Let a- b- c be non-zero real numbers such that a-b-c-0 - let q-a2-b2-c2 and r-a4-b4-c4 ThenA- q 2-2 r alwaysB- q2 - 2r can take both positive and negative valueC- q 2-2 r alwaysD- q2-2 r always

The correct option is D q2 = 2r always a + b + c = 0, a,b,c ϵ nbsp; R ≠ 0 a^2 +b^2 +c^2 + 2(ab + bc +ca) = 0 q = a^2 +b^2 +c^2, r = a^4 + b^4 +c^4 r = q^2 ...

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Standard XII

Physics

Potential Energy of a System of Multiple Point Charges

Let a, b, c b...

Question

Let a,b,c be non-zero real numbers such that a+b+c = 0; let $q = a^{2} + b^{2} + c^{2} a n d r = a^{4} + b^{4} + c^{4}$ Then

q2 < 2r always

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q2 = 2r always

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q2 > 2r always

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q2 - 2r can take both positive and negative value

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Solution

The correct option is B
q2 = 2r always

$a + b + c = 0, a, b, c ϵ R \neq 0 a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a) = 0 q = a^{2} + b^{2} + c^{2}, r = a^{4} + b^{4} + c^{4} r = q^{2} - 2 (a^{2} b^{2} + b^{2} c^{2} + c^{2} a^{2}) r = q^{2} - 2 [(a b + b c + c a)^{2} - 2 a b c (a + b + c)] r = q^{2} - 2 (q^{2} / 4) r = q^{2} / 2$

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Similar questions

Q. Let a,b,c be non-zero real numbers such that

a + b + c = 0

; let

q = a^{2} + b^{2} + c^{2}

and

r = a^{4} + b^{4} + c^{4}

Then

Q. Three concentric conducting spherical shells A, B and C of radius

R

2 R

and

4 R

carry charges

Q

- 2 Q

and

4 Q

respectively. Then the energy stored between shells B and C is

Q. If

a, b, c, p, q, r

are thre non-zero complex numbers such that

\frac{p}{a} + \frac{q}{b} + \frac{r}{c} = 1 + i

and

\frac{a}{p} + \frac{b}{q} + \frac{c}{r} = 0,

then value of

\frac{p^{2}}{a^{2}} + \frac{q^{2}}{b^{2}} + \frac{r^{2}}{c^{2}}

Q. If

a, b, c, p, q, r

are three non-zero complex number such that

\frac{p}{a} + \frac{q}{b} + \frac{r}{c} = 1 + i

and

\frac{a}{p} + \frac{b}{q} + \frac{c}{r} = 0

, then value of

\frac{p^{2}}{a^{2}} + \frac{q^{2}}{b^{2}} + \frac{r^{2}}{c^{2}}

Q. The figure shows two conducting concentric sperical shells of radii R and 2R.
The inner shell has a charge +Q and the outer one is neutral.

(A)

Energy stored in region given by R < r < 2R

\frac{Q^{2}}{32 π ϵ_{o} R}

(B)

Energy stored in region given by

2 R < r < \infty

\frac{Q^{2}}{16 π ϵ_{o} R}

(C)

Energy stored in region given by 2R < r < 4R

\frac{Q^{2}}{8 π ϵ_{o} R}

(D)

Heat generated when switch S is closed

S) zero

T) None

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Let a,b,c be non-zero real numbers such that a+b+c = 0; let q=a2+b2+c2 and r=a4+b4+c4 Then

The correct option is B q2 = 2r always a+b+c=0,a,b,c ϵR≠0a2+b2+c2+2(ab+bc+ca)=0q=a2+b2+c2,r=a4+b4+c4r=q2−2(a2b2+b2c2+c2a2)r=q2−2[(ab+bc+ca)2−2abc(a+b+c)]r=q2−2(q2/4)r=q2/2

Let a,b,c be non-zero real numbers such that a+b+c = 0; let $q = a^{2} + b^{2} + c^{2} a n d r = a^{4} + b^{4} + c^{4}$ Then