CS GATE 2017 PAPER 01 - Online Test

Q1. Let p, q, and r be propositions and the expression (p → q) → r be a contradiction. Then, the expression (r → p) → q is
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.

Q2. 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? 
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

Q3. 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 ? 

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.

Q4. The expression ((x + y) - |x - y|)/2 is equal to
Answer : Option B
Explaination / Solution:



Q5. 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
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.