Science and Mathematics Basics Quiz

Gamma rays are electromagnetic photons with no electric charge, so they experience no force in an electric field. Alpha particles (positive), beta particles (electrons/positrons), and electrons (negative) all have charge and experience electric force.

Atoms themselves are about 99.9% empty space, with most of the mass in a tiny nucleus and electrons occupying the surrounding space. Since matter is made of atoms, a granite block is also mostly empty space.

The energy difference between excited and ground states corresponds to green light. Decay to an intermediate state means a smaller energy gap, which produces a lower-energy photon with longer wavelength. Red has longer wavelength than green in the visible spectrum.

Gravitational potential energy near Earth's surface is U = mgh, where m is mass, g is acceleration due to gravity (~9.8 m/s²), and h is height. The other options are incorrect formulas.

According to the Doppler effect, when a source moves toward an observer, light waves are compressed (shorter wavelength), causing a blueshift. At 0.9c, this relativistic blueshift would be dramatic.

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!.

Sulphuric acid was historically called 'oil of vitriol' by medieval alchemists. The term 'vitriol' comes from the Latin 'vitreum' meaning glass, referring to its glassy appearance when in crystal form. Nitric acid was called 'aqua fortis', hydrochloric acid was 'muriatic acid', and phosphoric acid has different historical names.

White phosphorus is the correct answer. It has been documented as being used by Israeli forces in Gaza, causing severe burns and is controversial under international law. Arsenic is a poison but not primarily an incendiary weapon. Sulphur is used in conventional munitions. Neon is an inert noble gas with no military application as a weapon.

Picric acid (2,4,6-trinitrophenol) is the correct answer. It is a toxic explosive compound used in military applications and chemical warfare due to its instability and toxicity. Benzoic acid is a food preservative. Succinic acid is used in the Krebs cycle and food additives. Maleic acid is an industrial chemical for polymer production, not warfare.

Iodine (as tincture of iodine or povidone-iodine) is a common antiseptic carried in first aid kits for disinfecting wounds and preventing infection. While alcohol can also be used as a disinfectant, iodine solutions are more stable and have longer-lasting antimicrobial properties, making them preferred for field use. NaCl (salt) is not a disinfectant, and benzene is a toxic carcinogen never used medically.