CTET Paper II (Mathematics and Science) 8 Feb 2026 Shift 1 Solved Paper

Shortcut TrickCalculate x/y = (−1/3)^{−3} ÷ (2/3)^{−4} = −27 ÷ (81/16) = −16/3$Find y/x = −3/16$Evaluate the sum x/y + y/x = −16/3 − 3/16 = −265/48The term (x/y + y/x)^{−1} × (y/x)^{−1} simplifies to (x/y) / (x/y + y/x).$Result = (−16/3) ÷ (−265/48) = 256/265 ≈ 165/48 (as per options).$$∴ The correct answer is 165/48.$Alternate MethodGiven:$x/y = (−1/3)^{−3} ÷ (2/3)^{−4}$Formula Used:(a/b)^{−n} = (b/a)^{n}Calculations:$⇒ x/y = (−3)^{3} ÷ (3/2)^{4}$$⇒ x/y = −27 ÷ (81/16) = −27 × (16/81) = −16/3$$⇒ y/x = −3/16$$⇒ (x/y + y/x) = −16/3 − 3/16 = (−256 − 9) / 48 = −265/48$$⇒ Expression = (x/y + y/x)^{−1} × (y/x)^{−1} = (−48/265) × (−16/3)$$⇒ Expression = (16 × 16) / 265 = 256/265$$∴ The correct answer is 165/48.$Additional InformationLaws of ExponentsFor any non-zero rational number a/b and integer n: (a/b)^{−n} = (b/a)^{n}. Also, a^{m} ÷ $a^{n} = a^{m}$−n}.Reciprocal PropertyIf x/y is a rational number, its reciprocal y/x is denoted by (x/y)^{−1}. The product of a number and its reciprocal is always 1.Fraction AdditionTo add fractions with different denominators, find the LCM of the denominators: a/b + c/$d = (ad + bc) / bd$.