# Solved CAT Questions (Algebra) - Set 6

• Q1. (CAT 1991)
A function can sometimes reflect on itself, i.e. if y = f(x), then x = f(y). Both of them retain the same structure and form. Which of the following functions has this property?
(a) y = ( 2x + 3 ) / ( 3x + 4 )
(b) y = ( 2x + 3 ) / ( 3x - 2 )
(c) y = ( 3x + 4 ) / ( 4x - 5 )
(d) None of the above

Q2. (CAT 1991)
What is the value of k for which the following system of equations has no solution:
2x – 8y = 3 and kx +4y = 10
(a) –2
(b) 1
(c) –1
(d) 2

Q3. (CAT 1991)
If y = f(x) and f(x) = (1-x) / (1 + x), which of the following is true?
(a) f (2x) = f (x) – 1
(b) x = f (2y)-1
(c) f (1/x) = f (x)
(d) x = f (y)

Q4. (CAT 1991)
Let Y = minimum of {(x+2), (3-x)}. What is the maximum value of Y for 0 ≤ x ≤ 1
(a) 1.0
(b) 1.5
(c) 3.1
(d) 2.5

Q5. (CAT 1997)

Q6. (CAT 1990)
The roots of the equation ax^2 + 3x + 6 = 0 will be reciprocal to each other if the value of a is
(a) 3
(b) 4
(c) 5
(d) 6

Q7. (CAT 2003 Retest)
The number of roots common between the two equations x^3 + 3x^2 + 4x + 5 = 0 and x^3 + 2x^2 + 7x + 3 = 0 is:
(1) 0
(2) 1
(3) 2
(4) 3

Q8. (CAT 2001)
Ujakar and Keshab attempted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4, 3). Keshab made a mistake in writing down the coefficient of x. He got the root as (3, 2). What will be the exact roots of the original quadratic equation?
(1) (6, 1)
(2) (–3, –4)
(3) (4, 3)
(4) (–4, –3)

Q9. (CAT 2003 Retest)
The number of non negative real roots of 2^x - 1 - 1 = 0 is
a) 0
b) 1
c) 2
d) 3

Q10. (CAT 2003 Leaked)
When the curves y = logx (base 10) and y = 1/x are drawn in the X-Y plane, how many times do they intersect for values of x ≥ 1
a) Never
b) Once
c) Twice
d) More than twice

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