DU LLB Entrance Quantitative and Numerical Aptitude Syllabus

How does compound interest differ from simple interest for the same P, R, and T (T > 1)?

Compound interest is always greater than simple interest (for T > 1) because interest is earned on accumulated interest as well as on the principal.

For 2 years, what is the difference between compound and simple interest in terms of P and R?

Difference = P x (R/100)^2, when interest is compounded annually.

In a partnership, how are profits shared when partners invest different amounts for different time periods?

Profits are shared in the ratio of each partner's (investment x time). For partners A and B: profit ratio = (A's capital x months) : (B's capital x months).

What is the alligation rule used in mixture problems?

Alligation gives the ratio in which two ingredients at different prices are mixed: (Quantity cheaper)/(Quantity dearer) = (Price dearer - Mean price)/(Mean price - Price cheaper).

A vessel has milk and water in ratio 3:1. If total is 40 litres, how much water is present?

Water = 40 x (1/4) = 10 litres, since the ratio 3:1 means 4 parts total and water is 1 part.

If A can do a piece of work in n days, what fraction of the work does A do in one day?

A does 1/n of the work in one day.

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

Together they take (x y) / (x + y) days, because their combined one-day work is 1/x + 1/y.

State the basic relationship between speed, distance, and time.

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

How do you convert a speed from km/hr to m/s?

Multiply by 5/18. For example, 36 km/hr = 36 x 5/18 = 10 m/s.

What is the formula for average speed when equal distances are covered at speeds x and y?

Average speed = 2xy / (x + y), the harmonic mean of the two speeds.

What total distance does a train of length L cover when crossing a platform of length P?

It covers (L + P), the sum of the train's length and the platform's length; time = (L + P) / speed.

How long does a train of length L take to cross a stationary pole or man?

Time = L / speed, since it only needs to cover its own length to pass a point object.

Two trains of lengths L1 and L2 move in opposite directions at speeds u and v. What is the time to cross each other?

Time = (L1 + L2) / (u + v), because relative speed in opposite directions is the sum of the speeds.

In a race, what is meant by 'A beats B by 20 metres'?

It means when A finishes the race, B is still 20 metres behind the finishing line, i.e. A has run the full distance while B has run (distance - 20).

What is the algebraic identity for (a + b)^2 and (a - b)^2?

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

State the identity for a^2 - b^2 and a^3 + b^3.

a^2 - b^2 = (a + b)(a - b); a^3 + b^3 = (a + b)(a^2 - ab + b^2).

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

x = [-b ± sqrt(b^2 - 4ac)] / (2a), where b^2 - 4ac is the discriminant.

For 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 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.

State the area of a triangle given base b and height h, and Heron's formula.

Area = (1/2) x b x h. By Heron's formula, Area = sqrt[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2 is the semi-perimeter.

What is the Pythagorean theorem for a right-angled triangle?

In a right triangle, hypotenuse^2 = base^2 + height^2 (the square on the hypotenuse equals the sum of squares on the other two sides).

Give the formulas for the volume and total surface area of a cube of side a.

Volume = a^3; Total surface area = 6a^2.

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

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

What is the formula for the number of permutations of n distinct objects taken r at a time?

nPr = n! / (n - r)!.

What is the formula for the number of combinations of n distinct objects taken r at a time?

nCr = n! / [r! (n - r)!].

How do permutations and combinations differ conceptually?

Permutations count arrangements where order matters; combinations count selections where order does not matter. nPr = nCr x r!.

State the basic definition of the probability of an event.

Probability = (number of favourable outcomes) / (total number of equally likely outcomes), a value between 0 and 1.

In a Tables/Charts data interpretation question, what is the first step before calculating?

Carefully read the title, units, row and column headings (or axis labels) to understand exactly what data is presented and any footnotes, before doing any calculation.

In a pie chart, how is each sector's value related to its central angle?

Each component's share equals (its central angle / 360) x total; equivalently central angle = (component value / total) x 360 degrees.

In data sufficiency questions, what does it mean if 'either statement alone is sufficient'?

It means Statement 1 alone answers the question AND Statement 2 alone answers it independently; the data from each statement on its own is enough, so the combined answer is 'either alone is sufficient.'