MH CET Law Basic Mathematics and Numerical Aptitude Syllabus

How does compound interest differ from simple interest for the same principal, rate, and time?

SI is calculated only on the original principal each period, so it grows linearly. CI is calculated on principal plus accumulated interest, so it grows faster. For 2 years, CI - SI = P x (R/100) squared.

What is the formula relating Speed, Distance, and Time?

Speed = Distance / Time; Distance = Speed x Time; Time = Distance / Speed.

How do you convert km/h to m/s and m/s to km/h?

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

What is relative speed for two objects moving in the same direction versus opposite directions?

Opposite directions: relative speed = sum of speeds (s1 + s2). Same direction: relative speed = difference of speeds (s1 - s2).

How long does a train of length L take to pass a stationary pole versus a platform of length P?

To pass a pole: Time = L / Speed. To pass a platform: Time = (L + P) / Speed, since the train must cover its own length plus the platform length.

What is the basic time and work relationship for a person who finishes a job in n days?

If a person completes a job in n days, their one-day work = 1/n of the job. Work done = Rate x Time.

If A does a job in x days and B in y days, how long do they take working together?

Combined time = (x x y) / (x + y) days, because their combined one-day work is 1/x + 1/y.

What is the relationship between number of workers, days, and total work (man-days)?

Total work is constant: M1 x D1 x H1 / W1 = M2 x D2 x H2 / W2, where M = men, D = days, H = hours/day, W = work. Men and days are inversely proportional for fixed work.

In a data table, what is the difference between a row total and a column total, and why do they matter?

A row total sums all values across one category (one row); a column total sums all values for one variable (one column). They provide aggregate reference points and let you verify or compute missing entries and find percentages of the whole.

What does each section of a pie chart represent and how do you convert a value to its central angle?

Each sector represents a part's share of the whole (100% = 360 degrees). Central angle = (Part value / Total) x 360 degrees; equivalently, 1% = 3.6 degrees.

What is a caselet in data interpretation and how does it differ from a table or chart?

A caselet presents data in paragraph (text) form rather than a table or graph. The solver must extract the relevant numbers and relationships from the prose before calculating, so careful reading is essential.

In a line graph showing a trend over time, how do you identify the period of maximum increase?

Find the segment between two consecutive points with the steepest upward slope, i.e., the largest positive difference in values between consecutive time points; that segment shows the maximum increase.

What is the percentage-to-fraction shortcut for common values like 12.5%, 16.66%, and 33.33%?

12.5% = 1/8; 16.66% = 1/6; 20% = 1/5; 25% = 1/4; 33.33% = 1/3; 50% = 1/2. Memorizing these speeds up data interpretation calculations.

What is the quick technique to compare two fractions a/b and c/d without finding a common denominator?

Cross-multiply: compare a x d with b x c. If a x d > b x c then a/b > c/d; if smaller, then a/b < c/d (valid for positive denominators).

What is the approximation technique for quickly estimating answers in calculation-heavy questions?

Round numbers to convenient values (nearest 10, 100, or simple fractions), perform the easy calculation, and select the closest option. Useful when answer choices are far apart.

What are the identities for (a + b) squared, (a - b) squared, and a squared minus b squared?

(a+b)^2 = a^2 + 2ab + b^2; (a-b)^2 = a^2 - 2ab + b^2; a^2 - b^2 = (a+b)(a-b).

What is the quadratic formula for solving ax^2 + bx + c = 0?

x = [-b plus or minus the square root of (b^2 - 4ac)] / (2a), where a is not 0. The term b^2 - 4ac is the discriminant.

What does the discriminant (b^2 - 4ac) of a quadratic equation tell you about its roots?

If b^2 - 4ac > 0, two distinct real roots; if = 0, two equal real roots; if < 0, no real roots (roots are complex).

For a quadratic ax^2 + bx + c = 0, what are the sum and product of the roots?

Sum of roots = -b/a; Product of roots = c/a.

What is the method to solve a pair of linear equations in two variables?

Use substitution (solve one equation for a variable and substitute) or elimination (add/subtract equations to remove one variable). Both yield the unique values of x and y where the lines intersect.

What is the sum of the interior angles of a triangle, and what is the Pythagorean theorem?

The interior angles of a triangle sum to 180 degrees. Pythagorean theorem: in a right triangle, (hypotenuse)^2 = (base)^2 + (height)^2.

How do you classify triangles by their sides?

Equilateral: all three sides equal (all angles 60 degrees). Isosceles: two sides equal. Scalene: all three sides different.

What is the sum of the interior angles of a polygon with n sides?

Sum of interior angles = (n - 2) x 180 degrees. For example, a quadrilateral (n=4) sums to 360 degrees.

What are the formulas for the area and circumference of a circle of radius r?

Area = pi x r^2; Circumference = 2 x pi x r. Diameter = 2r.

What are the area formulas for a triangle, rectangle, and trapezium?

Triangle: (1/2) x base x height. Rectangle: length x breadth. Trapezium: (1/2) x (sum of parallel sides) x height.

What are the volume and total surface area of a cube and a cuboid?

Cube: Volume = a^3, Total surface area = 6a^2. Cuboid: Volume = l x b x h, Total surface area = 2(lb + bh + hl).

What are the volume and curved surface area of a cylinder of radius r and height h?

Volume = pi x r^2 x h; Curved surface area = 2 x pi x r x h; Total surface area = 2 x pi x r x (r + h).

What is the difference between a permutation and a combination?

A permutation is an arrangement where order matters (nPr = n! / (n-r)!). A combination is a selection where order does not matter (nCr = n! / [r! x (n-r)!]).

What is the fundamental counting principle (multiplication rule)?

If one event can occur in m ways and a second independent event in n ways, then both events can occur in m x n ways. This extends to any number of successive independent choices.

What is the basic formula for the probability of an event?

Probability = (Number of favourable outcomes) / (Total number of possible outcomes). The value always lies between 0 (impossible) and 1 (certain).

What is the probability of the complement of an event, and the addition rule for mutually exclusive events?

P(not A) = 1 - P(A). For mutually exclusive events A and B (cannot occur together): P(A or B) = P(A) + P(B).