[ { 9^{( n + 1/4 )} √3 × 3^-n }/3 × √3^-n ]^1/n = x
⇒ [ { 9ⁿ × 9^1/4 × √3 × √3^-n }/3 × √3^-n ]^1/n = x

सही विकल्प: B

[ { 9^{( n + 1/4 )} √3 × 3^-n }/3 × √3^-n ]^1/n= x
⇒ [ { 9ⁿ × 9^1/4 × √3 × √3^-n }/3 × √3^-n ]^1/n= x
⇒ [ { 9ⁿ × 3^1/2 × √3 }/3 ]^1/n= x
⇒ ( 9ⁿ )^1/n= x ⇒ x = 9 = 3²
∴ x = 3²
अतः x का मान 9 होगा ।

( ∜0.0625 + ∛0.008 + √0.09 - 1 )/∛[ 62.5( 32 )^1/5 ]
= ( ∜0.5⁴ + ∛0.2sup>3 + √0.3sup>2 - 1 )/∛[ 62.5( 2⁵ )^1/5 ]

सही विकल्प: C

( ∜0.0625 + ∛0.008 + √0.09 - 1 )/∛[ 62.5( 32 )^1/5 ]
= ( ∜0.5⁴ + ∛0.2sup>3 + √0.3sup>2 - 1 )/∛[ 62.5( 2⁵ )^1/5 ]
= ( 0.5 + 0.2 + 0.3 -1 )/∛[ 62.5 × 2 ] = (1 - 1 )/∛125
= 0 /5 = 0
अतः इसका मान 0 होगा ।

दिया है , ( 27 )^2/3 × ( 81 )^{- 1/2} = 3^x
⇒ ( 3³ )^2/3 × ( 3⁴ )^{- 1/2} = 3^x
⇒ ( 3 )² × ( 3 )^-2 = 3^x

सही विकल्प: B

दिया है , ( 27 )^2/3 × ( 81 )^{- 1/2} = 3^x
⇒ ( 3³ )^2/3 × ( 3⁴ )^{- 1/2} = 3^x
⇒ ( 3 )² × ( 3 )^-2 = 3^x
⇒ ( 3 )² ⁺^-2 = 3^x
⇒ 3^x = 3⁰
⇒ x = 0
अतः x के स्थान पर 0आएगा ।

8² × 7² ÷ √196 - 143 = 3^?
⇒ 8² × 7² ÷ 14 - 143 = 3^?
⇒ 64 × ( 49/14 ) - 143 = 3^?

सही विकल्प: D

8² × 7² ÷ √196 - 143 = 3^?
⇒ 8² × 7² ÷ 14 - 143 = 3^?
⇒ 64 × ( 49/14 ) - 143 = 3^?
⇒ 64 × ( 7/2 ) - 143 = 3^?
32 × 7 -143 = 3^?
⇒ 224 -143 = 3^?
⇒ 3^? = 81 = 3⁴
⇒ ? = 4
अतः ( ?) के स्थान पर 4आएगा ।

( 72 ÷ 2 )⁴ × ( 36 × 6 )³ = ( 6 )^? × ( 12960 ÷ 10 )
⇒ ( 36 )⁴ × ( 6² × 6 )³ = ( 6 )^? × ( 1296 )
⇒ ( 6²)⁴ × ( 6 )⁹ = ( 6 )^? × ( 6⁴ )

सही विकल्प: B

( 72 ÷ 2 )⁴ × ( 36 × 6 )³ = ( 6 )^? × ( 12960 ÷ 10 )
⇒ ( 36 )⁴ × ( 6² × 6 )³ = ( 6 )^? × ( 1296 )
⇒ ( 6²)⁴ × ( 6 )⁹ = ( 6 )^? × ( 6⁴ )
⇒ ( 6 )^? =[ ( 6)⁸ × ( 6 )⁹ ]/6⁴ ⇒ ( 6 )^? = [ ( 6)⁸ ⁺ ⁹ ]/6⁴
⇒ ( 6 )^? = ( 6 )¹³
दोनों ओर तुलना करने पर
∴ ? = 13
अतः ( ?) के स्थान पर 13आएगा ।