Best Online Course for CAT & Competitive Exams in INDIA-2021

Explore the classification of numbers into real and imaginary, including rational and irrational numbers, integers, decimals, and fractions - covering recurring and non-recurring decimals, proper, improper, and mixed fractions.

Explore how integers are classified into even and odd numbers, natural and whole numbers, and neither prime nor composite, with prime, composite, twin primes, and perfect numbers.

Learn the fibonacci sequence, built by adding two previous numbers, and apply bodmas—brackets, division, multiplication, addition, subtraction—to solve expressions step by step.

master decimal place value and face value, explore reading numbers up to millions, and apply rounding rules to hundreds, tens, units, and thousands.

Learn to convert decimals to fractions and recurring decimals using algebra, including bar notation, by multiplying to remove decimals and solving for x.

Find a common denominator to add and subtract fractions, then multiply or divide fractions using cancellation and reciprocals.

Convert proper fractions to mixed fractions and back using quotient, numerator, and denominator, then add and subtract mixed fractions by separating integers and fractions, and explore factors and multiples.

Explore how to find the least common multiple and the highest common factor, using multiples, factors, and prime factorization, with worked examples for 4,6,8 and 32,54,96.

Discover how to compute the lcm and hcf and determine sum and number of factors through prime factorization, using the divisor formulas shown with the example 480.

Count trailing zeros of factorials by tallying factors of five, using division method for large numbers. Determine the maximum power of six in 100 factorial by comparing twos and threes.

Master divisibility rules for common numbers using digit sums and last-digit checks. Apply these rules for two, three, four, five, seven, eight, nine, ten, eleven, and twelve.

Explore ratios and proportions, define the difference between ratio and fraction as a two-part vs part-of-whole relationship, and learn why combining class ratios cannot be added directly.

Learn how to divide a total value into proportional parts and combine ratios across multiple variables to determine shares.

Proportion shows how quantities relate, illustrated by 50 cents yielding 10 chocolates and 70 cents yielding 14, and explains extremes, means, and product of extremes equals product of means.

Understand five types of proportion—mean (main) proportion, third proportion, fourth proportion, direct proportion, and inverse proportion—alongside practical examples like speed versus distance and heat versus water level.

Explore percentage concepts, and learn that percentage equals obtained value divided by total value multiplied by 100, enabling comparisons such as 400/500 (80%) vs 600/1000 (60%).

Apply the percentage change formula (change over original value times 100) using the 350 to 450 marks example, and convert percentages to fractions by dividing by 100.

Master percent calculations through example problems, determining values for 10, 20, 40, and 50 percent of numbers and combining results for complex cases.

Explore percentage calculations through practical examples, including successive percent off, price reductions, and final prices for items like 4000, shirts, and televisions.

Master percentage changes with examples from price and population adjustments, starting from an initial value and applying increases or decreases using the percentage change formula.

Learn the basics of profit and loss, covering cost price, selling price, mark price, and formulas for profit, loss, and discount percentages with practical examples.

Analyze a 20% discount followed by a 20% profit on a mark price of 600, and compute the cost price; graphically relate cost price, selling price, and market price.

Learn to compute profit or loss percentage from selling price and cost price with practical examples, including gold price and two mobiles with mixed profit and loss.

Compute the original price from a final amount after successive 30% and 40% discounts using algebra, as illustrated with a final price of 1,026,000 dollars.

Compare simple and compound interest, define simple interest as interest on principal, compound interest as interest on accumulated amount, and illustrate with formulas and examples.

Explore averages by identifying linear data versus nonlinear data, and apply the first number plus last number divided by two to compute means in sequences of even and odd numbers.

Learn how to compute averages for nonlinear data using weighted averages, illustrated by a class example with boys, girls, and teachers to find the overall class mean.

Solve average problems by analyzing totals and duplicates, as shown in cricket scores and class averages, to compute individual scores from overall means.

This lecture introduces mixtures and allegations, showing how to use common multiples to equalize vessel quantities and combine mixtures to find the final milk-to-water ratios.

Compute volumes and mixing ratios for two vessels using common multiples, derive the final ratio of components, and conclude with a final composition of five to twelve to ten.

Solve a milk-to-water ratio problem, starting with 64 liters milk and 16 liters water to reach 1:4 by adding water; cross-multiplication gives X = 240 liters (caption states 40 liters).

learn how speed equals distance divided by time, and how average speed and relative speed are calculated. analyze chase scenarios to see how relative speed determines catch time.

Start with two trains; one runs at 6 am 60 mph, the other four hours later at 80 mph across 110 miles, to determine meeting time and distance from B.

Compute the average speed for a three-leg trip between X and Y by summing times at 40, 50, and 60 mph and dividing total distance by total time.

Solving a distance, speed, and time problem by equating distance to speed times time and using late and early time differences to determine the normal speed and distance.

Calculate how many bulbs are inspected by applying a proportional scale: seven inspected per 400, so for 20,000, compute seven times 20,000 divided by 400 to get 350.

Identify direct variation and apply a proportion to calculate earnings: the performer earns 120 for eight attendees, so for twenty attendees the earnings are 300 dollars by cross multiplying.

Calculate the true profit from a performance by subtracting 43% costs from $120; with eight attendees, the profit is about $68.4.

Calculate the earth’s orbital speed by dividing the annual distance traveled (about 580 million miles) by the year’s 8,760 hours to get roughly 66,210 miles per hour.

Compute the unknown element's atomic weight as about 20% less than calcium's 40 amu, yielding approximately 32 amu.

