1. cos1° + cos2° + cos3° + … + cos180° =
Answer: 0
2. The value of (tan70° – tan20°) / tan50° is
Answer: 1
3. If cos⁻¹x + cos⁻¹y + cos⁻¹z = 3π, then xy + yz + zx =
Answer: 0
4. sin(1/2 cos⁻¹(4/5)) =
Answer: 1/√10
5. If sin x + sin²x = 1, then cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x =
Answer: 1
6. sin²17.5° + sin²72.5° =
Answer: tan²45°
7. 0.5737373… is
Answer: 568/999
8. log₂2 + log₄4 + logₓx + log₁₆16 = 6, then x =
Answer: 32
9. In a class of 60 students, 25 play cricket, 20 play tennis, and 10 play both sports. The number of students who do not play any sport is
Answer: 35
10. If f(x) = 8x³ and g(x) = x⅓, then fog(x) =
Answer: 8x
11. tan⁻¹(x+1/x-1) + tan⁻¹(x-1/x) = tan⁻¹(-7), then x =
Answer: 1
12. The derivative of eˣ³ with respect to log x is
Answer: 3x²eˣ³
13. If √x + 1/√x = 2cosθ, then x⁶ + x⁻⁶ =
Answer: 2cos60
14. The maximum value of y = acosx + bsinx is
Answer: √(a² + b²)
15. If the vectors 3i + j – 2k, i + 2j – 3k, and 3i + λj + 5k are coplanar, then λ =
Answer: 4
16. If A = [2 3; 4 6] then A⁻¹ =
Answer: Does not exist
17. The area of the parallelogram determined by the vectors i + 2j + 3k and -3i – 2j + k (in square units) is
Answer: √40
18. If the vectors ai + j + 2k and -12i + 4j + 8k are perpendicular, then a =
Answer: -1
19. If a = 3i – 2j + 2k, b = 6i + 4j – 2k, and c = 3i – 2j – 4k, then a.(b x c) =
Answer: -120
20. The modulus and argument of (1+i)/(1-i) are
Answer: 1, π/4