SSC CGL 2023 PYQ — Question 68

The correct answer is Option 1 i.e. 30.

12(sin⁴ $\theta$ + cos⁴ $\theta$) + 18(sin⁶ $\theta$ + cos⁶ $\theta$) + 78sin² $\theta$ cos² $\theta$

On putting $\theta = 90°$

We know that,

sin 90° = 1 and cos 90° = 0

⇒ 12(sin⁴ $90°$ + cos⁴ $90°$) + 18(sin⁶ $90°$ + cos⁶ $90°$) + 78sin² $90°$ cos² $90°$

⇒ 12((1)⁴ + 0) + 18((1)⁶ + 0) + 78 × 1 × 0

⇒ 12(1) + 18(1) + 0 = 30