14. In the system of inear equations 2x+3y+ 4z = 1 5x-y+z=4 3x + ay-3z=3 has 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 number (A) Unique solution (B) No solution 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. ax+by+c=d₁ ax+by+cz=d₂ (C) Infinitely many solution (D) None of these 16. The partial differential equation of z=f(x+at)-g(x-at) is. (A) (C) a'z ar² =a² a'z ax² az Ə²= ar² ax² (B) 1.11 (A) xyz,-+-+- 2 / 20 (D) -0 ar 11 a'z a'z ar² ax² - 17. The first order partial differential equation by eliminat- ing the arbitary function from z=f(x²-y³) is (A) p+q=0 (C) ²p+x²q=0 (B) yp+xq=0 (D) 2y'p+3x'q=0 wwwww.pen wwwwwwww 18. The general solution of the partial differential equation x(y-2)p+y(2-x)q = ='(x-y) is 100% + (C)2 2 ential equation 4 (A) X(x) = ce) ² ce(). 21. If a(x, y)= X(x). Y(y) be the solution of the partial differ- du du +5 = dx dy solving it by the method of separation of variables, then X(x) (the function of x only in u(x, y)) is. [Note: Herec and k are arbitrary constants] (B) X(x)= ce (D) X(x) = ce² 22. Which of the following second order partial differential equations is an elliptic equation? (C) X(x) = d'u d'u (A) 3- +4 ar² axdy 2²M ax² (B) 3- (D) (C) -3- -4- d'u d'u +4- dx² axdy d'u dy² +5 +7 au d'u du du +5 ахду ду ах ду d'u d'u d'u +2- drdy dy + dx² d'u dy² 29 du du dx dy 0, which is obtained by (B) (D) +4x- + = 6x³y du ax du du dx dy +5 = 7x² DYT -7y dy 6xy² a-b =0 23. The Fourier cosine series of the function f(x) = 0≤xslis (A) 1 (C) 0

What's angel 2 and 4

70 90 100 110 80 60 50

Evaluate C, and P,. 8 5"

ps

9. V64a³b4

How many possible ways can five different pictures be hung along a wall?     5     120     50     50