Change set

Pick exam & year, then Go.

Question map
Not attempted Correct Incorrect ★ Bookmarked
Loading…
Q34 (CISF/2025) Science & Technology › Basic Science (Physics, Chemistry, Biology)

The rate of change of = with respect to x, where x varies from x1 to x2, is ;

Explanation

The average rate of change of a function f(x) as x varies from x1 to x2 is defined by the formula [f(x2) - f(x1)] / (x2 - x1). Although the question contains a typo ("="), the provided options indicate that the function in question is f(x) = 1/x.

By substituting f(x) = 1/x into the rate of change formula:

  • The change in function value (numerator) is: 1/x2 - 1/x1 = (x1 - x2) / (x1 × x2).
  • The change in x (denominator) is: x2 - x1.

Dividing the numerator by the denominator: [(x1 - x2) / (x1 × x2)] / (x2 - x1). Since (x1 - x2) is equal to -(x2 - x1), the expression simplifies to -1 / (x1 × x2). This corresponds to option B.

✓ Thank you! We'll review this.

SIMILAR QUESTIONS

IAS · 1996 · Q146 Relevance score: -2.57

The average of X1, X2 and X3 is 14. Twice the sum of X2 and X3 is 30. What is the value of X1 ?

NDA-I · 2011 · Q2 Relevance score: -3.82

A body initially at rest is acted upon by a constant force. The rate of change of its kinetic energy varies :

CDS-I · 2016 · Q3 Relevance score: -4.57

The rate of change of momentum of a body is equal to the resultant:

NDA-I · 2013 · Q4 Relevance score: -5.45

An object is undergoing a non-accelerated motion. Its rate of change in momentum is

CAPF · 2016 · Q30 Relevance score: -5.76

Which one of the following inequalities is always true for positive real numbers x,y?