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Jhanvi AgrawalEduRev Mathematics |
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Jhanvi Agrawal
EduRev Mathematics
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Content, tests & courses saved by you for accessing later. (visible to you only)
Discussed Questions
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Jhanvi Agrawal upvoted • 3 weeks ago |
If A and B are 3 × 3 real matrices such that rank (AB) = 1, then rank (BA) cannot be - a)3
- b)0
- c)2
- d)1
Correct answer is option 'A'. Can you explain this answer?
If A and B are 3 × 3 real matrices such that rank (AB) = 1, then rank (BA) cannot be
a)
3
b)
0
c)
2
d)
1
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Veda Institute answered |
Here A & B a re 3 × 2 real matrices such that rank (AB) = 1
So, |AB| = 0 ⇒ |A| |B| = 0 (∴ |AB| = |A| |B|)
⇒ either |A| or |B| should be zero
So, |BA| = |B||A| = 0
⇒ BA is singular
Hence rank (BA) cannot be 3. (Because BA is 3 × 3 matrix)
So, |AB| = 0 ⇒ |A| |B| = 0 (∴ |AB| = |A| |B|)
⇒ either |A| or |B| should be zero
So, |BA| = |B||A| = 0
⇒ BA is singular
Hence rank (BA) cannot be 3. (Because BA is 3 × 3 matrix)
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Jhanvi Agrawal upvoted • Feb 27, 2025 |
A cauchy sequence in Q which does not have a limit in Q is- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
A cauchy sequence in Q which does not have a limit in Q is
a)
b)
c)
d)
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Veda Institute answered |
Here sequence in option (A) is not convergent ⇒ it is not cauchy. Sequence in option (C) is convergent which converge to 0.
⇒ It be a cauchy sequence which converge in Q.
Similarly sequence in Option (D) has two subsequences.
and both are converging to 0.
But sequence in option (B) will converge to e.
⇒ It be a cauchy sequence which is not converging in Q.
⇒ It be a cauchy sequence which converge in Q.
Similarly sequence in Option (D) has two subsequences.
and both are converging to 0. But sequence in option (B) will converge to e.
⇒ It be a cauchy sequence which is not converging in Q.
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Jhanvi Agrawal upvoted • Feb 10, 2025 |
R is a closed planar region as shown by the shaded area in the figure below. Its boundary C consists of the circles C1 and C2.
If 
are all continuous everywhere in R, Green’s theorem states that
Which one of the following alternatives correctly depicts the direction of integration along C?... more
R is a closed planar region as shown by the shaded area in the figure below. Its boundary C consists of the circles C1 and C2.
If are all continuous everywhere in R, Green’s theorem states that
Which one of the following alternatives correctly depicts the direction of integration along C?
If
are all continuous everywhere in R, Green’s theorem states thatWhich one of the following alternatives correctly depicts the direction of integration along C?
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Veda Institute answered |
The region R is bounded by two closed circles C1 and C2, so it is doubly connected. To apply it in Green’s theorem, we need to convert it into simply connected region. For it, we apply cut AD and consider the region R having simple closed curve ABCADEFDA in the anticlockwise direction. So, the directions shown in figure, (c) is correct option.
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Jhanvi Agrawal upvoted • Feb 05, 2025 |
The sequence {Sn} of real numbers given by Sn = 
is- a)a divergent sequence
- b)a Cauchy sequence
- c)an oscillatory sequence
- d)not a Cauchy sequence
Correct answer is option 'B'. Can you explain this answer?
The sequence {Sn} of real numbers given by Sn = is
a)
a divergent sequence
b)
a Cauchy sequence
c)
an oscillatory sequence
d)
not a Cauchy sequence
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Veda Institute answered |
So <Sn> is monotonically increasing Next, we will show that it is bounded.
⇒ <Sn> is bounded. By the theorem's Every monotonic bounded sequence is convergent, Then <Sn> is convergent.
By the Lemma, if <Sn> is a convergent sequence of real numbers, Then <Sn> is a Cauchy-sequence.
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Jhanvi Agrawal upvoted • Jan 30, 2025 |
If y'1 (x) = 3y1(x) + 4y2(x) and y'2 (x) = 4y1(x) + 3y2(x), then y1(x) is- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
If y'1 (x) = 3y1(x) + 4y2(x) and y'2 (x) = 4y1(x) + 3y2(x), then y1(x) is
a)
b)
c)
d)
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Veda Institute answered |
we have (D - 3)y1 - 4y2 = 0
4y2 + (3 - D)y1 = 0
Solving equations, we get
So,
4y2 + (3 - D)y1 = 0
Solving equations, we get
So,
Lim n infty 1 sqrt n ( 1/(sqrt(3) + sqrt(6)) + 1/(sqrt(6) + sqrt(9)) +***+ 1 sqrt 3n + sqrt 3n+3 )=?
