Mathematics - Online Test
Q1. Let u and v be two vectors in R2 whose Euclidean norms satisfy ||u|| = 2 ||v||. What is the value
of α such that w = u + αv bisects the angle between u and v ?
Answer : Option A
Explaination / Solution:
Q2. 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.
Q3. Let A be n × n real valued square symmetric matrix of rank 2 with 
Consider
the following statements.
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
Q4. 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.
Q5. The expression ((x + y) - |x - y|)/2 is equal to
Answer : Option B
Explaination / Solution:
Q6. 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.
Q7. Consider a company that assembles computers. The probability of a faulty
assembly of any computer is p. The company therefore subjects each
computer to a testing process. This testing process gives the correct result for
any computer with a probability of q. What is the probability of a computer
being declared faulty?
Answer : Option D
Explaination / Solution:
No Explaination.
Q8. What is the probability that divisor of 1099 is a multiple of 1096?
Answer : Option B
Explaination / Solution:
No Explaination.
Q9. Consider the following matrix
If the eigenvalues of A are 4 and 8, then
Answer : Option B
Explaination / Solution:
No Explaination.
Q10. The weight of a sequence a0, a1,…,an-1 of real numbers is defined as a0 + a1/2 + ..... + an-1/2n-1. A subsequence of a sequence is obtained by deleting
some elements from the sequence, keeping the order of the remaining elements
the same. Let X denote the maximum possible weight of a subsequence of
a0, a1,..., an-1. Then X is equal to
Answer : Option D
Explaination / Solution:
No Explaination.
