SSC CGL 2024 PYQ — Question 56

The correct answer is option 1 i.e. $79\over128$.

sin⁴A + cos⁴A = (sin²A + cos²A)² - 2sin²Acos²A

⇒ 1 - 2sin²Acos²A    ...(i)

Given, sinA + cosA = $1\over{2\sqrt2}$

Squarying both the sides,

sin²A + cos²A + 2sinAcosA = 1/8

⇒ 1 - 2sinAcosA = 1/8

⇒ 2sinAcosA = 7/8

⇒ sinAcosA = 7/16

Now, sin²Acos²A = 49/256

Putting this value in equation (i),

⇒ 1 - 2(49/256)

⇒ 1 - 49/128 = 79/128