Mathematics
converges, then sequence 
BHARTI SHAKYA asked • 57 minutes ago
- a)1/2
- b)1/3
- c)1/4
- d)1
Correct answer is option 'A'. Can you explain this answer?
a)
1/2
b)
1/3
c)
1/4
d)
1
Jitender Ahlawat asked • 1 hour agoWhich of the following(s) is/are correct?- a)If A is unitary matrix, then A'is also unitary matrix.
- b)Inverse of unitary matrix is unitary matrix.
- c)Inverse of unitary matrix is diagonal matrix.
- d)None of these
Correct answer is option 'A,B'. Can you explain this answer?
Which of the following(s) is/are correct?
a)
If A is unitary matrix, then A'is also unitary matrix.
b)
Inverse of unitary matrix is unitary matrix.
c)
Inverse of unitary matrix is diagonal matrix.
d)
None of these
Mahalakshmi R asked • 1 hour agoWhich of the following(s) is/are correct?- a)In a Skew — Hermitian Matrix, the element of the principle diagonal must be purely imaginary.
- b)If A is Hermitian Matrix, then iA is Skew — Hermitian Matrix.
- c)If A is any square matrix, then A — Aθ is Skew — Hermitian Matrix.
- d)All of the above
Correct answer is option 'B,C'. Can you explain this answer?
Which of the following(s) is/are correct?
a)
In a Skew — Hermitian Matrix, the element of the principle diagonal must be purely imaginary.
b)
If A is Hermitian Matrix, then iA is Skew — Hermitian Matrix.
c)
If A is any square matrix, then A — Aθ is Skew — Hermitian Matrix.
d)
All of the above
RUCHI KHANNA asked • 1 hour agoIf A - {a, b, c} and R - {(a, a), (a, b) ( b, c), (b, b), (c, c), (c, a)} is a binary relation on A, then which one of the following is correct?- a)R is reflexive and symmetric, but not transitive
- b)R is reflexive and transitive, but not symmetric
- c)R is reflexive, but neither symmetric nor transitive
- d)R is reflexive, symmetric and transitive
Correct answer is option 'C'. Can you explain this answer?
If A - {a, b, c} and R - {(a, a), (a, b) ( b, c), (b, b), (c, c), (c, a)} is a binary relation on A, then which one of the following is correct?
a)
R is reflexive and symmetric, but not transitive
b)
R is reflexive and transitive, but not symmetric
c)
R is reflexive, but neither symmetric nor transitive
d)
R is reflexive, symmetric and transitive
Prabahar Mamcet asked • 1 hour agoConsider the following statement about the following p. d. e. p + q — pq = 0
(i) it has no singular solutions
(iv) It is a first order non — linear p. d. e. Then choose the
correct code.- a)Only (i) and (ii) true
- b)Only (ii) and (iv) are true
- c)(ii), (iii) and (iv) are true
- d)All are true
Correct answer is option 'D'. Can you explain this answer?
Consider the following statement about the following p. d. e. p + q — pq = 0
(i) it has no singular solutions
(iv) It is a first order non — linear p. d. e. Then choose the
correct code.
(i) it has no singular solutions
(iv) It is a first order non — linear p. d. e. Then choose the
correct code.
a)
Only (i) and (ii) true
b)
Only (ii) and (iv) are true
c)
(ii), (iii) and (iv) are true
d)
All are true
equals:
1; α, β ∈ R Then,
Kilaparti Sekhar asked • 6 hours agoLet
f(x,y) = x3 + y3- 63 (x + y) + 12xy,
then- a)the function has three stationary points
- b)the function is minimum at (-7, -7)
- c)the function is maximum at (3, 3)
- d)the function has neither minimum nor a maximum at (5,-1)
Correct answer is option 'D'. Can you explain this answer?
Let
f(x,y) = x3 + y3- 63 (x + y) + 12xy,
then
f(x,y) = x3 + y3- 63 (x + y) + 12xy,
then
a)
the function has three stationary points
b)
the function is minimum at (-7, -7)
c)
the function is maximum at (3, 3)
d)
the function has neither minimum nor a maximum at (5,-1)
A Great Mission asked • 6 hours agoLet W[y1(x), y2(x)] is the Wronskian formed for the solutions y1(x) and y2(x) of the differential equation y" + a1y' + a2y = 0. If W ≠ 0 for some x = x0 in [a, b] then - a)It vanishes for any x ∈ [a, b]
- b)it does not vanish only at x = a
- c)it does not vanish for any x ∈ [a, b]
- d)it does not vanish only at x = b
Correct answer is option 'C'. Can you explain this answer?
