

Af B2f Csin f Dtan f

Show answer

EnglishRajasthan TGT 2011

Q39.If a function f(z) u(x,y) i (x,y) = + θ = + θ = + θ = + θ be analytic in a domain D, then Cauchy-Riemann equations are

Au u; x y y x ∂ ∂θ ∂ ∂θ = ∂ ∂ ∂ ∂ Bu u; x y y x ∂ ∂θ ∂ ∂θ = ∂ ∂ ∂ ∂ Cu u; x y y x ∂ ∂θ ∂ ∂θ = − ∂ ∂ ∂ ∂ Du u; x y y x ∂ ∂θ ∂ ∂θ = − = − ∂ ∂ ∂ ∂

Show answer

EnglishUP PCS (Pre) 1998

Q40.If 3 3 2 2 1 2 2 x y x y xy u tan x xy y − − + + − + + − + + − + + − = − + the value of u u x y ∂ ∂ + ∂ ∂ is:

A1 sin 2u 2 Bsin 2u Csin u D0

Show answer