Domain & Range — CAT Previous-Year Questions
8 previous-year questions on Domain & Range from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.
Domain & Range · CAT PYQs
f(x) = is negative if and only if
The area of the region satisfying the inequalities |x| - y ≤ 1, y ≥ 0 and y ≤ 1 is
The shortest distance of the point (1/2,1) from the curve y = |x - 1| + |x + 1| is
The graph of y – x against y + x is as shown below. (All graphs in this question are drawn to scale and the same scale has been used on each axis). Then, which of the options given shows the graph of y against x.
Answer the next 2 questions based on the information given below.
Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.
In the X-Y plane, the area of the region bounded by the graph of |x + y| + |x – y| = 4 is
Answer the following question based on the information given below.
New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of projects in which Medha is involved. All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with Medha but without Gyani and 3 projects with Gyani but without Medha. The total number of projects for New Age Consultants is one less than twice the number of projects in which more than one consultant is involved.
When the curves, y = log10 x and y = x−1 are drawn in the X-Y plane, how many times do they intersect for values of x ≥ 1?
Answer the following question based on the information given below.
A city has two perfectly circular and concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR). There are also four (straight line) chord roads from E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR; from W1, the west end point of OR, to S2, the south end point of IR; and from S1, the south end point of OR to E2, the east endpoint of IR. Traffic moves at a constant speed of 30π km/hr on the OR road, 20π km/hr on the IR road, and km/hr on all the chord roads.
The function f(x) = |x − 2| + |2.5 − x| + |3.6 − x|, where x is a real number, attains a minimum at
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?