61.

62,

63.

64.

65.

67.

68.

69.

70.

Where is the minimum criterion used 7
(வ) When there is an AND operation (B) When there is an OR operation
(©) ‏ا‎ De Morgan's theorem (D) None of the above

Which of the following statements is true 7

(A) A number is rational if and only if ils square is rational

(8) An integer n is odd if and only if n?+ 21 is odd.

(ப) A number is irrational if and only if its square is irrational.
(D) A number n is odd if and only if n(r +1) is even.

Consider the following language L.={a"b"c"d"|jn 1] 1. 15:

(A) CFL but not regular (B) CSL but not CFL

(9) regular (D) type 0 language but not type 1
Which of the following is a level set of fix, ‏7ح (بجد‎ ആ

(ல (1), ೫2-23೧ 11] (0) [ജയ്‌ മു

(5) வ வருட (2) மடு விறலி

Which of the following is false ?

(ಗೈ) Product of T, - spaces is a T - space

(0) Product of completely regular spaces is completely regular
(©) Product of first countable spaces is first countable

(D) Product of two second countable spaces 18 second countable

What's the highest dimension a fractal can have ?

(५) 1 ® 2 © 3 യു 4
The Lorentz Butterfly is an example of what type of fractal ?

(^) Julia set (B) Mandelbrot set

(C) Strange Aftractor (D) None of the above

What integral equation is equivalent to the initial value problem y* = Ry, ‏)إل‎ -1(

i t
(A) y(:]-——1+j(§2-y(s})d§ (8) y(t)= 2+f(52—y(s)]ds
2 -1
t
(८) ` १८८) 2+ [ ६५(5)% (D) None of the above
−∣
↭⊦∎∘↭↽⋅↿⋅∊∐⋯⋯∘⋯∐∎⊡↕↿∃⋯⋅⋅∐⋯⊔↿↙∨≘∏≏⋍⇁∢⊴∾∎∁∥∄∐≡∎≀
(A) Newton and Laplace (ए) Newton and Euler
(C) Newton and Gauss (D) MNewton and Leibniz
For the differential equation 42’’’ +6x%y’ +y =0 the point at infinity is :
(ಗಿ) an ordinary point (1) ‏ده‎ 0111001 [೧101
(9) an irregular singular point (D) a regular singular point
11 121/2014

{P.T.O0.}