Engineering Mathematics - Online Test
Q2. The area of the region bounded by the parabola y = x2 +1 and the straight line x+y = 3 is
Answer : Option B
Explaination / Solution:
At the point of intersection of the curves, y = x2 +1 and x+y = 3 i.e., y=3-x, we have
Q3. The respective expressions for complimentary function and particular integral part of
the solution of the differential equation 
are
are
Answer : Option A
Explaination / Solution:
Q4. Four cards are randomly selected from a pack of 52 cards. If the first two cards are kings, what is
the probability that the third card is a king?
Answer : Option B
Explaination / Solution:
There are 4 kings in a pack of 52 cards.
If 2 cards are selected and both are kings, remaining cards will be 50 out of which 2 will be kings.
Q5. Given i = √-1 the value of the definite integral 
Answer : Option B
Explaination / Solution:
Q6. Let A = [ αij ], 1≤ i, j ≤ n with n ≥ 3 and aij = i.j . The rank of A is
Answer : Option B
Explaination / Solution:
is equal to
Q8. The two Eigen values of the matrix 
have a ratio of 3 : 1 for p = 2. What is another value
of p for which the Eigen values have the same ratio of 3 : 1?
have a ratio of 3 : 1 for p = 2. What is another value
of p for which the Eigen values have the same ratio of 3 : 1?
Answer : Option D
Explaination / Solution:
Let A = 
Given that two eigen values of A are in 3:1
Ratio for p = 2
⇒ Characteristic equation λ2 -4λ+3 = 0 (by substituting p=2)
⇒ λ=1,3
Eigen values 5, 5/3 are in ratio 3:1
P = 14/3
Q9. A fair (unbiased) coin was tossed four times in succession and resulted in the following
outcomes: (i) Head, (ii) Head, (iii) Head, (iv) Head. The probability of obtaining a 'Tail' when
the coin is tossed again is
Answer : Option B
Explaination / Solution:
No Explaination.
Q10. 
can be expressed as
can be expressed as
Answer : Option C
Explaination / Solution:
