The setting and the form of question paper for CAT-Quant. is not a routine matter, the types of questions and the format keep changing with every session.
There are certain topics like Algebra, Functions and Geometry which are repeatedly tested in the CAT Questions.
Algebra includes Polynomials, Progressions and Inequalities.
Let's pick up Polynomials.
In polynomials the stress is on Quadratics or Quadratic Inequalities.
Consider a Quadratic Polynomial f(x)= a x^2 +b x + c
It represents a Parabolic Curve;
If a> 0, then the Convexity is downwards with minimum value at x = -b/(2a)
If a<0,>Convexity is upwards with maximum value at x = -b/(2a)
Taking D = b^2 -4ac,
(1) If D <>, the polynomial has no real zeroes
(2) If D = 0, the polynomial has two equal zeroes , both equal to -b /(2a)
(3) If D > 0, it has two real and unequal zeroes
This shows the kinds of results from such an equation.
You may put any CAT Questions on Algebra as a comment to this post and get your Doubts clarified
Thank you God
2 years ago
3 comments:
Please solve this question
If f(x)= 3x^2 –x -4 ,
then
(i) Find the interval where f(x)>0
(ii)Find the nature of zeroes
(iii)Find the zeroes of f(x),if any.
(iv)Find the interval where f(x)<0
Thanks in advance
The roots of the equation (x-a)(x-b)+ (x-b)(x-c)+(x-c)(x-a)=0 are
(a) Unreal
(b) Real and equal
(c) Real and unequal
(d) None of these
The roots of the equation (x-a)(x-b)+ (x-b)(x-c)+(x-c)(x-a)=0 are, a, b, c are different
(a) Unreal
(b) Real and equal
(c) Real and unequal
(d) None of these
Solution:-
D=4(a+b+c)^2 -12(ab+bc+ca)
=2[ (a-b)^2 +(b-c)^2 +(c-a)^2]>0
Roots are real and different
Equal if a=b=c
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