Engineering Mathematics - Online Test
Q1. Let 
. Consider the set ܵ of all vectors 
such that a2 + b2 = 1 where 
Then ܵ is
. Consider the set ܵ of all vectors such that a2 + b2 = 1 where Then ܵ is
Answer : Option C
Explaination / Solution:
Q2. 
Let the probability density function of a random variable, X, be given as:
where u(x) is the unit step function.
Then the value of 'a' and Prob {X ≤ 0}, respectively, are
Answer : Option A
Explaination / Solution:
Q3. For a complex number z, 
is
is
Answer : Option D
Explaination / Solution:
Q4. The matrix 
has three distinct eigenvalues and one of its eigenvectors is 
Which one of the following can be another eigenvector of A?
has three distinct eigenvalues and one of its eigenvectors is Which one of the following can be another eigenvector of A?
Answer : Option C
Explaination / Solution:
By the properties of Eigen values and Eigen vectors, another eigen vector of A is 
The eigen vectors corresponding to distinct eigen values of a real symmetric matrix are
orthogonal i.e., pair wise dot product is zero
Q5. Consider the differential equation 
. There exists a
unique solution for this differential equation when t belongs to the interval
. There exists a
unique solution for this differential equation when t belongs to the interval
Answer : Option A
Explaination / Solution:
Q6. A function f(x) is defined as 
. Which one of the
following statements is TRUE?
. Which one of the
following statements is TRUE?
Answer : Option A
Explaination / Solution:
Q7. Consider the line integral 
The line C is shown in the figure
below.
The line C is shown in the figure
below.
Answer : Option B
Explaination / Solution:
Q8. The probability that a k-digit number does NOT contain the digits 0.5, or 9 is
Answer : Option C
Explaination / Solution:
Q9. The expression ((x + Y) - |x - y|)/2 is equal to
Answer : Option B
Explaination / Solution:
Q10. The value of the quantity P, where 
is equal to
is equal to
Answer : Option B
Explaination / Solution:
No Explaination.
