Tag: science & technology

Starting with Rs 100, adding 50% gives Rs 150 (100 + 50% of 100). Then subtracting 50% from Rs 150 gives Rs 75 (150 - 50% of 150 = 150 - 75 = 75). Option B is correct. Option A (Rs 50) incorrectly subtracts 50% of original amount. Option C (Rs 100) assumes the operations cancel out, which they don't. Option D (Rs 125) incorrectly adds instead of subtracts.

The square root of 289 is 17 because 17 × 17 = 289. Option B is correct. Option A (19) gives 361. Option C (13) gives 169. Option D (28.9) is not an integer and seems to be a decimal approximation error. Memorizing perfect squares up to 20×20 helps with quick mental math.

64 is both a perfect square (8²) and a perfect cube (4³). Option A is correct. Option B (243 = 3⁵) is only a fifth power. Option C (343 = 7³) is only a cube. Option D (121 = 11²) is only a square. Numbers that are both perfect squares and cubes are sixth powers (n⁶).

A prime number is only divisible by 1 and itself. 641 is prime (not divisible by 2, 3, 5, 7, 11, 13, 17, 19, or 23). 791 = 7×113, 687 = 3×229, and 323 = 17×19 are all composite.

A perfect number equals the sum of its proper divisors. 6 = 1+2+3, 28 = 1+2+4+7+14, and 8128 are all perfect numbers. 484 = 2² × 11² is NOT perfect.

sin(π/6) = 1/2 = 0.5. Option D '.5' is the decimal representation. π/6 radians equals 30 degrees, and sin 30° = 0.5.

Volume of sphere = (4/3)πr³. This is derived from integration. Option C correctly states this formula.

The derivative of sin x is cos x (d/dx[sin x] = cos x). This is a fundamental derivative rule from calculus.

Product rule: d(uv) = u·dv + v·du. Option A correctly states this fundamental differentiation rule.

7! means 7×6×5×4×3×2×1 = 5040. Option B (40320) is actually 8!, and option D (720) is 6!.