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Jhanvi Agrawal answered • Jan 08, 2025 |
Limit Evaluation
To evaluate the limit as n approaches infinity of the expression:
1/√n * (1/(√3) + √6) + 1/(√6 + √9) + ... + 1/(√3n + √(3n+3))
we can break it down into manageable parts.
Understanding the Expression
- The expression consists of a series of terms, each involving square roots.
- The terms range from 1/(√3 + √6) to 1/(√3n + √(3n+3)).
... more
To evaluate the limit as n approaches infinity of the expression:
1/√n * (1/(√3) + √6) + 1/(√6 + √9) + ... + 1/(√3n + √(3n+3))
we can break it down into manageable parts.
Understanding the Expression
- The expression consists of a series of terms, each involving square roots.
- The terms range from 1/(√3 + √6) to 1/(√3n + √(3n+3)).
... more
Three numbers, ,a b c are chosen from (0, 4) . The probability that the sum of these three numbers is greater than 2 is? Use the concept of geometric probability. The answer is 1/24
?
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Jhanvi Agrawal answered • Oct 06, 2024 |
Understanding the Problem
To find the probability that the sum of three numbers a, b, and c, chosen from the interval (0, 4), exceeds 2, we will use geometric probability.
Defining the Region of Interest
1. Domain of Selection: Each number a, b, and c can take values in the interval (0, 4). Thus, we are considering the cube defined by 0 < a,="" b,="" c="" />< />... more
To find the probability that the sum of three numbers a, b, and c, chosen from the interval (0, 4), exceeds 2, we will use geometric probability.
Defining the Region of Interest
1. Domain of Selection: Each number a, b, and c can take values in the interval (0, 4). Thus, we are considering the cube defined by 0 < a,="" b,="" c="" />< />... more
The function f defined by f(x) - x [1 + 1/3 sin (log x2)], a ≠ 0,/(0) = 0 ([] represents the greatest integer function) is- a)continuous and differentiable at origin
- b)not continuous but differentiable
- c)continuous but not differentiable
- d)not continuous and not differentiable
Correct answer is option 'C'. Can you explain this answer?
The function f defined by f(x) - x [1 + 1/3 sin (log x2)], a ≠ 0,/(0) = 0 ([] represents the greatest integer function) is
a)
continuous and differentiable at origin
b)
not continuous but differentiable
c)
continuous but not differentiable
d)
not continuous and not differentiable
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Jhanvi Agrawal answered • Jun 27, 2024 |
Continuity and Differentiability of the Given Function
The function f(x) is defined as f(x) = x[1 + 1/3 sin(log(x^2))], where x ≠ 0 and f(0) = 0. We need to determine if the function is continuous and differentiable at the origin (x = 0).
Continuity
For a function to be continuous at a point, the limit of the function as x approaches that point must exist and ... more
The function f(x) is defined as f(x) = x[1 + 1/3 sin(log(x^2))], where x ≠ 0 and f(0) = 0. We need to determine if the function is continuous and differentiable at the origin (x = 0).
Continuity
For a function to be continuous at a point, the limit of the function as x approaches that point must exist and ... more
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Jhanvi Agrawal asked • Jun 21, 2024 |
Consider the differential equestion 
and y = 0 and x → ∞ then 
is- a)
- b)
- c)0
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
Consider the differential equestion and y = 0 and x → ∞ then is
and y = 0 and x → ∞ then isa)
b)
c)
0
d)
none of these
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Veda Institute answered |
Given differential equestion is 
multiply bothe of side of equation by ey we get
Take ey = t
Integrating factor = 
solutions is
where c is an arbitrary constant
where u = ex
so 
now 
when x = log2
= not defind
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Jhanvi Agrawal asked • Jun 13, 2024 |
Find 
- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
Find
a)
b)
c)
d)
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Veda Institute answered |
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Jhanvi Agrawal asked • Jun 06, 2024 |
Let Pn (ℝ) be the vector space of all polynomials of degree atmost n.Let g(x) = x + 1 and define T : P2 (ℝ)→P2 (ℝ) byT(f (x)) = f'(x) g(x) + 2f (x).Then the trace of A is;- a)5
- b)6
- c)9
- d)12
Correct answer is option 'C'. Can you explain this answer?
