The general solution of y" - m^{2}y = 0 is

- a)c
_{j}sinh mx + c2 cosh mx - b)c
_{1}cos mx + c_{2 }sin mx - c)c
_{1 }cos mx + c_{2}sinh mx - d)c
_{1}sin mx + c_{2}cosh mx

Correct answer is option 'A'. Can you explain this answer?

Ayomide Attah answered • 4 hours ago

Y''-m^2y=0

r^2-m^2=0 characteristic

r=+-m

y=Ae^mx+Be^-mx

=Ce^mx+De^mx-Ce^-mx+De^-mx(Let A=C+D and B=D-C)

=C(e^mx-e^-mx)+D(e^mx+e^-mx)

=Csinh(mx)+Dcosh(mx)

r^2-m^2=0 characteristic

r=+-m

y=Ae^mx+Be^-mx

=Ce^mx+De^mx-Ce^-mx+De^-mx(Let A=C+D and B=D-C)

=C(e^mx-e^-mx)+D(e^mx+e^-mx)

=Csinh(mx)+Dcosh(mx)

Jenifer Sebastin asked • 11 hours ago

Integral surface of (2x y — l)p + (z — 2x^{2})q = 2(x — yz) passing through the line x_{0} (s) = 1 y_{0}(s) = 0 z_{0}(s) = s

- a)x
^{2}+ y^{2}- yz - x + z = - b)x
^{2}+ y^{2}- xz - y + z = 1 - c)x
^{2}+ y^{2}— xy — x + z = - d)y
^{2}+ z^{2}— xy + z — x = l

Correct answer is option 'D'. Can you explain this answer?

Preeti Lamba asked • 12 hours ago

Let be linear transformation such that T _{°} S is the identity map of Then

- a)S
_{°}T is the identity map of IR4. - b)S
_{°}T is one one but not onto - c)S
_{°}T is onto but not one one - d)S
_{°}T is neither one one not onto

Correct answer is option 'D'. Can you explain this answer?

RITU GUPTA asked • 12 hours ago

Let < a_{n} > and < b_{n}> be two sequences of real numbers such that a_{n} = b_{n} - b_{n + 1} for n = 1, 2 , 3 , 4 , . . . if Sb_{n} is convergent, then which is always true?

- a)Sa
_{n}may not be convergent - b)Sa
_{n}is convergent and Sa_{n}= b_{1} - c)Sa
_{n}is convergent and Sa_{n}= 0 - d)Sa
_{n}is convergent and Sa_{n}= a_{1}- b_{1} - e)

Correct answer is option 'B'. Can you explain this answer?

PARUL PATEL asked • 16 hours ago

Choose the correct option.

- a)(Q, +) is isomorphic to (R, +).
- b)(R, +) is not isomorphic to (R — {o}, •).
- c)There are two non-isomorphic cyclic group of order 2009
^{2009}. - d)There are 2009
^{2009}non-isomorphic cyclic groups of order 2009^{2009}.

Correct answer is option 'B'. Can you explain this answer?

Preeti Lamba asked • 16 hours ago

Let T be a 4 x 4 real matrix such that T^{4} = 0. Let k_{i} = dim(kerT^{i}) for 1 __<__ i __<__ 4 which of the following is not a possibility for the sequence k_{1} __<__ k_{2} __<__ k_{3} __<__ k_{4}?

- a)3
__<__4__<__4__<__4 - b)1
__<__3__<__4__<__4 - c)2
__<__4__<__4__<__4 - d)2
__<__3__<__4__<__4

Correct answer is option 'B'. Can you explain this answer?

Garima Chaurasia asked • 17 hours ago

Which one of the following is a subspace of the vector space R^{3} ?

- a){(x, y, z) ∈ R
^{3}: x + 2y = 0, 2x + 3z = 0} - b){(x, y, z) ∈ R
^{3 }: 2x + 3y + 4z – 3 = 0, z = 0} - c){(x, y, z) ∈ R
^{3}: x ≥ 0, y ≥ 0} - d){(x, y, z) ∈ R
^{3}: x – 1 = 0, y = 0}

Correct answer is option 'A'. Can you explain this answer?

Kilaparti Sekhar asked • 17 hours ago

The orthogonal trajectory to the family of circles x^{2} + y^{2} = 2cx (c arbitrary) is describe by the differential equation,

- a)(x
^{2}+ y^{2}) y' = 2xy - b)(x
^{2}- y^{2}) y' = 2xy - c)(y
^{2}- x^{2}) y' = xy - d)(y
^{2}- x^{2}) y' = 2xy

Correct answer is option 'D'. Can you explain this answer?

SUMNESH KANWAR asked • 19 hours ago

The Series

- a)convergent, if x
^{2}≥ 1 and divergent, if x^{2}< 1 - b)convergent, if x
^{2}< 1 and divergent, if x^{2}> 1 - c)convergent, if x
^{2}< 1 and divergent, if x^{2}≥1 - d)convergent, if x
^{2}≤ 1 and divergent, if x^{2}≥ 1.

Correct answer is option 'D'. Can you explain this answer?

Surbhi Chaddha asked • 19 hours ago

Let W_{1} and W_{2} be subspaces of the real vector space defined by

W_{1} = {(x_{1,}x_{2}, ...,x_{100}) : x_{i} = 0 if i is divisible by 4},

W_{2} = { (x_{1};x_{2}, ....x_{100}) : x_{i} = 0 if i is divisible by 5}.

Then the dimension of W_{1} ∩ W_{2} is ____

W

W

Then the dimension of W

Correct answer is between '0.42,0.43'. Can you explain this answer?

