1³/₇ का 5 ÷ 3/4 + 2/3 × 3/4 - 2/3 = ?
⇒ ? = 10/7 × 5 ÷ 3/4 + 2/3 × 3/4 - 2/3

सही विकल्प: B

1³/₇ का 5 ÷ 3/4 + 2/3 × 3/4 - 2/3 = ?
⇒ ? = 10/7 × 5 ÷ 3/4 + 2/3 × 3/4 - 2/3
⇒ ? = 10/7 × 5 × 4/3 + 1/2 - 2/3
⇒ ? = 200/21 + ( 3 - 4 )/6 ⇒ ? = ( 400 - 7 ) /42 = 393/42
⇒ ? = 131/14 = 9⁵/₁₄
∴ ? = 9⁵/₁₄
अतः इसका मान 9⁵/₁₄ होगा ।

1/4 + [ 2²/₃ ÷ 3/8 { 5/6 × ( 0.25 + 9/12 ) } ] = ?
⇒ ? = 1/4 + [ 8/3 ÷ 3/8 { 5/6 × ( 3 + 9)/12 } ]
⇒ ? = 1/4 + [ 8/3 ÷ 3/8 { 5/6 × 1 } ]

सही विकल्प: D

1/4 + [ 2²/₃ ÷ 3/8 { 5/6 × ( 0.25 + 9/12 ) } ] = ?
⇒ ? = 1/4 + [ 8/3 ÷ 3/8 { 5/6 × ( 3 + 9)/12 } ]
⇒ ? = 1/4 + [ 8/3 ÷ 3/8 { 5/6 × 1 } ]
⇒ ? = 1/4 + [ 8/3 ÷ 3/8 × 5/6 ]
⇒ ? = 1/4 + [ 8/3 × 8/3 × 5/6 ] ⇒ ? = 1/4 + 320/54 = ( 27 + 640 )/108 = 667/108
∴ ? =667/108
अतः इसका मान 667/108 होगा ।

2 [ 1 - { 4¹/₄ - 4 ( 1.2 × 1/2 + 1/3 ) } ] ÷ ( 1/2 + 1.25 ) का ( 1 - 1/7 ) = ?
⇒ ? = 2 [ 1 - { 17/4 - 4 ( 1.2 × ( 3 + 2 )/6 } ] ÷ ( 1/2 + 1.25 ) × ( 7 - 1 )/7

सही विकल्प: A

2 [ 1 - { 4¹/₄ - 4 ( 1.2 × 1/2 + 1/3 ) } ] ÷ ( 1/2 + 1.25 ) का ( 1 - 1/7 ) = ?
⇒ ? = 2 [ 1 - { 17/4 - 4 ( 1.2 × ( 3 + 2 )/6 } ] ÷ ( 1/2 + 1.25 ) × ( 7 - 1 )/7
⇒ ? = 2 [ 1 - { 17/4 - 4 ( 1.2 × 5/6 } ] ÷ ( 1+ 1.25 )/2 × 6/7
⇒ ? = 2 [ 1 - { 17/4 - 4 } ] ÷ 3.5 /2 × 6/7
⇒ ? = 2 [ 1 - { 17/4 - 4 } ] ÷ 3/2 ⇒ ? = 2 [ 1 - 1/4 ] × 2/3 ⇒ ? = 6/4 × 2/3 = 1
∴ ? = 1
अतः इसका मान 1 होगा ।

[ 12¹/₃ + 4³/₁₅ का 1/3 ]/[ 8/9 × 3/2 + 5/2 × 3/5 ] ÷ [ 4/5 का 7/8 ( 1/4 ÷ 5/4 + 3/2 ) ]/[ 7/4 + 5/8 -1/8 ] = ?
⇒ ? = [ 37/3 + 63/15 × 1/3 ]/( 4/3 + 3/2 ) ÷ [ 4/5 ×7/8 ( 1/4 × 4/5 + 3/2 ) ]/( 14 + 5 - 1 )/8
⇒ ? = [ 37/3 + 21/15 ]/( 8 + 9 )/6 ÷ [ 4/5 ×7/8 ( 1/5 + 3/2 ) ]/18/8

सही विकल्प: D

[ 12¹/₃ + 4³/₁₅ का 1/3 ]/[ 8/9 × 3/2 + 5/2 × 3/5 ] ÷ [ 4/5 का 7/8 ( 1/4 ÷ 5/4 + 3/2 ) ]/[ 7/4 + 5/8 -1/8 ] = ?
⇒ ? = [ 37/3 + 63/15 × 1/3 ]/( 4/3 + 3/2 ) ÷ [ 4/5 ×7/8 ( 1/4 × 4/5 + 3/2 ) ]/( 14 + 5 - 1 )/8
⇒ ? = [ 37/3 + 21/15 ]/( 8 + 9 )/6 ÷ [ 4/5 ×7/8 ( 1/5 + 3/2 ) ]/18/8
⇒ ? = [ 206/15]/17/6 ÷ 7/10 ( 17/10 )/18/8
⇒ ? = 206/15 × 6/17 ÷ 119/100 × 8/18
⇒ ? = 412/85 ÷ 476/900 = 412/85 × 900/476 = 18540/2023
∴ ? = 18540/2023

8¹/₂ - [ 3¹/₅ ÷ 4¹/₂ का 5¹/₃ + { 11 - ( 3 - 5/4 - 5/8) } ] = ?
⇒ ? = 17/2 - [ 16/5 ÷ 9/2 का 16/3 + { 11 - ( 3 - 5/4 - 5/8) } ]
⇒ ? = 17/2 - [ 16/5 ÷ 9/2 का 16/3 + { 11 - ( 3 - ( 10 - 5 )/8) } ]
⇒ ? = 17/2 - [ 16/5 ÷ 9/2 का 16/3 + { 11 - ( 3 - 5/8 ) } ]
⇒ ? = 17/2 - [ 16/5 ÷ 9/2 का 16/3 + { 11 - ( 24 - 5)/8 } ]

सही विकल्प: B

8¹/₂ - [ 3¹/₅ ÷ 4¹/₂ का 5¹/₃ + { 11 - ( 3 - 5/4 - 5/8) } ] = ?
⇒ ? = 17/2 - [ 16/5 ÷ 9/2 का 16/3 + { 11 - ( 3 - 5/4 - 5/8) } ]
⇒ ? = 17/2 - [ 16/5 ÷ 9/2 का 16/3 + { 11 - ( 3 - ( 10 - 5 )/8) } ]
⇒ ? = 17/2 - [ 16/5 ÷ 9/2 का 16/3 + { 11 - ( 3 - 5/8 ) } ]
⇒ ? = 17/2 - [ 16/5 ÷ 9/2 का 16/3 + { 11 - ( 24 - 5)/8 } ] ⇒ ? = 17/2 - [ 16/5 ÷ 9/2 का 16/3 + { 11 - 19/8 } ]
⇒ ? = 17/2 - [ 16/5 ÷ 9/2 का 16/3 + 69/8 ]
⇒ ? = 17/2 - [ 16/5 ÷ 9/2 × 16/3 + 69/8 ]
⇒ ? = 17/2 - [ 16/5 ÷ 24 + 69/8 ]
⇒ ? = 17/2 - [ 2/15 + 69/8 ] ⇒ ? = 17/2 - 1051/120 = ( 1020 - 1051 )/120 = - 31/120
∴ ? = - 31/120
अतः इसका मान - 31/120 होगा।