Let Pn (ℝ) be the vector space of all polynomials of degree atmost n.
Let g(x) = x + 1 and define T : P2 (ℝ)→P2 (ℝ) by
T(f (x)) = f'(x) g(x) + 2f (x).
Then the trace of A is;
a)
5
b)
6
c)
9
d)
12
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Jiya Choudhury answered |
Understanding the Problem
To find the trace of the linear transformation T defined on the vector space P2(), we need to examine the transformation closely.
Definition of T
The transformation T is given by:
T(f(x)) = f(x) * g(x) + 2f(x), where g(x) = x + 1.
This means T takes a polynomial f(x) from P2() and transforms it into another polynomial of the same deg... more
To find the trace of the linear transformation T defined on the vector space P2(), we need to examine the transformation closely.
Definition of T
The transformation T is given by:
T(f(x)) = f(x) * g(x) + 2f(x), where g(x) = x + 1.
This means T takes a polynomial f(x) from P2() and transforms it into another polynomial of the same deg... more
Suppose that the number of typographical errors on a single page of a certain book has a Poisson distribution with parameter λ = 1/2. In 600 pages book, the average number of errors in the book is- a)300
- b)150
- c)600
- d)393
Correct answer is option 'A'. Can you explain this answer?
Suppose that the number of typographical errors on a single page of a certain book has a Poisson distribution with parameter λ = 1/2. In 600 pages book, the average number of errors in the book is
a)
300
b)
150
c)
600
d)
393
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Jhanvi Agrawal answered • Mar 23, 2024 |
Calculation of Average Number of Errors
To calculate the average number of errors in a 600-page book, we need to first find the average number of errors on a single page. Given that the number of errors on a single page follows a Poisson distribution with parameter λ = 1/2, we know that the mean of this distribution is equal to λ.
Mean of Poisson Distribution<... more
Let T : R2 → R2 be a linear transformation such that T((1, 2)) = (2, 3) and T((0, 1)) = (1, 4).Then T((5, -4)) is
- a)(-4, -41)
- b)(-1, 6)
- c)(-6, 1)
- d)(1, -6)
Correct answer is option 'A'. Can you explain this answer?
Let T : R2 → R2 be a linear transformation such that T((1, 2)) = (2, 3) and T((0, 1)) = (1, 4).Then T((5, -4)) is
a)
(-4, -41)
b)
(-1, 6)
c)
(-6, 1)
d)
(1, -6)
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Jhanvi Agrawal answered • Jan 28, 2024 |
Let's assume that T is a linear transformation from R2 to R2.
A linear transformation is a function that preserves vector addition and scalar multiplication. In other words, if u and v are vectors in R2 and c is a scalar, then T(u + v) = T(u) + T(v) and T(cu) = cT(u).
Since T is a transformation from R2 to R2, it takes in a vector in R2 and produces another vector in R2. We ... more
A linear transformation is a function that preserves vector addition and scalar multiplication. In other words, if u and v are vectors in R2 and c is a scalar, then T(u + v) = T(u) + T(v) and T(cu) = cT(u).
Since T is a transformation from R2 to R2, it takes in a vector in R2 and produces another vector in R2. We ... more
For n ε Z, Let nZ= {nk : k ε Z}. Then the number of units of Z/11Z and Z/12Z, respectively, are- a)11,12
- b)10, 11
- c)10, 4
- d)10, 8
Correct answer is option 'C'. Can you explain this answer?
For n ε Z, Let nZ= {nk : k ε Z}. Then the number of units of Z/11Z and Z/12Z, respectively, are
a)
11,12
b)
10, 11
c)
10, 4
d)
10, 8
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Jhanvi Agrawal answered • Dec 22, 2023 |
There is no specific definition for "n" in your question. Please provide more context so I can assist you better.
Total number of finite order elements in (Q, +) group?
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Jhanvi Agrawal answered • Nov 30, 2023 |
The group (Q, +) is the set of rational numbers under addition. In this group, we are interested in finding the total number of finite order elements.
Definition of Finite Order Elements
An element g in a group is said to have finite order if there exists a positive integer n such that g^n = e, where e is the identity element of the group.
Identity Elem... more
In the group (Q, +), the identity element is 0. For any rational number q, q + 0 = q and 0 + q = q.
Finite Order Elements in (Q, +)
Let's consider an arbitrary rational number q in (Q, +). In order for q to have finite order, there must exist a positive integer n such that q^n = 0.
