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[(a/b)^(sqrt(p)+sqrt(q))]^(sqrtp-sqrtq)[...

`[(a/b)^(sqrt(p)+sqrt(q))]^(sqrtp-sqrtq)[(a/b)^(sqrt(q)+sqrt(r))]^(sqrtq-sqrtr)[(a/b)^(sqrt(r)+sqrt(p))]^(sqrtr-sqrtp)`

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(i) (a^(p+q))^(p-q) (a^(q+r))^(q-r)(a^(r+p))^(r-p) (ii) [(a/b)^(sqrt(p)+sqrt(q))]^(sqrt(p)-sqrt(q))[(a/b)^(sqrt(q)+sqrt(r))]^(sqrt(q)-sqrt(r)) [(a/b)^(sqrt(r)+sqrt(p))]^(sqrt(r)-sqrt(p))

[((a)/(b))^(sqrt(p)+sqrt(q))]^(sqrt(p)-sqrt(q))[((a)/(b))^(sqrt(q)+sqrt(r))]^(sqrt(q)-sqrt(r))[((a)/(b))^(sqrt(r)+sqrt(p))]^(sqrt(r)-sqrt(p))

a((sqrt(a)+sqrt(b))/(2b sqrt(a)))^(-1)+b((sqrt(a)+sqrt(b))/(2a sqrt(b)))^(-1)

cot(7((1)/(2))^(@)=sqrt(p)+sqrt(q)+sqrt(r)+sqrt(s)

If p and q are distinct primes and xxDelta = |(sqrt(pq),p i,q+sqrt(pq)),(psqrt(q),sqrt(p)+psqrt(p)i,qsqrt(p)+sqrt(p) qi),(qsqrt(p), sqrt(p)+psqrt(q)i,qsqrt(q)+p i)|xx

sqrt(x^(p-q))sqrt(x^(q-r))sqrt(x^(r-p))=1

Evaluate : ( sqrt(a) + sqrt(b) ) ( sqrt(a) - sqrt(b) )

sqrt(a/b+b/a-2)= 1) sqrt(a/b)+sqrt(b/a) 2) sqrt(a/b)-sqrt(b/a) 3) sqrt(a)/b-b/sqrt(a) 4) sqrt(a)/b-sqrt(b)/a

Show that : sqrt( a/b ) = sqrt(a)/ sqrt( b )

The conjugate surd of sqrt(a)+b is sqrt(a)-b b- "sqrt(a) sqrt(a)+sqrt(b) sqrt(a)-sqrt(b)

PEARSON IIT JEE FOUNDATION-INDICES-Test Your Concepts (Short Answer Type Questions)
  1. Simplify (5(81)^(n+1)-3^(4n+5))/(3xx3^(4n)+(81)^n).

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  2. (1) If 5^(n+2)=625 ,f i n d[(n+3)]^(1/3): (2) If (32/243)^n=8/27 ,f i...

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  3. If ((32)/(243))^(n)= (8)/(27), then find ((n+0.4)/(1024))^(-n)

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  4. simplify (2^(2/3)-2^(- 2/3))(2^(4/3)+1+2^(- 4/3))

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  5. (i) Simplify (2^(2/3)-2^((-2)/3))(2^(4/3)+1+2^((-4)/3)) (ii) [(root(...

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  6. If 16200=2^(a)xx3^(b)xx^(c), then find a, b, c.

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  7. Simplify ((p^(a))/(p^(b))) xx ((p^(b))/(p^(c ))) xx ((p^(c ))/(p^(a)))...

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  8. If [root(9)((2/3)^5)]^(sqrt(x-5)) = a^0, find the value of x.

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  9. Simplify ((p^(a+b))^(5).(p^(b+c))^(5).(p^(c+a))^(5))/((p^(a). p^(b). p...

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  10. If 5^(3x+2)=25xx5^((4x-1)), find the value of x.

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  11. Which of the following is greater between each of the two numbers ? ...

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  12. Which of the following is greater between each of the two numbers ? ...

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  13. Which of the following is greater between each of the two numbers ? ...

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  14. If 5^x=3^y=45^z, prove that 1/z=1/x+2/y.

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  15. Prove that 1/(1+p+q^(- 1))+1/(1+q+r^(- 1))+1/(1+r+p^(- 1))=1,if pqr=1 ...

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  16. ((a+b+c)^(a+b)(a+b+c)^(b+c)(a+b+c)^(c+a))/([(a+b+c)^(a) (a+b+c)^(b) (a...

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  17. Simplify the given expressions (a^(p+q))^(p-q) (a^(q+r))^(q-r) (a^(r...

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  18. [(a/b)^(sqrt(p)+sqrt(q))]^(sqrtp-sqrtq)[(a/b)^(sqrt(q)+sqrt(r))]^(sqrt...

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  19. Prove that ((x^(-1)+y^(-1))/x^(-1))^(-1)+((x^(-1)-y^(-1))/x^(-1))^(...

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  20. If a, b, c are real numbers, then show that root(5)(ab^-1)xxroot( 5)...

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