Bihar Polytechnic flashcards

33 cards. Read the term and the definition here. The deck at the top of this page is optional.

Newton's second law

The net force on a body equals the product of its mass and acceleration, F = ma. Force is measured in newtons, where one newton accelerates one kilogram at one metre per second squared.

Ohm's law

At constant temperature, the current through a conductor is directly proportional to the potential difference across it, so V = IR. Resistance R is measured in ohms.

Snell's law

When light crosses a boundary, n₁ sin θ₁ = n₂ sin θ₂, where n is refractive index and θ is the angle from the normal. Higher n means a denser optical medium.

Lens formula

For a thin lens, 1/v − 1/u = 1/f, relating image distance, object distance and focal length. Magnification is m = v/u, with sign conventions deciding real or virtual images.

de Broglie wavelength

A particle of momentum p has an associated wavelength λ = h/p, where h is Planck's constant. This wave nature becomes measurable only for very small masses such as electrons.

First law of thermodynamics

Heat supplied to a system equals the change in its internal energy plus the work done by it: ΔQ = ΔU + ΔW. In an adiabatic process ΔQ is zero.

Mole concept

One mole contains 6.022 × 10²³ particles and has a mass in grams equal to the molar mass. It converts between particle counts and measurable masses in reactions.

Molarity

Molarity is the number of moles of solute dissolved per litre of solution, written M. It changes slightly with temperature because solution volume expands on heating.

pH scale

pH equals the negative logarithm of hydrogen ion concentration. At 25 degrees Celsius, pH below 7 is acidic, 7 is neutral, and above 7 is basic.

Le Chatelier's principle

When a system at equilibrium is disturbed by a change in concentration, pressure or temperature, it shifts in the direction that partly opposes the change.

Hybridisation and shape

Steric number gives hybridisation: two means sp and linear, three means sp² and trigonal planar, four means sp³ and tetrahedral. Lone pairs distort the ideal bond angles.

Oxidation number

A bookkeeping charge assigned to an atom assuming bonds are fully ionic. Oxidation number rising indicates oxidation, and falling indicates reduction in a redox reaction.

Bond order

Bond order equals half the difference between bonding and antibonding electrons in molecular orbital theory. Higher bond order means a shorter, stronger bond and greater stability.

Quadratic discriminant

For ax² + bx + c = 0, the discriminant D = b² − 4ac. Positive D gives two real roots, zero gives equal roots, and negative D gives complex conjugate roots.

Sum of AP terms

For an arithmetic progression with first term a and common difference d, the nth term is a + (n−1)d and the sum of n terms is n/2 times twice a plus (n−1)d.

Sum of GP terms

For a geometric progression with first term a and ratio r, the sum of n terms is a(rⁿ − 1)/(r − 1) when r is not 1. If |r| < 1, the infinite sum is a/(1 − r).

Pythagorean identity

For any angle θ, sin²θ + cos²θ = 1. Dividing by cos²θ gives 1 + tan²θ = sec²θ, and dividing by sin²θ gives 1 + cot²θ = cosec²θ.

Power rule of derivatives

The derivative of xⁿ with respect to x is nxⁿ⁻¹ for any real n. Combined with the product and quotient rules, it differentiates most polynomial and rational expressions.

Slope of a line

The slope through two points is (y₂ − y₁)/(x₂ − x₁). Two lines are perpendicular when the product of their slopes equals −1, and parallel when slopes are equal.

Circle equation

A circle with centre (h, k) and radius r satisfies (x − h)² + (y − k)² = r². In general form x² + y² + 2gx + 2fy + c = 0, the centre is (−g, −f).

Classical probability

For equally likely outcomes, the probability of an event is the number of favourable outcomes divided by the total number of outcomes. Values always lie between 0 and 1.

Integration by substitution

If the integrand contains a function and its derivative, substitute u for that function so du replaces the derivative term. This reduces the integral to a standard form.

Compound interest formula

The amount after n years is P(1 + R/100)ⁿ, so compound interest is amount minus principal. Interest is charged on both principal and previously earned interest.

Average speed formula

Average speed is total distance divided by total time. For equal distances covered at speeds x and y, the average speed is 2xy/(x + y), not the arithmetic mean.

Time and work rule

If A alone finishes work in x days and B in y days, working together they finish it in xy/(x + y) days. Rates add; times do not add directly.

Alligation rule

To mix two ingredients priced c (cheaper) and d (dearer) to get mean price m, the quantity ratio is (m − c) : (d − m). It solves mixture and profit problems quickly.

Permutation formula

The number of arrangements of r items chosen from n distinct items is nPr = n!/(n−r)!. Order matters in permutations but not in combinations, where nCr = n!/[r!(n−r)!].

Successive percentage change

Two successive changes of a percent and b percent produce a net change of a + b + ab/100 percent. A rise followed by an equal fall always leaves a net decrease.

Syllogism validity rule

A conclusion follows only if it is true in every possible arrangement of the premises, drawn as Venn diagrams. A conclusion true in just one arrangement is not valid.

Bihar state symbols

Bihar's capital is Patna, and its state animal is the gaur while the state bird is the house sparrow. The state tree is the peepal and the state flower is the marigold.

Fundamental duties

Article 51A of the Indian Constitution lists fundamental duties of citizens, added by the 42nd Amendment in 1976. They are not enforceable by courts directly.

Bodh Gaya significance

Bodh Gaya in Bihar is where Gautama Buddha attained enlightenment under the Bodhi tree. The Mahabodhi Temple there is a UNESCO World Heritage Site.

Nalanda and Vikramshila

Nalanda and Vikramshila were ancient Buddhist monastic universities in Bihar, attracting scholars from across Asia. Both flourished under the Pala dynasty before declining.