Case 1: q = 0
If q = 0, then q^n = 0^n = 0 for any positive integer n. Therefore, 0 has finite order.
Case 2: q ≠ 0
If q ≠ 0, then q^n = 0 implies that q = 0. However, by assumption, q ≠ 0. Therefore, there are no nonzero rational numbers with finite order in the group (Q, +).
Total Number of Finite Order Elements
From the above analysis, we can conclude that the only rational number with finite order in the group (Q, +) is 0. Therefore, the total number of finite order elements in (Q, +) is 1.
Summary
- The group (Q, +) consists of rational numbers under addition.
- An element g in a group has finite order if there exists a positive integer n such that g^n = e, where e is the identity element of the group.
- In (Q, +), the identity element is 0.
- The only rational number with finite order in (Q, +) is 0.
- Therefore, the total number of finite order elements in (Q, +) is 1.
Definition of Finite Order Elements
An element g in a group is said to have finite order if there exists a positive integer n such that g^n = e, where e is the identity element of the group.
Identity Elem... more
In the group (Q, +), the identity element is 0. For any rational number q, q + 0 = q and 0 + q = q.
Finite Order Elements in (Q, +)
Let's consider an arbitrary rational number q in (Q, +). In order for q to have finite order, there must exist a positive integer n such that q^n = 0.
Case 1: q = 0
If q = 0, then q^n = 0^n = 0 for any positive integer n. Therefore, 0 has finite order.
Case 2: q ≠ 0
If q ≠ 0, then q^n = 0 implies that q = 0. However, by assumption, q ≠ 0. Therefore, there are no nonzero rational numbers with finite order in the group (Q, +).
Total Number of Finite Order Elements
From the above analysis, we can conclude that the only rational number with finite order in the group (Q, +) is 0. Therefore, the total number of finite order elements in (Q, +) is 1.
Summary
- The group (Q, +) consists of rational numbers under addition.
- An element g in a group has finite order if there exists a positive integer n such that g^n = e, where e is the identity element of the group.
- In (Q, +), the identity element is 0.
- The only rational number with finite order in (Q, +) is 0.
- Therefore, the total number of finite order elements in (Q, +) is 1.
The value of C1 + 3C3 + 5C5 + 7C7 + ...., where C0, C3, C5, C7,..... are binomial coefficients is - a)n.2n -1
- b)n.2n +1
- c)n.2n
- d)n.2n-2
Correct answer is option 'D'. Can you explain this answer?
The value of C1 + 3C3 + 5C5 + 7C7 + ...., where C0, C3, C5, C7,..... are binomial coefficients is
a)
n.2n -1
b)
n.2n +1
c)
n.2n
d)
n.2n-2
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Jhanvi Agrawal answered • Nov 08, 2023 |
The given expression involves binomial coefficients, which are calculated using the formula C(n, r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items chosen at a time.
To understand the given expression, let's break it down step by step:
Step 1: C1
C1 represents the binomial coefficient when n = 1 and r = 1. Plugging these values into ... more
To understand the given expression, let's break it down step by step:
Step 1: C1
C1 represents the binomial coefficient when n = 1 and r = 1. Plugging these values into ... more
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Jhanvi Agrawal asked • Oct 01, 2023 |
The probability of a defective piece produced in a manufacturing process is 0.01. The probability that out of 5 successive pieces, only one is defective, is- a)(0.99)2 (0.01)
- b)(0.99) (0.01)4
- c)5 x (0.99)(0.01)4
- d)5x(0.99)4(0.01)
Correct answer is option 'D'. Can you explain this answer?
The probability of a defective piece produced in a manufacturing process is 0.01. The probability that out of 5 successive pieces, only one is defective, is
a)
(0.99)2 (0.01)
b)
(0.99) (0.01)4
c)
5 x (0.99)(0.01)4
d)
5x(0.99)4(0.01)
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Chirag Verma answered |
The required probability = 
The total number of selections of at most n things from (2n + 1) different things is 63. Then the value of n is- a)3
- b)2
- c)4
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
The total number of selections of at most n things from (2n + 1) different things is 63. Then the value of n is
a)
3
b)
2
c)
4
d)
none of these
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Jhanvi Agrawal answered • Sep 04, 2023 |
To solve this problem, we need to use the concept of combinations.
Let's assume that the number of things we select is k.
