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

(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.

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Let A be n × n real valued square symmetric matrix of rank 2 with Consider
the following statements. **A. ** Both (I) and (II)

**B. ** (I) only

**C. ** Neither (I) nor (II)

**D. ** (II) only

**Answer : ****Option B**

**Explaination / Solution: **

(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?

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

∴ (II) is false

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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 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.

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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: **

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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.

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.

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