Let W[y1(x), y2(x)] is the Wronskian formed for the solutions y1(x) and y2(x) of the differential equation y" + a1y' + a2y = 0. If W ≠ 0 for some x = x0 in [a, b] then
a)
It vanishes for any x ∈ [a, b]
b)
it does not vanish only at x = a
c)
it does not vanish for any x ∈ [a, b]
d)
it does not vanish only at x = b
Akhilesh Kumar asked • 7 hours agoLet ∑un be a series of positive terms and let 
, then which among the following does not express the condition for the Cauchy’s nth root test?- a) If l < 1, ∑un converges
- b)If l > 1 , ∑un diverges
- c)If l = 1, the test fails and the series may either converge or diverge
- d)If l = 0, the series neither converges nor diverges
Correct answer is option 'D'. Can you explain this answer?
Let ∑un be a series of positive terms and let , then which among the following does not express the condition for the Cauchy’s nth root test?
, then which among the following does not express the condition for the Cauchy’s nth root test?a)
If l < 1, ∑un converges
b)
If l > 1 , ∑un diverges
c)
If l = 1, the test fails and the series may either converge or diverge
d)
If l = 0, the series neither converges nor diverges
are respectively
is equal to 
where b1 = 1, b2 = 1 and bn+2 = bn + bn+1, 
Then
is:
and 
is 
Nabakumar Das asked • 10 hours agoLet M be the space of all 4 x 3 matrices with entries in the finite field of three elements. Then the number of matrices of Rank three In M is- a)(34 - 3) (34 - 32)(34 - 33)
- b)(34 - 1)(34 - 2)(34 - 3)
- c)(34 - 1)(34 - 3) (34 - 32)
- d)34(34 - 1)(34 - 2)
Correct answer is option 'C'. Can you explain this answer?
Let M be the space of all 4 x 3 matrices with entries in the finite field of three elements. Then the number of matrices of Rank three In M is
a)
(34 - 3) (34 - 32)(34 - 33)
b)
(34 - 1)(34 - 2)(34 - 3)
c)
(34 - 1)(34 - 3) (34 - 32)
d)
34(34 - 1)(34 - 2)
be its general solution and u(x) = x3 then the value of v(x) at x=2 is, _________
Jineva Dolui asked • 12 hours ago{u} and {v} are two Cauchy sequence. Prove that {uv} is a Cauchy sequence?
Jenifer Sebastin asked • 12 hours agoIntegral surface of (2x y — l)p + (z — 2x2)q = 2(x — yz) passing through the line x0 (s) = 1 y0(s) = 0 z0(s) = s- a)x2 + y2 - yz - x + z =
- b)x2 + y2 - xz - y + z = 1
- c)x2 + y2 — xy — x + z =
- d)y2+ z2 — xy + z — x = l
Correct answer is option 'D'. Can you explain this answer?
Integral surface of (2x y — l)p + (z — 2x2)q = 2(x — yz) passing through the line x0 (s) = 1 y0(s) = 0 z0(s) = s
a)
x2 + y2 - yz - x + z =
b)
x2 + y2 - xz - y + z = 1
c)
x2 + y2 — xy — x + z =
d)
y2+ z2 — xy + z — x = l
is given by T (x, y, z) = (x - y, y + 3z, x + 2y). Then T-1 is
Suman Mondal asked • 14 hours agoIf x + 2y - 2u = 0, 2x - y - u = 0, x + 2z - u = 0, 4x -y + 3 z - u= 0 is a system of equations, then it is- a)consistent with trivial solution
- b)consistent without trivial solution
- c)inconsistent with trivial solution
- d)inconsistent without trivial solution
Correct answer is option 'A'. Can you explain this answer?
If x + 2y - 2u = 0, 2x - y - u = 0, x + 2z - u = 0, 4x -y + 3 z - u= 0 is a system of equations, then it is
a)
consistent with trivial solution
b)
consistent without trivial solution
c)
inconsistent with trivial solution
d)
inconsistent without trivial solution
ASHIMA JAIN asked • 14 hours agoIf general solution of the differential equation ay",+ by"- cy’+ dy = 0 is linearly spanned by ex sin x and cos x, then which one of the following holds?- a) a + b - c - d = 0
- b)a + b + c + d = 0
- c)a - b + c - d = 0
- d) a - b - c - d = 0
Correct answer is option 'B'. Can you explain this answer?