The total number of selections of at most n things from (2n - 1) different things can be split into two cases:
1. Selecting k things from the first n things and (n - k) things from the remaining (n - 1) things.
2. Selecting (k - 1) things... more
Let's assume that the number of things we select is k.
The total number of selections of at most n things from (2n - 1) different things can be split into two cases:
1. Selecting k things from the first n things and (n - k) things from the remaining (n - 1) things.
2. Selecting (k - 1) things... more
What is the range of f(x) = cos 2x - sin 2x?- a)[2,4]
- b)[- 1 , 1]
- c)[-√2, √2]
- d)(-√2. 2)
Correct answer is option 'C'. Can you explain this answer?
What is the range of f(x) = cos 2x - sin 2x?
a)
[2,4]
b)
[- 1 , 1]
c)
[-√2, √2]
d)
(-√2. 2)
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Jhanvi Agrawal answered • Sep 04, 2023 |
To find the range of the function f(x) = cos 2x - sin 2x, we can rewrite it as a single trigonometric function using the identities cos(A-B) = cos A cos B + sin A sin B and sin(A-B) = sin A cos B - cos A sin B.
f(x) = cos 2x - sin 2x
= cos(π/2 - 2x) - sin(π/2 - 2x)
= sin(2x) + cos(2x)
Now, let's consider the possible values of sin(2x) and cos(2x). The range of both ... more
f(x) = cos 2x - sin 2x
= cos(π/2 - 2x) - sin(π/2 - 2x)
= sin(2x) + cos(2x)
Now, let's consider the possible values of sin(2x) and cos(2x). The range of both ... more
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Jhanvi Agrawal asked • Aug 17, 2023 |
Can I get admission to M.Sc. Physics at IITs based on the cutoff of previous years?
|
Naina Rana answered |
Admission to M.Sc. Physics at IITs based on previous year cutoff
Introduction:
Admission to the M.Sc. Physics program at the Indian Institutes of Technology (IITs) is highly competitive and is based on various factors, including the cutoff marks of previous years. The cutoff marks are the minimum scores required for admission and are determined by the IITs based on va... more
Introduction:
Admission to the M.Sc. Physics program at the Indian Institutes of Technology (IITs) is highly competitive and is based on various factors, including the cutoff marks of previous years. The cutoff marks are the minimum scores required for admission and are determined by the IITs based on va... more
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Jhanvi Agrawal asked • Aug 14, 2023 |
What details do I need to provide to access the answer key for the IIT JAM Mathematics Exam?
|
Oishi Bajaj answered |
Accessing the Answer Key for the IIT JAM Mathematics Exam
To access the answer key for the IIT JAM Mathematics Exam, you need to follow a few steps. The answer key is usually released by the organizing institute shortly after the examination. Here are the details you need to provide and the steps to access the answer key:
1. Exam Details:
You need to provid... more
To access the answer key for the IIT JAM Mathematics Exam, you need to follow a few steps. The answer key is usually released by the organizing institute shortly after the examination. Here are the details you need to provide and the steps to access the answer key:
1. Exam Details:
You need to provid... more
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Jhanvi Agrawal asked • Aug 07, 2023 |
What are the best books for improving time management during the IIT JAM Mathematics Exam?
|
Radha Mehta answered |
Best Books for Improving Time Management during the IIT JAM Mathematics Exam
Time management is crucial when preparing for the IIT JAM Mathematics Exam. To effectively manage your time during the exam, it is important to have a solid understanding of the concepts and practice solving a variety of problems. Here are some recommended books that can help you improve your time manage... more
Time management is crucial when preparing for the IIT JAM Mathematics Exam. To effectively manage your time during the exam, it is important to have a solid understanding of the concepts and practice solving a variety of problems. Here are some recommended books that can help you improve your time manage... more
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Jhanvi Agrawal asked • Aug 02, 2023 |
Can I take short breaks during my study sessions to stay refreshed and focused for the IIT JAM Mathematics Exam?
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Nakul Bajaj answered |
Yes, taking short breaks during study sessions can help you stay refreshed and focused for the IIT JAM Mathematics Exam.
- Our brains have a limited capacity to focus and retain information for long periods of time. Taking regular breaks can help prevent mental fatigue and improve overall productivity.
- Short breaks allow our brains to rest and recharge, leading to better concentration and retention of information.... more
Why are breaks important?
- Our brains have a limited capacity to focus and retain information for long periods of time. Taking regular breaks can help prevent mental fatigue and improve overall productivity.
- Short breaks allow our brains to rest and recharge, leading to better concentration and retention of information.... more
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