Name of the Organisation : University Of Library - Cochin University of Science and Technology
Name of the Exam : Common Admission Test (CAT)
Document Type : Sample Question Paper
Year: 2016
Subject: Mathematics (FINAL)

Website : www.library.cusat.ac.in/cat/2016/
Download Model/Sample Question Papers: http://www.indianjobtalks.com/upload...ATHEMATICS.pdf

CAT PG Mathematics Model Question Paper :
1. The system of equations
A. has no solution
B. has one and only one solution
C. has infinite number of solutions
D. None of the above

2. The eigen values of the matrix
A. 1,1,1
B. 2,2,2
C. –2, –2, –2
D. –1, –1, –1

3. The rank of the matrix
A. 5
B. 4
C. 3
D. 2

4. The algebraic equation xn + yn = zn has no integer solution when
A. n > 2
B. n < 2
C. n = 0
D. n < 2

5. Which of the function f : R -> R is one-one and onto?
A. f (x) = x3 + 2
B. f (x) = sin x
C. f (x) = cos x
D. f x() = x4 - x2

6. Let P(x) be a non-constant polynomial such that P(n) = P(n) for all n-N . Then P'(0) is
A. –1
B. 1
C. 0
D. –2

7. If A is any non-identity 3?3matrix such that A2 ? A, then A is
A. Singular
B. Non singular
C. Regular
D. None of the above

8. If every cross-section of a bounded surface in three dimensions is a circle, then the surface must be a
A. cylinder
B. sphere
C. cone
D. third-degree surface

9. For any complex number z,the minimum value of |z| + z - 1 is
A. 1
B. 0
C. 1/2
D. 3/2

10. The number having a recurring decimal representation 1.414141… is
A. real but irrational
B. not real
C. rational
D. neither rational nor real

11. The quadratic function on a single variable attains its maximum value 5 at 3. The function is
A. ax2 - 6ax + 9a + 5, a < 0
B. ax2 - 6ax + 9a + 5, a > 0
C. ax2 + 6ax - 9a + 5, a < 0
D. None of the above

12. Let n be a two digit number. P(n) is the product of the digits of n and S (n) is the sum of the digits of n. If n = P(n) + S (n) then the unit digit of n is
A. 1
B. 5
C. 7
D. 9

13. If 27 3 log x ? log 27, then x is
A. 27
B. 3
C. 327
D. 273

14. If G is a group and for a=G no positive integer m exists such that am = e , then the order of a is
A. finite
B. m
C. m + 1
D. infinite

15. A non-decreasing sequence which is bounded above is
A. divergent
B. convergent
C. oscillating
D. unbounded