Nabakumar Das asked • 23 hours ago

Let {v_{1},v_{2}, ..., v_{16}} be an ordered basis for If T is a linear transformation on V defined by T(v_{i}) = v_{i+1} for 1 __<__ i __<__ 15 and T (v_{16}) = - (v_{1} + v_{2} + .... + v_{16}) then

- a)T is singular with ration eigenvalues.
- b)T is singular but has no rational eigenvalues.
- c)T is regular with rational eigenvalues.
- d)T is regular but has no rational eigenvalues.

Correct answer is option 'D'. Can you explain this answer?

Om Prakash Yadav asked • yesterday

Let S and T be linear transformations from a finite dimensional vector space V to itself such that S(T(v)) = 0 for all v ∈ V. Then

- a)rank(T) ≥ nullity(S)
- b)rank(S) ≥ nullity(T)
- c)rank(T) ≤ nullity(S)
- d)rank(S) ≤ nullity(T)

Correct answer is option 'C,D'. Can you explain this answer?

Toto Kinimi asked • yesterday

Which of the following(s) is/are correct?

- a)The transpose of a symmetric matrix need not be summetric matrix.
- b)If A and B are symmetric matrix of same order, then AB + BA must be symmetric matrix.
- c)If A is symmetric matrix, then all positive integral powers of A are symmetric matrices.
- d)If A is any square matrix, then A + A'is always symmetric

Correct answer is option 'B,C,D'. Can you explain this answer?

Charul Sharma asked • yesterday

Which of the following statements is or are correct. The trace of a matrix A = is defined by Tr(A) = a11 + a22&nb... more

a)Trace of a unit matrix is always a fixed natural number

b)Trace of the sum of two matrices is equal to sum of their traces

c)Trace of the scalar matrix is some multiple of its order

d)Tr(AB) = Tr(BA)

Correct answer is option 'A,B,D'. Can you explain this answer?

Shikha Pradhan asked • yesterday

Let a_{1} = b_{1} = 0, and for each n ≥ 2, let a_{n} and b_{n} be real numbers given by

Then which one of the following is TRUE about the sequences {a_{n}} and {b_{n}}?

- a)Both {a
_{n}} and {b_{n}} are divergent - b){a
_{n}} is convergent and {b_{n}} is divergent - c){a
_{n}} is divergent and {b_{n}} is convergent - d)Both {a
_{n}} and {b_{n}} are convergent

Correct answer is option 'D'. Can you explain this answer?

Ankita Saha asked • 2 days ago

Which of the following subsets of a basis of

B_{1} = {(1,0,0,0), (1,1,0,0), (1,1,1,0), (1,1,1,))

B_{2} = {(1,0,0,0), (1,2,0,0), (1,2,3,0), (1,2,3,4)}

B_{3} = {(1,2,0,0), (0,0,1,1), (2,1,0,0), (-5,5,0,0))

B

B

B

- a)B
_{1}and B_{2}but not B_{3} - b)B
_{1}, B_{2}and B_{3} - c)B
_{1}and B_{3}but not B_{2} - d)only B
_{1}

Correct answer is option 'A'. Can you explain this answer?

Curiosity With Wickedmin asked • 2 days ago

A necessary and sufficient condition for a non-empty subset H o f a finite group G to be a subgroup is that

- a)a ∈ H, b ∉ H which implies a, b ∈ H
- b)a ∈ H, b ∈ H ⇒ (a + b) ∈ H
- c)a ∈ H, b ∈ H ab ∈ H
- d)a ∈ H, h ∈ H ⇒ (a - h) ∈ H

Correct answer is option 'C'. Can you explain this answer?

Mr Rehan asked • 2 days ago

Using the Stoke’s theorem, evaluate [(x + 2y) dx + (x-2) dy+ (y - z)dz], where C is the boundary of the triangle with vertices (2, 0, 0), (0, 3, 0) and (0, 0, 6) oriented in the anti-clockwise direction.

- a)12
- b)15
- c)9
- d)zero

Correct answer is option 'B'. Can you explain this answer?

Nabakumar Das asked • 2 days ago

Let V be the space of twice differentiable functions satisfying f" - 2f' + f = 0. Define by T(f') = (f'(0), f(0)), then T is

- a)one to one and onto
- b)one to one but not onto
- c)onto but not one one
- d)neither one to one nor onto

Correct answer is option 'A'. Can you explain this answer?

Curiosity With Wickedmin asked • 2 days ago

Statement A : Every isomorphic image of a cyclic group is cyclic.

Statement B : Every homomorphic image of a cyclic group is cyclic

Statement B : Every homomorphic image of a cyclic group is cyclic

- a)Both A and B are true
- b)Both A and B are false
- c)A is true only
- d)B is true only

Correct answer is option 'A'. Can you explain this answer?

Mr Rehan asked • 2 days ago

For a positive integer n let denotes the vector space of polynomials in one variable x with real coefficients and with degree less than n. Consider the map defined byT(p(x)) = p(x^{2}).Then

- a)T is a linear transformation and dim(range (T)) = 5
- b)T is a linear transformation and dim(range(T)) = 3
- c)T is a linear transformation and dim(range (T)) = 2
- d)T is not a linear transformation

Correct answer is option 'B'. Can you explain this answer?

Vishal Suresh asked • 3 days ago

Let < a_{n}> —> a. Let for every positive integer k, A_{k} be the set of all positive integer n such that | a_{n}- a | < —1/k. Then,

- a)A
_{k}is finite for all k - b)A
_{k}is finite for some k - c)every A
_{k}contains all but finitely many positive integers - d)A
_{k}contains all positive integers

Correct answer is option 'D'. Can you explain this answer?

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