Ok, as you want the sample algebra questions of Common Admission Test CAT exam so here I am providing you.

CAT exam sample algebra questions

Q 1. Find the positive integer solutions for an equation.

Q 2. Identify the coefficients of (x +y) ^ n; when x, y are equal to 1. (Application of Binomial Theorem)

Q 3. When is the first half of the coefficients the same as the second half, when n is odd?
This problem was, in reality, presented in the garb of a permutation-combination question. Of course, this variety did not recur in the CAT.

Q 4. (a, b) is a function equal to HCF (a, b). If there are “n” numbers, how many times do we have to operate on ‘h’ to find the HCF of all the numbers?
This question is nothing but a linguistic puzzle, if one knows, to begin with, how to find the HCF of ‘n’ numbers.

Q 5. If ‘An’ indicates the nth term of the series…A1 was given, A (n+1) was given in terms of An. Find out A100.
This question type has been repeated very often in the CAT. One could have comfortably done this question using the given options as enough clues were there in the choices given.

Q 6. You are given a series with n terms. You have to find the sum of these terms.
The series was such that every term got split into 2 terms… and when all these terms were added, the entire summation came to a couple of terms.

Q 7. User defined functions: @ (A, B) = avg (A, B)….. 3 such definitions were given, followed by 2 questions based on them. In many such algebra questions, you are tested on the number properties and a bit of logical thinking, too.

Q 8. If f(x,y,z) = min ( max(x,y), max (y,z), max(x,z)) g(x,y,z) = max(min(x,y), min(y,z), min(x,z))…….
All these can be simplified by using the properties of numbers and a little Arithmetic.

Q 9. F(0,y) = y+1 ; f(x+1,0) = f(x,1) ; f(x+1,y+1) = f(x,f(x+1,y))…. You are to find f(1,2) Some number play on your part is expected in this question.
Q 10. The equations x^2 + y^2 = 1 and |x-y|=0.2 are given. You have to find out the max value of |x| + |y|.

Q 11. Find the area enclosed by 3 modulus graphs |x+y| = 1; |x| = 1 and |y| = 1.