Q35. Value of " S5 x²y²z² dxdydz is abc 27 27 Q36. The integral S“, N Vat-y f(x,y)dxdy after changing the order of integration a) So LIf(x, y)dydx b) LaL f (x, y)d> c) So L dydx d) None of these Q37. Value of S* x(x² + y²)dxdx is ə) 5* - b) 5° + c)5 Q38. Value of the integral f S , dxdydz is a) 1 c) 3 Q39. Volume of the solid bounded by the planes x = 0, y = 0,x + y +z = a & z = b) 2 d) 4. a) So S-* dydx b) Sº Sª dzdydx c)S“ S* *-Y dzdydx d) None of these Q40. To change the rectangular coordinates (x, y, z) to cylindrical coordinates (p, a) x = p cos o, y = p sin o,z = z b) x = p cos o, y = p cos c) x = p sin o, y = p sin o,z = 2 d) None of these Q41. If f(x, y) = x³ + y³ +x then & is %3D a) 3x? + 3y? + 1,3y² + 1 b) 3x? + 1, 3y? c)x? +1,y? d) 3x?, y? Q42. Total derivative of z = tan-1 (). (x, y) + (0,0) is ydx+ydy x2+y2 ydx-xdy b) x2+y2 c)ydx – xdy d) ydx + x Q43. If w = x? + y?,x = ", y = b) 1 dw at t = 1 is dt then a) 0 c) 2 d) 3 Q44. If f(x,y) = x* – x²y² + y* then % at (-1,1) is b) 2 a) -2 c) 1 d) -1 Q45. If z = log az then x ax is x²+y² b)z c) 2z a) 0 d) 3z Q46. If cot- (E) + y +1 = 0,x > 0, y > 0 then 2 is d) x+3x (x²+y² y e x+3y2(x2+y2) x+3y?(x²+y²) 'x+3y2 Q47. If u = x3 + y³, then is b) 6x c)6 d) 0 a) 3x?
Q35. Value of " S5 x²y²z² dxdydz is abc 27 27 Q36. The integral S“, N Vat-y f(x,y)dxdy after changing the order of integration a) So LIf(x, y)dydx b) LaL f (x, y)d> c) So L dydx d) None of these Q37. Value of S* x(x² + y²)dxdx is ə) 5* - b) 5° + c)5 Q38. Value of the integral f S , dxdydz is a) 1 c) 3 Q39. Volume of the solid bounded by the planes x = 0, y = 0,x + y +z = a & z = b) 2 d) 4. a) So S-* dydx b) Sº Sª dzdydx c)S“ S* *-Y dzdydx d) None of these Q40. To change the rectangular coordinates (x, y, z) to cylindrical coordinates (p, a) x = p cos o, y = p sin o,z = z b) x = p cos o, y = p cos c) x = p sin o, y = p sin o,z = 2 d) None of these Q41. If f(x, y) = x³ + y³ +x then & is %3D a) 3x? + 3y? + 1,3y² + 1 b) 3x? + 1, 3y? c)x? +1,y? d) 3x?, y? Q42. Total derivative of z = tan-1 (). (x, y) + (0,0) is ydx+ydy x2+y2 ydx-xdy b) x2+y2 c)ydx – xdy d) ydx + x Q43. If w = x? + y?,x = ", y = b) 1 dw at t = 1 is dt then a) 0 c) 2 d) 3 Q44. If f(x,y) = x* – x²y² + y* then % at (-1,1) is b) 2 a) -2 c) 1 d) -1 Q45. If z = log az then x ax is x²+y² b)z c) 2z a) 0 d) 3z Q46. If cot- (E) + y +1 = 0,x > 0, y > 0 then 2 is d) x+3x (x²+y² y e x+3y2(x2+y2) x+3y?(x²+y²) 'x+3y2 Q47. If u = x3 + y³, then is b) 6x c)6 d) 0 a) 3x?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Question
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Q35. Value of " S x²y²z² dxdydz is
abc
a)
b)
a²b²c?
27
27
Q36. The integral a Jo
ra Naz-yi
f(x, y)dxdy after changing the order of integration
a) o Lvazf (x, y)dydx
b) LaLaif(x, y)d}
c) S dydx
d) None of these
Q37. Value of * x(x² + y²)dxdx is
b) 5°; +
a)
c)56
Q38. Value of the integral . S S, dxdydz is
c) 3
а) 1
b) 2
d) 4
Q39. Volume of the solid bounded by the planes x = 0, y = 0,x + y +z = a & z =
a) " S* dydx
ra-x
b) fº Sª Sª dzdydx
c) a-* a-x-Y dzdydx
d) None of these
Q40. To change the rectangular coordinates (x, y, z) to cylindrical coordinates (p,
a) x = p cos p, y = p sin o,z = z
b) x = p cos ¢, y = p cos
c) x = p sin , y = p sin o , z = z
d) None of these
Q41. If f(x, y) = x³ + y3 +x then % & L
a) 3x? + 3y? + 1,3y² + 1
b) 3x? + 1,3y?
c)x? + 1,y?
d) 3x?, y?
Q42. Total derivative of z = tan-1(), (x, y) + (0,0) is
a) ydx+ydy
x2+y2
ydx-xdy
b)
x2+y2
с)ydx — xdy
d) ydx +x
Q43. If w = x2 + y?,x = , y =
b) 1
then
t2+1
at t = 1 is
а) 0
c) 2
d) 3
Q44. If f (x,y) = x* – x²y² + y* then 2 at (-1,1) is
b) 2
a) -2
c) 1
d) -1
[x?-y²
dz is
Q45. If z = log , then x
+ y
ax
a) 0
b)z
c) 2z
d) 3z
Q46. If cot-1 (E) + y +1 = 0,x > 0, y > 0 then 2 is =
y
x+3y2(x²+y²)
b)
x+3y (x²+y?)
x+3x2(x2+y2
Q47. If u = x3 + y3, then
is
a) 3x?
b) 6x
c)6
d) 0
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