#Q5 Let V={f│f:R→R} over R. Then which of the following is not a subspace of V over R
Anonymous Quiz
2%
W1={f∈V:f is bounded}
31%
W2={f∈V:f is continuous}
38%
W3={f∈V:f is Monotonic}
29%
W4={f∈V:f is of bounded variation}
#Q6 Which of the following is/are not a subspace of V={f:f:[a,b]→R} over R
Anonymous Quiz
16%
{f∈V:f is periodic}
16%
{f∈V:f is odd function}
26%
{f∈V:f is even function}
42%
{f∈V:f holds intermediate value property}
#Q7 Let C[x]={P(x)| P(x) is a polynomial with coefficient from field F} . For which of the following F,C[x] is not a vector space of infinite dimension.
Anonymous Quiz
20%
F=R
27%
F=Q
29%
F= Qc
24%
F=Q[√2]
#Q8 Which of the following is/are subspaces of C(R).
Anonymous Quiz
12%
R(Q)
49%
Q(√2)(R)
31%
R(R)
8%
Q(√2)(Q)
#Q9 Which of the following is true for S=set of all polynomials p(x) with degree less equal &∫_(-1) [p (x)dx=0]
Anonymous Quiz
38%
S forms a vector space
49%
S does not form a vector space
13%
S does not satisfies additive closure
0%
S does not have zero vectors
#Q10 Consider Z[√p]={a+b√p,a,b∈Z} where p is a prime. Then
Anonymous Quiz
15%
Z[√p] Does form a vector space over Z
34%
Z[√p] forms a vector space over Z
38%
Z[√p] Forms a vector space over R
13%
Z[√p] Does not form a vector space over R
❤1
#Q1 Which of the following is not a vector space?
Anonymous Quiz
14%
R(Q)
16%
R(R+)
50%
Z(Z+)
20%
Q(√2)(Q)
#Q2 Let V be the (real) vector space of all functions defined from R to R then which of all following set of functions are subspace of V.
Anonymous Quiz
20%
All h which are continuous
14%
Allh s.t. h(0)= ℏ(1)
16%
All h s.t. h(6)=0
51%
All of the above.
#Q3 Let V be a vector space over field f then which of the following is correct.
Anonymous Quiz
10%
There must be two binary operations in V.
13%
V is an abelian group under addition
13%
V is closed w.r.t. Scaler multiplication
64%
All of the above
#Q4 Let V be a vector Space of all 3×3 matrix and W Consist of all 3×3 matrices with zero determinant
Anonymous Quiz
16%
W is not a subspace of v.
43%
W May or may not be subspace of v
25%
W is not a subspace of v
16%
None of these
#Q5 Which of the following are true?
Anonymous Quiz
56%
Any field forms a vectors space over itself
8%
Any field does not Forms a vector space over itself
21%
Any field, R is vector space over C
16%
All of the above
#Q6 The necessary and sufficient condition for a nonempty subset W of a vector space V(F) to be a subspace is/are-
Anonymous Quiz
18%
u+v ∈ W and au ∈ W ∀ u, v ∈ W and a ∈ F
15%
au+v ∈ W ∀ u, v ∈ W and a ∈ F
25%
au+bv ∈ W for all u,v ∈W and a,b ∈ F
43%
All of the above
#Q7 Let V be real Vector space of all mapping from R to R { f ∈V | f( -x)=f( x)}(b) { f ∈V |f (-x)=-f( x) } then
Anonymous Quiz
52%
Both A and B are Subspace
15%
Neither A nor B is subspace
25%
A is subspace but not B
8%
A is not Subspace But B is
#Q8 Let V=R³ and w= {x,y,z ∈ V|4x-2y+z=0} then which of the following is not true
Anonymous Quiz
21%
W is subspace of V
16%
α, β ∈ W ⇒ α+β ∈ W
59%
W is not a subspace of V
5%
α, β ∈ W ⇒ α-β ∈ W
#Q9 If S1 and S2 are subspaces of linear space L then
Anonymous Quiz
19%
S1+[S]2 is a Subspace of L
24%
S1-[ S]2 is a Subspace of L
51%
Both (a) & (b) are true
7%
Neither (a) Nor (b) is true
#Q10 V be vector space of all 2×2 matrices over R and S be the set of idempotent matrices then.
Anonymous Quiz
19%
S is not Subspace of V as vector addition is not closed
28%
S is not subspace as Scaler multiplication is not closed
41%
Both (a) & (b)
13%
None of these
𝐓𝐡𝐞𝐲 𝐰𝐞𝐫𝐞 𝐨𝐧𝐜𝐞 𝐢𝐧 𝐲𝐨𝐮𝐫 𝐞𝐱𝐚𝐜𝐭 𝐩𝐨𝐬𝐢𝐭𝐢𝐨𝐧. 𝐓𝐡𝐞𝐲 𝐚𝐜𝐜𝐞𝐩𝐭𝐞𝐝 𝐭𝐡𝐞 𝐜𝐡𝐚𝐥𝐥𝐞𝐧𝐠𝐞. 𝐓𝐡𝐞𝐲 𝐬𝐮𝐜𝐜𝐞𝐞𝐝𝐞𝐝. 𝐓𝐡𝐞 𝐨𝐧𝐥𝐲 𝐪𝐮𝐞𝐬𝐭𝐢𝐨𝐧 𝐢𝐬: 𝐖𝐢𝐥𝐥 𝐲𝐨𝐮?
𝐄𝐧𝐫𝐨𝐥𝐥 𝐍𝐨𝐰 :- https://bit.ly/49PVrCW
𝐄𝐧𝐫𝐨𝐥𝐥 𝐍𝐨𝐰 :- https://bit.ly/49PVrCW
❤1
𝐓𝐡𝐞𝐲 𝐰𝐞𝐫𝐞 𝐨𝐧𝐜𝐞 𝐢𝐧 𝐲𝐨𝐮𝐫 𝐞𝐱𝐚𝐜𝐭 𝐩𝐨𝐬𝐢𝐭𝐢𝐨𝐧. 𝐓𝐡𝐞𝐲 𝐚𝐜𝐜𝐞𝐩𝐭𝐞𝐝 𝐭𝐡𝐞 𝐜𝐡𝐚𝐥𝐥𝐞𝐧𝐠𝐞. 𝐓𝐡𝐞𝐲 𝐬𝐮𝐜𝐜𝐞𝐞𝐝𝐞𝐝. 𝐓𝐡𝐞 𝐨𝐧𝐥𝐲 𝐪𝐮𝐞𝐬𝐭𝐢𝐨𝐧 𝐢𝐬: 𝐖𝐢𝐥𝐥 𝐲𝐨𝐮?
𝐄𝐧𝐫𝐨𝐥𝐥 𝐍𝐨𝐰 :- https://bit.ly/49PVrCW
𝐄𝐧𝐫𝐨𝐥𝐥 𝐍𝐨𝐰 :- https://bit.ly/49PVrCW
#Q1 Let F be countably infinite field, V is non – finitely generated vector space and S is also countably infinite L(S)=V, then
Anonymous Quiz
36%
V is uncountable
21%
|V|=|P(R)|
28%
|V|=|Z|
16%
|V|=|P(N)|
#Q2 Which of the following statements is/are true?
Anonymous Quiz
16%
A finitely generated vector space vector space V over a finite field can be expressed as infinite
32%
A vector space V can be expressed as finite union of proper subspace of V on an infinite field
47%
A vector space V can not be expressed as finite union of proper subspace of V over an infinite field
5%
None of these
❤2