please answer 19 through 24 Inbox (13,580) - thomaskielbasins X).pdf(A)ÔNE14. If the system of linear equations2x + 3y + 4z= 15x-y+z=4mm3D--(C) Infinitely many solution(D) None of these(C)16. The partial differential equation ofz=f(x+at)- g (x-at) isdºz3x + ay-3z = 3has a unique solution, then the value of a + 4(A) must be equal to 0,(B) should not be equal to 0(C) can be any real number,(D) can be any rational number15. If a, b, c, d,, a, b,, c, and d, are any non zero realnumbers, then which of the following types of solutionis NOT possible for the system of linear equations.ax+by+cz=d₁+by+cz=d₂(A) Unique solution(B) No solutionard²z d²zdr du=a(A) p+q=0(C) yp+rq=0(B) Oe11•(A) xyz,-+-+-=0x y42(C) --+17. The first order partial differential equation by eliminat-ing the arbitary function from z = f(x²³ -²¹) is(B) yp + xq=0(D) 2y p+ 3x³q=0102 CREATIVE WRITERS-contract fe XX y18. The general solution of the partial differential equationx(y-2) p+y(2-x)q = ='(x - y) is21 1 1 1+Z xB)21 1 1(D)41(B)(D)-+-+X2 / 20+/+) = 0.00IY70=0at dxəz Əºz+di² ax²0-a100%+(A) r²¹+y² = (x −y)(B) x²+z=(x² – z²)(C) x²-y²=(²– zª²)(D) -2=(x−y² − z³)20. The solution of (p-q)(z-xp-y q) = 1 is(B) z= axbyUntitled (4)(A) z= ax by +(C) z = ax + by(A) X(x)=ce²(C) X(x) = ce(i)21. Ifu(x, y)= X(x). Y(y) be the solution of the partial differ-du duential equation 4 +5. = 0, which is obtained byəx dy(C) -3(D)solving it by the method of separation of variables, thenX(x) (the function of x only in u(x, y)) is[Note: Herec and k are arbitrary constants]a²u d'u(B) 3- -4. +5dr² əxəy dy²(A)1a+b22. Which of the following second order partial differentialequations is an elliptic equation?d'u d'u d'u du du(A) 3- +45 +7dr² dxdydx dyd'u d'u+4-Əxəyd'uf(x) = ++20 ≤x≤lis(A) 1(C) 0+5(D) z= ax +by+d'u du(B) X(x) = ce(D) X(x) = cedxaudu+Әхду ду dx(B)(D)(B)+4x-duaxduди+5.24. The Fourier series of f(x) = e in the(0, 2n) is+= 6x²ydu23. The Fourier cosine series of the function f(x) =11/10A= 6.xy²a-b19420intervalΣα a, cos nx+b, sin nex, then the value of+ΣN

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(A) (C) 14. If the system of linear equations 2x + 3y + 4z= 1 5x-y+z=4 -3 (A) must be equal to 0, (B) should not be equal to 0 (C) can be any real number, (D) can be any rational number 3x + ay-32= 3 has a unique solution, then the value of a + 4 (A) Unique solution (B) No solution (C) Infinitely many solution (D) None of these (A) 15. If a, b, c,, d., a, b, c, and d, are any non zero real numbers, then which of the following types of solution is NOT possible for the system of linear equations. (C) ax+by+cz=d₁ ax+by+cz=d, 16. The partial differential equation of z=f(x+at) - g (x-at) is a'z a¹z Əx² (B) =a (C) 0¹2 dr ax (A) p+q=0 (C) y'p+xq=0 (D) B) JE (D) 11 1 (A) xyz, +-+-=0 x y 1 1 11 1 + + ** y² zx y 1 X y 1 (B) (D) drª 17. The first order partial differential equation by eliminat- ing the arbitary function from z=f(x³ -y²³) is dz dr 2 / 20 0 -4 18. The general solution of the partial differential equation x(y-z) p+y³(2-x)q=z'(x-y) is 11 1 z³x² y² 22 + 11 1 <=0 əz 0 191 dx (B) yp+xq=0 (D) 2y³p+ 3x³q=0 a²z dr² 100% (A) r²+²=(x²-y) (B) x²¹+z² = (x² - z²¹) (C) x²-y²=(−z²³) (D) y²-2²= (x²-yª² − z²) 20. The solution of (p-q)(z-xp-y q) = 1 is (A) z= ax-by+ (B) z-ax-by + (C) z = ax + by a-b 21. Ifu(x, y)= X(x). Y(y) be the solution of the partial differ- du du (A) X(x) = cek) ² (C) X(x) = c(i) H ential equation 4- +5 = 0, which is obtained by ax dy solving it by the method of separation of variables, then X(x) (the function of x only in u(x, y)) is [Note: Here e and k are arbitrary constants] (B) 3- (D) 22. Which of the following second order partial differential equations is an elliptic equation? 1 a+b d'u d'u d'u du du (A) 3 +4 -5- +7 dxdy dy Әх ду dx² a²u dx² (A) d'u (C) -3 +4 drª axdy dy² 0 ≤x≤lis (A) 1 (C) 0 a 99 is f(x) = + (D) z= ax+by+ (B) X(x)= ce (D) X(x) = ce)² 4 d'u d'u du du +5 + = 6x²y axdy ду² Әх ду +5 d'u d'u au du du +2+ 2 +5 dxdy dy dx dy + Əx² d'u d'u du +4x -7y ax 24. The Fourier series of f(x) = e in the (0, 2n) is 1 23. The Fourier cosine series of the function f(x) = 2 Σa, cos mx+ = (B) (D) = 7x² (B) du dy 6.xy² =0 19 42 interval +Σb, sin nx, then the value of