If general solution of the differential equation ay",+ by"- cy’+ dy = 0 is linearly spanned by ex sin x and cos x, then which one of the following holds?
a)
a + b - c - d = 0
b)
a + b + c + d = 0
c)
a - b + c - d = 0
d)
a - b - c - d = 0
into a vector space 
with U as finite dimensional. The rank of T is the dimension of the
then the value of 
is _______ .
be defined by T(x1, x2) = (x1, x2 + x2, x2). Then the nullity of T is
converges to
Then the value fo F(α) . F(β) is
Sneha Mote asked • yesterdayTwo finite sets m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Then the values of m and n are respectively.- a)8,5
- b)6,3
- c)4,1
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Two finite sets m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Then the values of m and n are respectively.
a)
8,5
b)
6,3
c)
4,1
d)
none of these
Shikha Pradhan asked • yesterdayLet a1 = b1 = 0, and for each n ≥ 2, let an and bn be real numbers given by
Then which one of the following is TRUE about the sequences {an} and {bn}? - a)Both {an} and {bn} are divergent
- b){an} is convergent and {bn} is divergent
- c){an} is divergent and {bn} is convergent
- d)Both {an} and {bn} are convergent
Correct answer is option 'D'. Can you explain this answer?
Let a1 = b1 = 0, and for each n ≥ 2, let an and bn be real numbers given by
Then which one of the following is TRUE about the sequences {an} and {bn}?
a)
Both {an} and {bn} are divergent
b)
{an} is convergent and {bn} is divergent
c)
{an} is divergent and {bn} is convergent
d)
Both {an} and {bn} are convergent
Curiosity With Wickedmin asked • yesterdayLet H = Z2 x Z6 and K = Z2 x Z4, then- a)H is isomorphic to K, since both are cyclic.
- b)H is isomorphic to K since 2 divides 6 and gcd(3,4) = 1
- c)H is not isomorphic to K, since K is cyclic where as H is number.
- d)H is not isomorphic to K, since there is no homomorphism from H to K.
Correct answer is option 'C'. Can you explain this answer?
Let H = Z2 x Z6 and K = Z2 x Z4, then
a)
H is isomorphic to K, since both are cyclic.
b)
H is isomorphic to K since 2 divides 6 and gcd(3,4) = 1
c)
H is not isomorphic to K, since K is cyclic where as H is number.
d)
H is not isomorphic to K, since there is no homomorphism from H to K.
be a scalar field, 
be a vector filed and let 
be a constant vector. If 
represents the position vector 
then which one of the following is FALSE?
such that 
(x, y) = (2x - y, x)
such that 
(x,y, z) = (z,x + y)
such that 
(x) = (2x, 3x)
such that 
(x ,y ,z) = (x + 1 ,y + z)
HIRAL THAKAR asked • yesterdayConsider the following statements:
1. A group of order 289 is abelian.
2. In S3 there are four elements satisfying x2= e and six elements satisfying y3 = e.
3. Every proper subgroup of S3 is cyclic.
4. (Z30, 
has 4 subgroups of order 15 .
Correct statements are:- a)l and 4
- b)1 ,3 and 4
- c)1 and 2
- d)1 and 3
Correct answer is option 'D'. Can you explain this answer?
Consider the following statements:
1. A group of order 289 is abelian.
2. In S3 there are four elements satisfying x2= e and six elements satisfying y3 = e.
3. Every proper subgroup of S3 is cyclic.
4. (Z30,has 4 subgroups of order 15 .
Correct statements are:
1. A group of order 289 is abelian.
2. In S3 there are four elements satisfying x2= e and six elements satisfying y3 = e.
3. Every proper subgroup of S3 is cyclic.
4. (Z30,
has 4 subgroups of order 15 .Correct statements are:
a)
l and 4
b)
1 ,3 and 4
c)
1 and 2
d)
1 and 3
is
is equal to
are the vectors reciprocal to vectors 
then, the value of 
is 
then 
JAYESH KUMAR LABHU asked • yesterdayIf f(x) is differentiable on interval l and 
such that |f'(x)| ≤ a on l, then f(x) is- a) Continuous but not uniformly continuous on l
- b)Uniformly continuous but not continuous on l
- c)Uniformly continuous but not differentiable on l
- d)Continuous, uniformly continuous and differentiable on l
Correct answer is option 'A'. Can you explain this answer?
If f(x) is differentiable on interval l and such that |f'(x)| ≤ a on l, then f(x) is
such that |f'(x)| ≤ a on l, then f(x) isa)
Continuous but not uniformly continuous on l
b)
Uniformly continuous but not continuous on l
c)
Uniformly continuous but not differentiable on l
d)
Continuous, uniformly continuous and differentiable on l
convergent for
be defined as f (t) = 
f(t )dt
is equal to:Fetching relevant content for you
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