AISSEE flashcards

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

HCF and LCM relation

For any two positive integers, the product of the numbers equals the product of their HCF and LCM. This lets you find the fourth value when three are known.

Successive discount formula

Two successive discounts of a percent and b percent are not simply added. The single equivalent discount is a + b − ab/100 percent, always less than a + b.

Profit percent formula

Profit percent equals selling price minus cost price, divided by cost price, then multiplied by 100. Loss percent is calculated on the same base, the cost price.

Simple interest formula

Simple interest equals principal × rate × time divided by 100. Interest is charged only on the original principal, so the same amount is added each year.

Speed unit conversion

One kilometre per hour equals five-eighteenths of a metre per second. Multiply km/h by 5/18 to get m/s, and multiply m/s by 18/5 to return to km/h.

Circle area and circumference

A circle of radius r has area πr² and circumference 2πr. Since diameter is twice the radius, the circumference also equals π multiplied by the diameter.

Sum of first n natural numbers

The sum 1 + 2 + 3 + … + n equals n(n+1)/2. The sum of the first n odd numbers equals n², so 1 + 3 + 5 gives 9.

Divisibility test for 8

A number is divisible by 8 when its last three digits form a number divisible by 8. For example, 5,120 qualifies because 120 is divisible by 8.

Pythagoras theorem

In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c², where c is the hypotenuse.

Average after adding a value

The new average equals the old total plus the new value, divided by the new count. Adding a value above the old average raises it; a value below lowers it.

Letter position anchors EJOTY

Remember E = 5, J = 10, O = 15, T = 20 and Y = 25. These five anchor points let you count quickly to any other letter of the alphabet.

Opposite letters sum to 27

Letters facing each other from the two ends of the alphabet add to 27: A with Z, B with Y, C with X, and M with N. Useful in coding questions.

Ranking total formula

When a person's rank from the left and rank from the right are both given, total persons = left rank + right rank − 1, because that person is counted twice.

Clock hands angle formula

The angle between the hands is |30H − 5.5M| degrees, where H is the hour and M the minutes. Take the smaller angle by subtracting from 360 if needed.

Right turn direction rule

Turning right means rotating 90 degrees clockwise: North to East, East to South, South to West, West to North. Left turns rotate anticlockwise by the same amount.

Mirror versus water image

A mirror image swaps left and right while keeping top and bottom unchanged. A water image swaps top and bottom while keeping left and right unchanged.

Number series first check

Compare consecutive differences first. If they are constant it is an arithmetic series; if not, check ratios, squares, cubes, or two alternating interleaved series.

Syllogism basic rule

'All A are B' implies 'Some B are A' and that no A lies outside B. 'Some A are B' is reversible, but it never supports the conclusion 'All A are B'.

Article a versus an

Use 'a' before a consonant sound and 'an' before a vowel sound, judged by pronunciation: an hour, an M.A., a university, a one-rupee coin.

Since versus for

Use 'since' with a point of time, such as since 2019 or since Monday. Use 'for' with a length of time, such as for three years, usually with present perfect.

Passive voice formation

Make the object the new subject, add the correct tense of 'be', then the past participle: The letter was written by her. The original tense stays unchanged.

Comparative and superlative forms

Short adjectives take -er and -est; longer ones take more and most. Comparatives are followed by 'than', while superlatives take 'of' or 'in'.

Prepositions of time at on in

Use 'at' for clock times, 'on' for days and dates, and 'in' for months, years, seasons and longer periods: at 5 p.m., on Monday, in July.

Each and every take singular

Words such as each, every, either, neither and everyone take a singular verb and singular pronoun: Each of the boys was given his book.

Direct to indirect tense shift

When the reporting verb is in the past, move the reported verb one step back: present becomes past, past becomes past perfect, and will becomes would.

Synonym and antonym

A synonym is a word with a similar meaning to the given word, while an antonym has the opposite meaning. Placing the word in a sentence helps confirm the sense.

National symbols of India

The Bengal tiger is India's national animal, the peacock the national bird, the lotus the national flower, the mango the national fruit and the banyan the national tree.

Constitution adoption dates

India's Constitution was adopted by the Constituent Assembly on 26 November 1949 and came into force on 26 January 1950, celebrated every year as Republic Day.

Longest river in India

The Ganga is the longest river flowing within India. It rises in the Gangotri glacier of the Himalayas and drains into the Bay of Bengal.

Dandi March year

Mahatma Gandhi led the Dandi March, also called the Salt Satyagraha, in 1930, walking from Sabarmati Ashram to Dandi to break the British salt law.

Largest planet

Jupiter is the largest planet of the solar system. Mercury is closest to the Sun, and Mars is called the red planet because of iron oxide dust.

First President of India

Dr Rajendra Prasad was the first President of India, serving from 1950 to 1962. Jawaharlal Nehru was the country's first Prime Minister.