NIMCET flashcards
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31 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Discriminant of a quadratic
- The value D = b² - 4ac for ax² + bx + c = 0. It tells whether roots are real and distinct (D > 0), equal (D = 0), or complex conjugates (D < 0).
- AM-GM-HM inequality
- For positive numbers, the arithmetic mean is at least the geometric mean, which is at least the harmonic mean. Equality holds only when every number in the set is identical.
- Sum of first n cubes
- The sum 1³ + 2³ + … + n³ equals [n(n+1)/2]², which is the square of the sum of the first n natural numbers.
- nth term of a GP
- For a geometric progression with first term a and common ratio r, the nth term equals a multiplied by r raised to the power n minus one.
- Combination identity
- nCr equals n factorial divided by r factorial times (n-r) factorial. It counts unordered selections and satisfies nCr = nC(n-r).
- General term of binomial
- In the expansion of (x+y)ⁿ, the term containing y^r is nCr x^(n-r) y^r, obtained by choosing y from exactly r of the n factors.
- Conditional probability
- P(A|B) equals P(A∩B) divided by P(B), provided P(B) is not zero. It measures the chance of A once B is known to have occurred.
- Perpendicular lines condition
- Two straight lines are perpendicular exactly when the product of their slopes equals -1, that is m₁m₂ = -1, with vertical and horizontal lines as the special case.
- Derivative of sine
- The derivative of sin x with respect to x is cos x, while the derivative of cos x is negative sin x; both are used in maxima and minima problems.
- Contrapositive equivalence
- The statement "if P then Q" is logically equivalent to "if not Q then not P". The converse, "if Q then P", is not equivalent and may be false.
- Distributed term in syllogism
- A term is distributed when a statement covers all members of its class. A valid conclusion cannot distribute a term that was undistributed in the premises.
- Clock hand gain rate
- The minute hand moves 6 degrees per minute and the hour hand 0.5 degrees per minute, so the minute hand gains 5.5 degrees per minute on the hour hand.
- Odd days of a year
- An ordinary year has 365 days, leaving one odd day beyond complete weeks; a leap year has 366 days, leaving two odd days. These shift the weekday.
- Percentage change formula
- Percentage change equals the new value minus the old value, divided by the old value, then multiplied by 100. A negative result indicates a decrease.
- Right turn twice
- Two consecutive right turns change the facing direction by 180 degrees, so the person ends up facing exactly opposite the original direction.
- Letter position coding
- Letters map to numbers A=1 through Z=26. Coding puzzles often shift each letter by a fixed amount or reverse the alphabet, so test shifts first.
- Blood relation tree method
- Draw parents above children with vertical lines, and siblings or spouses with horizontal lines. Gender must come from an explicit clue, never from the name.
- Binary to decimal conversion
- Multiply each binary digit by 2 raised to its position index counted from the right starting at zero, then add the products to obtain the decimal value.
- Byte and storage units
- One byte is 8 bits. Storage grows from kilobyte (2¹⁰ bytes) to megabyte, gigabyte, and terabyte, each step multiplying by 1024.
- XOR gate behaviour
- An XOR gate outputs 1 only when its inputs differ, and 0 when they are the same. It is widely used in parity checking and half-adder circuits.
- Role of the ALU
- The arithmetic logic unit inside the CPU performs integer arithmetic and logical operations such as addition, subtraction, AND, OR, and comparisons under control-unit direction.
- Volatile versus non-volatile memory
- Volatile memory, such as RAM, loses stored data when power is removed. Non-volatile memory, such as ROM and flash, retains data without power.
- Zero-based array indexing
- In C, the first element of an array sits at index 0, so an array declared with n elements has valid indices from 0 through n-1 only.
- TCP versus UDP
- TCP is connection-oriented, ordered, and reliable, retransmitting lost segments. UDP is connectionless and does not guarantee delivery, suiting streaming and DNS queries.
- OSI layer count
- The OSI reference model defines seven layers: physical, data link, network, transport, session, presentation, and application, each handling a distinct communication concern.
- Subject-verb agreement rule
- A verb must match its subject in number. Phrases between them do not change this, so "the box of pens is" uses a singular verb.
- Each and everyone take singular
- Indefinite pronouns such as each, either, everyone, somebody, and nobody are grammatically singular, so they take singular verbs and singular possessive pronouns.
- Between versus among
- Use "between" when referring to two distinct items or parties, and "among" when referring to three or more considered as a group.
- Passive voice formation
- The passive is built from a form of the verb "be" plus the past participle of the main verb, and the active object becomes the passive subject.
- Reported speech tense shift
- When the reporting verb is past, shift the reported tense one step back: present to past, past to past perfect, and will to would.
- Affect versus effect
- "Affect" is usually a verb meaning to influence something. "Effect" is usually a noun meaning the result or consequence of an action.