CAT-2009-Paper

CAT-2009-Paper
Question:-
Option (A)
35
Option (B)
30
Option (C)
20
Option (D)
16
Correct Option:
C
Question Solution:
q ∝ 1/s and s ∝ 1/r
∴ q ∝ r
∴ p ∝ q and q ∝ r, p ∝ r
When q = 3, r = 5
∴ q = 2 => r = 10/3
Ie, when p = 1, r = 10/3
=> r = 20 when p = 6
Question:-
Option (A)
1
Option (B)
2
Option (C)
3
Option (D)
4
Correct Option:
A
Question Solution:
(a2 - ab + b2)/(a2 + ab + b2) = 1/3
∴ 2(a2 + b2)/(-2(ab) = 4/-2
(By componendo-dividendo)
∴ (a2 + b2)/ab = 2
∴ a2 + b2 = 2ab
∴ a2 - 2ab + b2 = 0
∴ (a-b)2 = 0
∴ a = b ∴ a/b = 1
Question:-
Option (A)
(5/3), (5/3)
Option (B)
(5/3), (5/2)
Option (C)
(7/4), (3/2)
Option (D)
Data insufficient
Correct Option:
A
Question Solution:
The point which divides all the medians in the ratio 2:1 is the centroid of the triangle
Centroid of &ΔXYZ = 0 ≡ {(6-3+2)/3}, {(4+5-4)/3}
≡ (5/3), (5/3)
Question:-
Option (A)
12 sq cm
Option (B)
10 sq cm
Option (C)
4 sq cm
Option (D)
6 sq cm
Correct Option:
A
Question Solution:
Since LO is the angle bisector of ∠MLN and the median of MN.
∴ By interior angle bisector theorem,
LM/LN = MO/ON and MO = ON
∴ LM / LN = 1
∴ LM = LN
∴ &ΔLMN is isosceles triangle
&Δ LOM ≡ &ΔLON
∴ ∠ LON = ∠ LOM = 90°
In right angle &ΔLOM, LM = 5, LO = 3
∴ MO = 4
∴ Area of &ΔLMN = (1/2) x MN x LO
= (1/2) x 2 x 4 x 3 = 12sq cm
Question:-
Option (A)
0
Option (B)
1
Option (C)
2
Option (D)
None of these
Correct Option:
A
Question Solution:
an - bn is divisible by (a + b) and (a – b), if n is even.
∴ 774 - 574 is divisible by 12 and 2, and consequently by 4.
Question:-
Option (A)
Rs 2000
Option (B)
Rs 3000
Option (C)
Rs 3600
Option (D)
Rs 4500
Correct Option:
B
Question Solution:
The marked price of bicycle is Rs 5000. Let the cost price be p.
Successive discounts are 10% and 20%
∴ 5000 x 0.9 x 0.8 – 0.2P = P
∴ P = (5000 x 0.72)/1.2
=> P = Rs 3000.