Maharashtra SSC Pali (MSBSHSE) flashcards

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

Quadratic formula

For ax^2 + bx + c = 0 with a not zero, the roots are x = [-b ± sqrt(b^2 - 4ac)] / 2a. The discriminant b^2 - 4ac decides whether roots are real and distinct, equal, or non-real.

Arithmetic progression nth term

In an arithmetic progression with first term a and common difference d, the nth term is t_n = a + (n - 1)d. The sum of the first n terms is S_n = n/2 [2a + (n - 1)d].

Basic Proportionality Theorem

If a line parallel to one side of a triangle intersects the other two sides in distinct points, it divides those two sides in the same ratio. Its converse is also used in proofs.

Sector area and arc length

For a circle of radius r and central angle θ in degrees, sector area = (θ/360) × πr^2 and arc length = (θ/360) × 2πr. Both scale linearly with the angle.

Ohm's law and electric power

At constant temperature, V = IR across a conductor. Electrical power is P = VI = I^2R = V^2/R. Commercial energy is measured in kWh, where 1 kWh = 3.6 × 10^6 J.

pH scale

pH measures hydrogen ion concentration on a 0 to 14 scale. A pH below 7 is acidic, exactly 7 is neutral, and above 7 is basic. Each unit represents a tenfold change in concentration.

Fundamental rights vs directive principles

Fundamental rights in the Constitution are justiciable and enforceable in courts. Directive principles of state policy guide government policy but are not directly enforceable by any court.

Food chain and trophic levels

A food chain starts with a producer and passes energy to consumers. Only about ten percent of energy transfers to the next trophic level, which limits chains to about four or five levels.

Photosynthesis equation

In the presence of chlorophyll and sunlight, 6CO2 + 6H2O produces C6H12O6 + 6O2. Carbon dioxide is reduced and water is oxidised; the process occurs mainly in chloroplasts of green leaves.

Snell's law of refraction

When light passes between two media, n1 sin i = n2 sin r, where i is the angle of incidence and r the angle of refraction. Light bends toward the normal when entering a denser medium.

Mirror and lens formula

For spherical mirrors, 1/v + 1/u = 1/f. For thin lenses, 1/v - 1/u = 1/f. Magnification m = v/u for mirrors and m = v/u for lenses, with signs set by the sign convention.

Mean of grouped data

For a grouped frequency distribution, the mean is Σfx/Σf, where x is the class mark and f the frequency. The step-deviation method simplifies calculation when class intervals are equal.

Probability complement rule

For any event E, the probability of E lies between 0 and 1. The probability that E does not occur is P(not E) = 1 - P(E). The sum of probabilities of all outcomes is 1.

Cramer's rule

For two linear equations in x and y, compute determinants D, Dx and Dy from the coefficients. If D is not zero, x = Dx/D and y = Dy/D gives the unique solution.

Distance and midpoint formulas

The distance between points (x1,y1) and (x2,y2) is sqrt((x2-x1)^2 + (y2-y1)^2). The midpoint is ((x1+x2)/2, (y1+y2)/2). The slope is (y2-y1)/(x2-x1).

Similar triangles area ratio

If two triangles are similar, the ratio of their areas equals the square of the ratio of any pair of corresponding sides. Corresponding angles are equal and corresponding sides are proportional.

Tangent perpendicular to radius

A tangent to a circle is perpendicular to the radius drawn to the point of contact. Conversely, a line perpendicular to a radius at its outer end is a tangent to the circle.

Mensuration volume formulas

Volume of a cylinder is πr^2h, of a cone is (1/3)πr^2h, and of a sphere is (4/3)πr^3. Total surface area of a cylinder is 2πr(r + h).

Standard trigonometric values

sin 0°=0, sin 30°=1/2, sin 45°=1/√2, sin 60°=√3/2, sin 90°=1. Cos values run in reverse order. Tan θ = sin θ / cos θ, and tan 45° equals 1.

Balancing chemical equations

Adjust coefficients so the number of atoms of each element is equal on both sides. Never change subscripts. Add state symbols (s, l, g, aq) and conditions such as heat or catalyst above the arrow.

Newton's second law

The acceleration of a body is directly proportional to the net force and inversely proportional to its mass, giving F = ma. Force and acceleration are both vectors in the same direction.

Series and parallel resistance

In series, total resistance R = R1 + R2 + R3. In parallel, 1/R = 1/R1 + 1/R2 + 1/R3. Parallel combination always gives a total resistance smaller than the smallest individual resistance.

Homologous series

A family of organic compounds with the same functional group where successive members differ by one CH2 unit. Members show similar chemical properties and a gradual change in physical properties.

Roasting versus calcination

Roasting heats a sulphide ore strongly in excess air to form an oxide and sulphur dioxide. Calcination heats a carbonate ore in limited air to drive off carbon dioxide and leave the oxide.

Mendel's law of segregation

The two alleles of a gene separate during gamete formation, so each gamete carries only one allele. At fertilisation, alleles pair again, which explains dominant and recessive phenotypes in offspring.

Sex determination in humans

Human females have XX sex chromosomes and males have XY. The mother always contributes an X; the father contributes either X or Y, so the father's gamete determines the child's sex.

Formal letter format

Include sender address, date, receiver address, subject line, salutation, body paragraphs and closing with signature. The subject line is a single short phrase stating the letter's purpose.

Report writing structure

A report opens with a headline, then a dateline and byline, followed by a lead paragraph answering what, when, where and who, and a body giving details in past tense and third person.

Upama and rupak alankar

Upama (simile) compares two objects using words such as like or as. Rupak (metaphor) identifies one object directly with another, without a comparing word. Both are figures of speech.

Active to passive voice

The object becomes the subject, the verb changes to a form of be plus the past participle, and the original subject becomes an agent introduced by 'by'. Tense must be preserved.

Five-year plan objectives

India's five-year plans set targets for growth, employment, self-reliance and removal of poverty. They are formulated by the Planning Commission and later by NITI Aayog's approach documents.

Monsoon mechanism

The southwest monsoon brings rain from June to September when moist winds from the Indian Ocean are drawn toward the low-pressure landmass. The Western Ghats force air upward, causing heavy rain.