﻿ If the tangent tothe curve, y = f(x) = xlogex, (x > 0) at a point (c, f(c)) is parallel to the line-segment joining the points (1, 0) and (e, e), then c is equal to : | Relations and Functions

## Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

## Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

## Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

# Relations and Functions

#### Multiple Choice Questions

101.

Suppose f(x) = x(x + 3)(x - 2), x $\in$ [- 1, 4]. Then, a value of c in (- 1, 4) satisfying f'(c) = 10 is

• 2

• $\frac{5}{2}$

• 3

• $\frac{7}{2}$

102.

103.

For the function f(x) = (x - 1)(x - 2) defined on [0, ½] the value of c satisfying Lagrange's mean value theorem is

• $\frac{1}{5}$

• $\frac{1}{3}$

• $\frac{1}{7}$

• $\frac{1}{4}$

104.

• $\frac{\sqrt{17}}{2}$

105.

Let f(x) be a quadratic polynomial such that f( – 1) + f(2) = 0. If one of the roots of f(x) = 0 is 3, then its other root lies in :

• (1, 3)

• ( - 1, 0)

• ( - 3, - 1)

• (0, 1)