Math Chapter Wise

EnglishPGT 2013

Q261.2 2 1 cos ax + D a value is:

Acos 2 x ax a Bsin 2 x ax a − Csin 2 x ax a DNone of these

Show answer

EnglishPGT 2013

Q262.If d D dx ≡ ≡, then what will 2 1 sin x D D 1 + + be equal?

A–cos x Bcos x Ccos x – sin x Dsin x

Show answer

EnglishPGT 2013

Q263.Differential equation 2 2 1 Z px qy p q = + + + + = + + + + = + + + + = + + + + what will be general solution

A2 2 1 Z ax by a b = + + + + BZ ax by c = + + C2 2 Z ax by a b = + + + DNone of the above

Show answer

EnglishPGT 2013

Q264.1 sin− − = a x y e satisfies which of the following differential equation:

A(1–x2)y"–2xy'+ay=0 B(1+x2)y"+2xy'+a2 y=0 C(1–x2)y"–xy+ay=0 D(1–x2)y"–xy'–a2 y=0

Show answer

EnglishPGT 2013

Q265.General solution of the differential equation xp2 –yp+a=0:

Axc+yc2 +a=0 Bxc–yc2 +a=0 Cxc2 –yc+a=0 Dxc2 –yc–a=0

Show answer

EnglishPGT 2010

Q266.The integral factor of the differential equation (((()))) ((()) 2 dx 1 y yx ay, 1 y 1 dy − + = − < < − + = − < < − + = − < < − + = − < < is

A2 1 1 y − B2 1 1 y + C2 1 y − D() 3/ 2 2 1 1 y +

Show answer

EnglishPGT 2009

Q267.Solution of the equation y2 log y = xy p + p2 is

Alog y = cx + x2 Blog y = cx2 + ex Clog x = cy + y2 DNone of these

Show answer

EnglishPGT 2009

Q268.Differential coefficient of (logex)sinx is

Asin sin (log) cos log (log) log + x e e e e x x x x x x Bcos 1 2 x C1 (log)sin cos − x e x x DNone of these

Show answer

EnglishPGT 2005, 2009

Q269.The general integral of partial differential equation xzp + yzp = xy is

Axyz Bxy + z2 = a Cx b y = Dxy – z2 = x f y

Show answer

EnglishPGT 2009

Q270.Complementary function (C.F.) of the differential equation 2 d y dy (x a) 4(x a) 6y x dx + − + + = + − + + = + − + + = + − + + = is

A2 3 1 2 + C x C x B3 2 1 2 () () + + + C x a C x a C3 2 1 2 + x x C e C e DNone of these

Show answer

EnglishPGT 2009

Q271.The order of the differential equation 4 3 2 4 3 2 4 5 3 6 0 − + − + = − + − + = − + − + = − + − + = d y d y d y dy y dx dx dx dx is

A3 B6 C4 D2

Show answer

EnglishPGT 2009

Q272.The differential equation of the family of curves y = acos () sin() + x b x µ where a and b are arbitrary constants is?

A2 0 + = d y y dx µ B2 0 − = d y y dx µ C2 = d y dx µ D2 − d y dx µ

Show answer

EnglishPGT 2009

Q273.Singular solution of (xp – y)2 = p2 – 1 is

Ax2 + y2 = 1 Bx2 – y2 = 1 Cx2 – y2 + 1 = 0 DNone of these

Show answer

EnglishPGT 2005

Q274.The solution of the differential equation 2 dy y y dx x + = + = is:

A2 xy log(c/ x) 1 = Bxlog(c/ x) y = Cxylog(c/ x) 1 = D2 xlog(c/ x) y =

Show answer

EnglishPGT 2005

Q275.General solution of the differential equation (D+3)(D–1)3 y=ex is

A2 x 3x 3 x 1 2 3 4 1 (C C x C x)e C e x e 24 − + + + + Bx 2x 3 x 1 2 1 (C e C e) x e 24 − + + C2 x 2x 3 x 1 2 3 4 1 (C C x C x)e C e x e 18 − + + + + Dx 2x 3 x 1 2 1 (C e C e) x e 18 − + +

Show answer

EnglishPGT 2005

Q276.The differential equation arising from φ(z/x3, y/x) = 0 is

Apx + qy = 2z Bpx + qy = 3z Cpx – qy = 2z Dpx – qy = 3z

Show answer

EnglishPGT 2004

Q277.Two linearly independent solutions of differential equation 2 0 d y dy y dx + + = + + = + + = + + = are

A/ 2 3 cos 2 x x e− and / 2 3 sin 2 x x e B/ 2 3 cos 2 x x e− and / 2 3 sin 2 x x e− C/ 2 3 cos 2 x x e and / 2 3 sin 2 x x e D/ 2 3 cos 2 −x x e and / 2 3 sin 2 x x e

Show answer

EnglishPGT 2004

Q278.The general solution of the differential equation 3 2 4 5 2 0 d y d y dy y dx dx dx − + − = − + − = − + − = − + − = is

A2 1 2 3 () x x c c x e c e − + + B2 1 2 3 () x x c c x e c e − − + + C2 1 2 3 () x x c c x e c e + + D2 1 2 3 () x x c c x e c e + +

Show answer

EnglishPGT 2004

Q279.The singular solution of (a2 -x2)p2 +2xyp+b2 -y2 =0 is

A2 2 2 2 + = b x a y ab B2 2 2 2 + = a x b y ab C2 2 2 2 2 2 + = b x a y a b D2 2 2 2 2 2 + = a x b y a b

Show answer

EnglishPGT 2003

Q280.Find the solution of the equation 3x 2 d y dy 7 6y 2e dx dx 2 − + = − + = − + = − + = which satisfies the conditions dy y 1, 0atx 0 dx = =

A5 3 7 1 1 15 3 5 = − − x x x y e e e B5 3 7 1 1 15 6 5 = − − x x x y e e e C6 3 7 1 1 15 6 5 = − − x x x y e e e DNone of these

Show answer