Mathematical Science MCQ Quiz in தமிழ் - Objective Question with Answer for Mathematical Science - இலவச PDF ஐப் பதிவிறக்கவும்
Last updated on Apr 14, 2025
Latest Mathematical Science MCQ Objective Questions
Top Mathematical Science MCQ Objective Questions
Mathematical Science Question 1:
The set T= {(x1, x2,..., xn....): x1, x2,..., xn... ∈ {1, 3, 5, 7, 9}} is
Answer (Detailed Solution Below)
Mathematical Science Question 1 Detailed Solution
Concept -
(1) The collection of all the sequences on two symbols or more than two symbols is uncountable.
Explanation -
The set T= {(x1, x2,..., xn,...): x1, x2,..., xn, ... ∈ {1, 3, 5, 7, 9}}
Now we have 5 symbols and T represents the collection of all the sequences.
Hence the set T is Uncountable.
Mathematical Science Question 2:
Let W be the column space of the matrix
Answer (Detailed Solution Below)
Mathematical Science Question 2 Detailed Solution
Explanation:
Let w1 =
then orthogonal projection of u on W is
\(\frac{}{
=
=
(2) correct
Mathematical Science Question 3:
Number of onto homomorphism from
Answer (Detailed Solution Below)
Mathematical Science Question 3 Detailed Solution
Explanation -
Results -
(i) Number of homomorphism from
(ii) Number of onto homomorphism from
(iii) Number of 1-1 homomorphism from
Hence option(2) is correct.
Mathematical Science Question 4:
Let S = {x5 - x4<=100 where x ∈ R} and T = { x2 - 2x <67 where x ∈ (0, ∞)} then S∩ T is
Answer (Detailed Solution Below)
Mathematical Science Question 4 Detailed Solution
Concept use:
Bounded set : A set S is bounded if it has both upper and lower bounds.
Closed set: If a set contain each of its limit point in the set
Calculations:
S = {x5 - x4<=100 where x ∈ R} is unbounded and Closed
T = { x2 - 2x <67 where x ∈ (0, ∞)} is Open and bounded
Hence the Intersection of the Closed set and Open Set need not be closed set, but it is bounded also.
So, The Correct option is 2.
Mathematical Science Question 5:
The series
Answer (Detailed Solution Below)
Mathematical Science Question 5 Detailed Solution
Concept -
(i) ∑ |an | is convergent then ∑ an is absolutely convergent.
(ii) Ratio Test -
If
Explanation -
We have the series
Now for Absolutely convergent -
Now using Ratio Test -
Hence the series
Hence Option (i) is true.
Mathematical Science Question 6:
If the sequence
Answer (Detailed Solution Below)
Mathematical Science Question 6 Detailed Solution
Concept -
(i) If n is even then (-1)n = 1
(ii) If n is odd then (-1)n = -1
(iii)
Explanation -
We have the sequence
Now as n → ∞ ,
an = 0 + (-1)n cos3(0) + (-1)n
Now we make the cases -
Case - I - If n is even then put (-1)n = 1 in the above equation we get
an = 0 + 1 x cos3(0) + 1 x
Case - II - If n is odd then put (-1)n = -1 in the above equation, we get
an = 0 - 1 x cos3(0) - 1 x
Hence largest and smallest limit points are 2 & 0.
So Options (i) & (iv) are wrong.
And we know that limit of the sequence is different in both the cases so not convergent.
Hence option (iii) is correct and (ii) is wrong.
Mathematical Science Question 7:
Let
Answer (Detailed Solution Below)
Mathematical Science Question 7 Detailed Solution
Explanation:
T: ℝ2 →ℝ2 be defined by
So,
So, matrix representation is
Option (3) is true and others are false
Mathematical Science Question 8:
If
Answer (Detailed Solution Below)
Mathematical Science Question 8 Detailed Solution
Concept:
L’Hospital’s Rule: If
Explanation:
=
=
Again using L'hospital rule
=
=
It will be 0/0 form if
x - 2a = 0
⇒ a = 0
Option (1) is correct
Mathematical Science Question 9:
The sequence an =
Answer (Detailed Solution Below)
Mathematical Science Question 9 Detailed Solution
Concept use:
Cauchy's first theorem on limits: If an is a sequence of positive terms such that
Explanation:
Let an =
⇒
Hence, by Cauchy's first theorem on limits, we have
⇒
⇒
Now,
Sequence converges to 0
Option (1) is correct
Mathematical Science Question 10:
The value of integral
Answer (Detailed Solution Below)
Mathematical Science Question 10 Detailed Solution
Concept:
If f(z) is an analytic function within and on a simple closed curve C and if a is any point within C, then
f(a) =
Here, the integral should be taken in the positive sense around C.
Solution - Given , function
f(z) =
and the function has singularity at z = i, z = - i
C : {z : |z - i| < 1}
So z = - i does not lie on the curve and z = i lies inside the curve
Hence
I = 2πi ×
Now, log (i) = log 1 + i tan-1(1/0) = 0 + i
hence I = π
Therefore, Correct Option is Option 4).