general knowledge Online Quiz - 3551

Let the number be N and divisor be D. We have: (1) N ≡ 24 (mod D), (2) 2N ≡ 11 (mod D). From (2), 2N - 11 is divisible by D. Since N = kD + 24, we have 2(kD + 24) - 11 = 2kD + 48 - 11 = 2kD + 37. For this to be divisible by D, 37 must be divisible by D. Therefore, D = 37. We also need D > 24 (since remainder must be less than divisor), which 37 satisfies.

Numbers 1-9: 9 numbers × 1 digit = 9 keystrokes. Numbers 10-99: 90 numbers × 2 digits = 180 keystrokes. Numbers 100-999: 900 numbers × 3 digits = 2700 keystrokes. Number 1000: 1 number × 4 digits = 4 keystrokes. Total = 9 + 180 + 2700 + 4 = 2893 keystrokes.

Let the divisor be d. Then: 242 = a×d + 8, so 242 - 8 = 234 = a×d. 698 = b×d + 9, so 698 - 9 = 689 = b×d. Also: 242 + 698 = 940 = c×d + 4, so 940 - 4 = 936 = c×d. The divisor d must divide all three: 234, 689, and 936. GCD of 234 and 936: 234 divides 936 (936/234 = 4), so GCD = 234. Factors of 234: 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234. Since d > remainders (8, 9), and d divides 689, we test: 689/13 = 53 exactly. So d = 13.

For a number to be divisible by 4, its last two digits must be divisible by 4. From {1,2,3,4,5,6}, the pairs divisible by 4 are: 12, 16, 24, 32, 36, 52, 56, 64 (8 pairs). For each pair, we need to fill the first 3 positions from remaining 4 digits. Number of ways = 4P3 = 4 × 3 × 2 = 24. Total = 8 × 24 = 192.

Using the Remainder Theorem, for a polynomial P(x) to be divisible by (x + 3), P(-3) must be 0. P(-3) = (-3)^3 + 4(-3)^2 - 7(-3) + 12 = -27 + 36 + 21 + 12 = 42. Thus, 42 must be subtracted to make the remainder zero.

To get 3 trailing zeros, we need three factors of 5×10 = at least three 5s and three 2s in the prime factorization. Counting from 20: 20 contributes one 5, 25 contributes two 5s. By the 6th number (20×21×22×23×24×25), we have three 5s (one from 20, two from 25) and many 2s, giving exactly 3 trailing zeros. Option A (11) would give 4+ trailing zeros.

Edison is a recording tool in FL Studio that allows direct audio recording. The term 'Edison' refers to the integrated audio editor/recorder in FL Studio, named after Thomas Edison. Buzz effect adaptor, Vocal bundle, and Fruity wrapper are not FL Studio recording tools.

An 8:1 ratio is commonly recommended for vocal compression in FL Studio and other DAWs. This means for every 8 dB the input exceeds the threshold, only 1 dB is output - aggressive compression suitable for vocals. Lower ratios like 3:1 or 4:1 are used for gentler compression on instruments or buses.

A multiband compressor is an audio EFFECT plugin, not an INSTRUMENT plugin. It splits audio into frequency bands and compresses each separately. Sytrus, Wavestation, and Toxic Biohazard are all software synthesizers (VST instruments) that generate sound, while multiband compressors process existing audio.

The Piano Roll in FL Studio is the workspace where you can manually paste, edit, and draw musical notes. It displays notes on a grid where the vertical axis represents pitch and horizontal axis represents time. The step sequencer is for pattern creation, playlist for arrangement, and there's no 'Virtual pianist' tool.

FPC (Fruity Pad Controller) is indeed a drum kit/plugin instrument in FL Studio version 9.0. It's a drum machine plugin that allows users to create drum patterns using pads, similar to hardware drum machines. FPC has been a staple drum kit in FL Studio for many versions.

AR Rahman used the Toxic Biohazard VST plugin for background scoring in Slumdog Millionaire. This is part of the FL Studio plugin collection and was used to create distinctive synth sounds. FPC is a drum plugin, Sytrus is a synthesizer, and Simsynth is a simpler synth plugin.

The Greek letter Epsilon corresponds to 'e' in the Latin alphabet. It's the fifth letter of the Greek alphabet (α, β, γ, δ, ε) and is used in mathematics, science, and engineering contexts. The lowercase epsilon (ε) is commonly used to represent small positive numbers in calculus and analysis.

The question asks about '?' which corresponds to Zeta in the Greek alphabet. Zeta (ζ) is the sixth letter of the Greek alphabet, following Epsilon. It's pronounced 'zay-ta' and represents the 'z' sound in ancient Greek.

The question asks about '?' which corresponds to Eta in the Greek alphabet. Eta (η) is the seventh letter of the Greek alphabet, following Zeta. In ancient Greek it represented a long 'e' sound, while in modern Greek it's pronounced 'ee-ta'.

The question asks about '?' which corresponds to Xi in the Greek alphabet. Xi (ξ) is the fourteenth letter of the Greek alphabet. It's pronounced 'ksee' or 'zai' and is used in mathematics, physics, and statistics - notably in the Chinese name of the Western symbol.

The question asks about '?' which corresponds to Chi in the Greek alphabet. Chi (χ) is the twenty-second letter of the Greek alphabet. It's pronounced 'kai' (like 'ky' in sky) and appears in 'chi-squared' tests in statistics. Xi comes before Chi in alphabetical order.

The question asks about 'f' which corresponds to Phi in the Greek alphabet. Phi (φ or Φ) is the twenty-first letter of the Greek alphabet. It's pronounced 'fi' (like 'fee') and is famous for representing the golden ratio (φ ≈ 1.618) in mathematics. Note that option A has a typo - 'Albha' should be 'Alpha'.