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GATE Exam
CS Computer Science and Information Technology
Engineering Mathematics
TEST : 5
# GATE Exam
# CS Computer Science and Information Technology
# Engineering Mathematics
# EE GATE 2016 SET 2
Prepare / Learn
Q1.
Let
. Consider the set ܵ of all vectors
such that
a
2
+ b
2
= 1 where
Then ܵ is
A.
B.
C.
D.
View Solution
Add Work Space
Answer :
Option C
Explaination / Solution:
# GATE Exam
# CS Computer Science and Information Technology
# Engineering Mathematics
# EE GATE 2016 SET 2
Prepare / Learn
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
A.
B.
C.
D.
View Solution
Add Work Space
Answer :
Option A
Explaination / Solution:
# GATE Exam
# CS Computer Science and Information Technology
# Engineering Mathematics
# EE GATE 2017 PAPER 01
Prepare / Learn
Q3.
For a complex number z,
is
A.
-2i
B.
-i
C.
i
D.
2i
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
# GATE Exam
# CS Computer Science and Information Technology
# Engineering Mathematics
# EE GATE 2017 PAPER 01
Prepare / Learn
Q4.
The matrix
has three distinct eigenvalues and one of its eigenvectors is
Which one of the following can be another eigenvector of A?
A.
B.
C.
D.
View Solution
Add Work Space
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
# GATE Exam
# CS Computer Science and Information Technology
# Engineering Mathematics
# EE GATE 2017 PAPER 01
Prepare / Learn
Q5.
Consider the differential equation
. There exists a unique solution for this differential equation when t belongs to the interval
A.
(-2,2)
B.
(-10,10)
C.
(-10,2)
D.
(0,10)
View Solution
Add Work Space
Answer :
Option A
Explaination / Solution:
# GATE Exam
# CS Computer Science and Information Technology
# Engineering Mathematics
# EE GATE 2017 PAPER 01
Prepare / Learn
Q6.
A function f(x) is defined as
. Which one of the following statements is TRUE?
A.
f(x) is NOT differentiable at x=1 for any values of a and b.
B.
f(x) is differentiable at x = 1 for the unique values of a and b
C.
f(x) is differentiable at x = 1 for all values of a and b such that a + b = e
D.
f(x) is differentiable at x = 1 for all values of a and b.
View Solution
Add Work Space
Answer :
Option A
Explaination / Solution:
# GATE Exam
# CS Computer Science and Information Technology
# Engineering Mathematics
# EE GATE 2017 PAPER 01
Prepare / Learn
Q7.
Consider the line integral
The line C is shown in the figure below.
A.
(1/2)i
B.
(2/3)i
C.
(3/4)i
D.
(4/5)i
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
# GATE Exam
# CS Computer Science and Information Technology
# Engineering Mathematics
# EE GATE 2017 PAPER 01
Prepare / Learn
Q8.
The probability that a k-digit number does NOT contain the digits 0.5, or 9 is
A.
0.3
k
B.
0.6
k
C.
0.7
k
D.
0.9
k
View Solution
Add Work Space
Answer :
Option C
Explaination / Solution:
# GATE Exam
# CS Computer Science and Information Technology
# Engineering Mathematics
# EE GATE 2017 PAPER 01
Prepare / Learn
Q9.
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
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
# GATE Exam
# CS Computer Science and Information Technology
# Engineering Mathematics
# EE GATE 2010
Prepare / Learn
Q10.
The value of the quantity P, where
is equal to
A.
0
B.
1
C.
e
D.
1/e
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
No Explaination.
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