MH CET MBA Quantitative Aptitude Flashcards

24 sample cards from the Quantitative Aptitude deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. What does the discriminant D = b^2 - 4ac tell you about the nature of quadratic roots?

   D>0: two distinct real roots; D=0: two equal real roots; D<0: two complex (no real) roots.

2. State the three basic laws of indices (exponents).

   a^m x a^n = a^(m+n); a^m / a^n = a^(m-n); (a^m)^n = a^(mn). Also a^0 = 1 and a^(-n) = 1/a^n.

3. What is the definition of a logarithm, and state the product and power rules.

   If a^x = N then log_a(N) = x. Rules: log(mn) = log m + log n; log(m^p) = p log m; log(m/n) = log m - log n.

4. How do you rationalize the denominator of a surd like 1/(sqrt(a) - sqrt(b))?

   Multiply numerator and denominator by the conjugate (sqrt(a) + sqrt(b)), giving (sqrt(a)+sqrt(b))/(a-b).

5. When multiplying or dividing both sides of an inequality by a negative number, what must you do?

   Reverse (flip) the direction of the inequality sign.

6. For an Arithmetic Progression with first term a and common difference d, give the nth term and sum of n terms.

   nth term = a + (n-1)d; Sum S_n = (n/2)[2a + (n-1)d] = (n/2)(first term + last term).

7. For a Geometric Progression with first term a and common ratio r, give the nth term and the sum of n terms (r ≠ 1).

   nth term = a r^(n-1); Sum S_n = a(r^n - 1)/(r - 1). Infinite sum (|r|<1) = a/(1 - r).

8. What are the sum of the first n natural numbers and the sum of their squares?

   1+2+...+n = n(n+1)/2; 1^2+2^2+...+n^2 = n(n+1)(2n+1)/6.

9. What is the BODMAS/order-of-operations rule used in simplification?

   Brackets, Orders (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).

10. What is the sum of the interior angles of a triangle, and what is the exterior angle property?

    Interior angles sum to 180 degrees; an exterior angle equals the sum of the two opposite (remote) interior angles.

11. State the Pythagoras theorem for a right-angled triangle.

    In a right triangle, (hypotenuse)^2 = (base)^2 + (perpendicular)^2.

12. What is the relationship between a central angle and an inscribed angle subtending the same arc of a circle?

    The central angle is twice the inscribed (angle at circumference) angle subtending the same arc.

13. What is the sum of the interior angles of an n-sided polygon, and the sum of its exterior angles?

    Sum of interior angles = (n - 2) x 180 degrees; sum of exterior angles is always 360 degrees.

14. What is the distance formula between two points (x1, y1) and (x2, y2)?

    Distance = sqrt[(x2 - x1)^2 + (y2 - y1)^2].

15. Give the midpoint formula and the slope formula for two points (x1,y1) and (x2,y2).

    Midpoint = ((x1+x2)/2, (y1+y2)/2); Slope m = (y2 - y1)/(x2 - x1).

16. State the area and perimeter/circumference formulas for a circle and a rectangle.

    Circle: area = pi r^2, circumference = 2 pi r. Rectangle: area = length x breadth, perimeter = 2(length + breadth).

17. What is the area of a triangle given base and height, and using Heron's formula?

    Area = (1/2) x base x height; Heron's: Area = sqrt[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2.

18. Give the volume and total surface area of a cube and a sphere.

    Cube: volume = a^3, TSA = 6a^2. Sphere: volume = (4/3) pi r^3, surface area = 4 pi r^2.

19. Give the volume, curved surface area, and total surface area of a cylinder of radius r and height h.

    Volume = pi r^2 h; CSA = 2 pi r h; TSA = 2 pi r (h + r).

20. State the divisibility rules for 3, 9, and 11.

    Divisible by 3 if digit sum is divisible by 3; by 9 if digit sum is divisible by 9; by 11 if the difference of alternate digit sums is 0 or a multiple of 11.

21. What is the difference between a Permutation and a Combination, with their formulas?

    Permutation (order matters): nPr = n!/(n-r)!. Combination (order does not matter): nCr = n!/[r!(n-r)!].

22. What is the classical (theoretical) probability of an event, and the range of probability values?

    P(E) = (favorable outcomes)/(total equally likely outcomes); 0 <= P(E) <= 1, and P(not E) = 1 - P(E).

23. State the inclusion-exclusion (Venn) formula for the union of two sets, n(A union B).

    n(A union B) = n(A) + n(B) - n(A intersection B).

24. In clock problems, how many degrees do the hour hand and minute hand move per minute, and when are the hands at right angles?

    Minute hand moves 6 degrees/min, hour hand 0.5 degrees/min (relative gain 5.5 degrees/min); the hands are perpendicular (90 degrees) 22 times in 12 hours, when the relative angle is 90 degrees.

What this deck covers

Quantitative Aptitude flashcards FAQ