CAT 2012 based questions

1. There are 2 concentric circles. A man runs at speed 60 km/hr from point A on outer circle to B on same circle such that his run is tangent to inner circle for 50 minutes. Find radius of outer circle.

a) 25√2
b) 40
c) 60
d) 30√2

2. Which of the following is the roots of the equation 4x^3− 3x^2 + 4x – 5 =0

(1) -1/√3
(2) -1
(3) 0
(4) 1

3. When the curves y = log10x and y = x–1 are drawn in the x-y plane, how many times do they intersect for values x ≥ 1 ?

1.Never
2. Once
3. Twice
4. More than twice
4. Let f(x) = max (2x + 1, 3 – 4x), where x is any real number. Then the minimum possible value of f(x) is:(1) 1/3   (2) 1/2(3) 2/3   (4) 5/3

5. If  f(x)=-5x ; g(x)=3x-5. Which of the following is true

a)f[g(x)] = g[f(x)]
b)f[g(x)] not equal g[f(x)]
c)f[g(x)] = 0
d)g[f(x)] = 0

6. A person starts from hill top A, goes downhill on car, then along a plain walking and finally climbs to hill top B. He takes a total of 4 hours for the jouney travelling downhill @72kmph, on plains @63kmph and uphill @56kmph. However while returning back, from B to A, he takes 4 hours 40 mins with speeds being same. Find distance AB.
a) 273
b) 427
c) 723
d) 373

7. If (BE)^2 = MPB,

where B, E, M and P are distinct integers. Then M =

a. 2
b. 3
c. 9
d. None

CAT 2012 based question
8. What is the equation of the line that is parallel to the line 3x + 7y = 10 and passes through the point (4, 8 )
7x – 3y = 46
3x + 7y = 44
9x + 21y + 184 = 0
3x + 7y = 68

CAT 2012 questions
9. Equation of a circle is
x^2 + y^2 – 2x – 4y = 4
Where does the point (2,3) lies

a. Within the circle
b. Outside the circle
c. On the curve
d. Not clear

10. The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x ≤ y is:

(1) 7   (2) 13

(3) 14   (4) 18

Solutions for these CAT 2012 based questions…