CAT 2003 Slot 1 — QA Question 45
Each question is followed by two statements, A and B. Answer each question using the following instructions
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
Consider the following two curves in the X-Y plane
y = x3 + x2 + 5
y = x2 + x + 5
Which of the following statements is true for −2 ≤ x ≤ 2?
Answer & solution
- A
The two curves intersect once
- B
The two curves intersect twice
- C
The two curves do not intersect
The two curves intersect thrice
y = x3 + x2 + 5 … (i)
y = x2 + x + 5 … (ii)
Solving (i) and (ii), we get,
x3 + x2 + 5 = x2 + x + 5
x(x2 − 1) = 0
∴ x = 0, 1, −1
∴ All three solutions for (i) and (ii) lie between −2 and 2.
∴ The two curves intersect thrice in the given range.
Hence, option (d).