Explore lines and angles, including lines, line segments, parallel and perpendicular relationships, and supplementary, complementary, and vertical opposite angles, plus transversals creating equal angles and proportional segments.

Discover triangle basics: the largest angle lies opposite the longest side, angles sum to 180 degrees, and any two sides exceed the third while exterior angles equal opposite interior sums.

Explain triangle area calculations from base and height, and from three sides using semi-perimeter s and inradius r. Derive equilateral triangle area from altitude via Pythagoras, yielding (sqrt(3)/4) a^2.

Apply the pythagorean theorem to find the hypotenuse and recognize 3-4-5 triplets and their multiples. Explore similar triangles with proportional sides and congruent triangles with identical shape and size.

Explore scaling triangles and other types—right angle, obtuse, isosceles, equilateral—and learn centers such as in center, circle center, X center, centroid, plus the midpoint theorem for area and perimeter.

Explore special triangles, including 30-60-90 and 45-45-90, to determine side ratios and the hypotenuse via right-triangle properties and equilateral triangle construction.

Explore quadrilaterals, including parallelograms, squares, rectangles, rhombuses, and trapeziums, with key ideas of angle sums, diagonals that bisect, and area formulas for parallelograms, rectangles, squares, rhombuses, and trapeziums.

Explore how polygons form by adding sides, from quadrilaterals to hexagons and beyond, and learn interior angle sums (n-2)180, exterior sums 360, diagonals n(n-3)/2, and regular polygon concepts.

Explore circles basics, including radius, diameter, center, chord, tangent, sector, arc, and major and minor segments, and explain arc length and sector area in relation to circumference and radius.

Triangle in a semicircle is right-angled; angles in same segment are equal; central angle equals twice inscribed angle; opposite angles of a cyclic quadrilateral sum to 180 degrees.

Explore three-dimensional geometry by examining cuboids and cubes, along with cylinders, cones, spheres, and hemispheres, and learn to calculate lateral surface area, total surface area, volume, and the space diagonal.

Examine cylinders, cones, spheres, hemispheres, prisms, and pyramids by calculating volumes, lateral and total surface areas, using height, radius, base area, and perimeter.

Explore coordinate geometry basics across quadrants, distance between points, slope, and midpoint; learn line equations from slope-intercept and two-point forms, including x- and y-intercepts.

Master algebra basics by exploring algebraic expressions with variables and constants, using operations like plus and minus, and distinguishing single-term, binomial, and trinomial forms.

Master factoring to solve quadratics, turning x^2+3x-6 into (x+3)(x-2)=0 for roots -3 and 2, and explore discriminant and sum-product relationships.

Explore exponents and basic formulas, mastering power rules, square and cube expansions, and binomial identities for expressions like x squared, x y, and x squared plus y squared.

Explore functions and algebraic expressions with one variable, and learn to solve simple equations by equalizing coefficients, recognizing parallel lines with zero solutions or coincident lines with infinite solutions.

Explore inequalities introduction by solving for x with >, <, ≥, ≤, and plotting results on a number line; learn how negative multipliers flip directions.

Understand how absolute values shape inequality solutions, including cases like |x| ≥ 5 or |x| ≤ 5, and show |x-3| ≤ 2 yielding 1 ≤ x ≤ 5.

the lecture factors x^2-4x+3 as (x-3)(x-1), finds zeros at 1 and 3, and uses sign analysis to show outside the roots for >=0 and inside for <=0.

Explore graphical and algebraic solutions to a quadratic expression, revealing roots at x = 1 and x = 3 and where the expression is greater or less than zero.

Explore permutations and combinations, distinguishing arrangement from selection; illustrate six arrangements of A, B, C taken two at a time and when order matters in permutation versus selection.

Explore counting three-person selections from ten using permutations and combinations. Compare the slot method with factorial formulas and see that 10P3 equals 720 and 10C3 equals 120.

Learn four steps to solve permutations and combinations: identify the target, decide if order matters, draw slots, and apply permutation or combination rules, illustrated by 30-student handshake example yielding 435.

Examine conditional slots by counting diagonals in an octagon through vertex selection, showing how eight by one and five by two yield a 40 total.

Learn to count combinations for selecting three boys and two girls using slot-based counting, and count rectangles and squares on a five-by-five chessboard.

Lecture defines probability as the ratio of favorable to total outcomes, between zero and one, and uses coin toss and rain examples to illustrate complementary probability and at least one.

Identify independent events and multiply probabilities; distinguish dependent events where the first outcome changes the second, and apply or and intersection concepts with ball and card examples.

Learn how probability tallies outcomes for coins and dice, with 2, 4, and 8 outcomes for coin tosses, and 6 outcomes per die, forming 6^n totals.

Explore arithmetic, geometric, and harmonic progressions, sums of natural numbers, squares, and cubes. Learn formulas for AP and GP sums, and HP as the reciprocal of an arithmetic progression.

Explore the difference between a list and a set, and learn core set operations such as union, intersection, and not E, using Venn diagrams, universal sets, and subset relationships.

Apply the two-sets method using a Venn diagram or the union-intersection formula to solve problems, such as finding how many of 40 students play both cricket and football.

Apply three-set Venn diagrams and the inclusion-exclusion principle to compute the total number of students, including those in none, using counts for cricket, football, and tennis.

Master the grid method to solve four-category CAT problems by classifying students into boys and girls, vegetarian and non-vegetarian, then fill the grid and compute non-vegetarians from given totals.