CS GATE 2017 PAPER 01 (Test 5)

Tag: cs gate 2017 paper 01
Let p, q, and r be propositions and the expression (p → q) → r be a contradiction. Then, the expression (r → p) → q is
A. a tautology
B. a contradiction
C. always TRUE when p is FALSE
D. always TRUE when q is TRUE
Answer : Option D
Explaination / Solution:

(p →q) → r is contradiction only when

And now for the above combination, the expression (r → p) → q is always true when q is true. When q is false in the above combination (third one) (r → p) → q will be false.

Let A be n × n real valued square symmetric matrix of rank 2 with  Consider the following statements. 
(I) One eigen value must be in [-5, 5]
(II) The eigen value with the largest magnitude must be strictly greater than 5. 
Which of the above statements about eigen values of A is/are necessarily CORRECT? 
A. Both (I) and (II)
B. (I) only
C. Neither (I) nor (II)
D. (II) only
Answer : Option B
Explaination / Solution:

∴One eigen value must be in [−5,5] and largest eigen value magnitude is not greater than 5 
∴ (II) is false

A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25m intervals in this plot. If in a flood, the water level rises to 525m, which of villages P,Q, R, S,T get submerged ? 

A. P,Q
B. P,Q,T
C. R,S,T
D. Q,R,S
Answer : Option C
Explaination / Solution:

The given contour is a hill station, the peak point of this hill station is P, it is under a contour of 550 . At floods, the water level is 525m. So the village of R, S and T are under a contour of 500. Therefore these villages are submerged.

The expression ((x + y) - |x - y|)/2 is equal to
A. the maximum of x and y
B. the minimum of x and y
C. 1
D. None of the above
Answer : Option B
Explaination / Solution:

Six people are seated around a circular table. There are at least two men and two women . There are at least three right-handed persons. Every woman has a left-handed person to her immediate right. None of the women are right-handed. The number of women at the table is
A. 2
B. 3
C. 4
D. Cannot be determined
Answer : Option A
Explaination / Solution:

Out of six people, 3 place definitely occupied by right handed people as atleast 2 women are there so these two will sit adjacently. Now as only one seat is left it will be occupied by a left handed man because on right side of this seat is sitting an right handed man.

Therefore, answer should be 2 women.