Practice over 1000+ GATE-level questions from this topic!
Designed to match the latest GATE pattern with topic-wise precision, difficulty tagging, and detailed solutions.
Consider the following equation in a 2-D real-space.
Which of the following statement(s) is/are true.
When 
, the area enclosed by the curve is 
.
When 
tends to 
, the area enclosed by the curve tends to 4.
When tends to 0, the area enclosed by the curve is 1.
When 
, the area enclosed by the curve is 2.
(a) if p = 2
Equation 
This equation represents a circle of radius = 1
(b) if p → ∞ then x1 & x2 ≤ 1 else if any of these values is > 1 then 
or 
so sum cannot be 1
If |x1| < 1 
∴ |x2| = 1 for sum to be 1
If |x2| < 1 
∴ |x1| = 1 for sum to be 1
The shape looks like as shown below,
(c) if 
then 
non-zero values of 
& 
Sum = 2
Hence if x1 ≠ 0 x2 must be zero & vice versa so curve looks like as shown below,
No closed curve exists & area = 0
(d) if P = 1, equation becomes |x1| + |x2| = 1
Curve looks like as shown below
