Download App

Limits and Derivatives — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSLimits and Derivatives1 Mark
MCQ
Choose the correct answer.
$\lim\limits_{\text{x} \rightarrow0}\frac{\text{x}^{\text{m}}-1}{\text{x}^{\text{n}}-1}$ is equal to:
  • A
    $1$ 
  • B
    $\frac{\text{m}}{\text{n}}$ 
  • C
    $\frac{-\text{m}}{\text{n}}$ 
  • D
    $\text{m}^{2}\text{n}^{2}$ 
✓

Answer

  1. $\frac{\text{m}}{\text{n}}$

Solution:

Given $\lim\limits_{\text{x} \rightarrow 1}\frac{\text{x}^{\text{m}}-1}{\text{x}^{\text{n}}-1}=\lim\limits_{\text{x} \rightarrow 1}\frac{\frac{\text{x}^{\text{m}-(1)^\text{m}}}{\text{x}-1}}{\frac{\text{x}^{\text{n}-(1)^{\text{n}}}}{\text{x}-1}}$ 

$=\frac{\text{m}(1)^{\text{m}-1}}{\text{n}(1)^{\text{n}-1}}=\frac{\text{m}}{\text{n}}$

$=\frac{\text{m}}{\text{n}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Limits and Derivatives→Limits and Derivatives — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

The inclination of the line x - y + 3 = 0 with the positive direction of x-axis is:

→
If  $\omega $ is a complex cube root of unity, then for positive integral value of$n$, the product of $\omega .{{\omega }^{2}}.{{\omega }^{3}}........{{\omega }^{n}}$, will be [Roorkee 1991]
→
In the expansion of (a + b)n, if n is odd then the number of middle term is:
→
If 9(x) = 3x4 - 5x2 +, then value of f(x - 1) is:
→
General solution of $\tan5\text{x}=\cot2\text{x}$  is:

  1. $\frac{\text{n}\pi}{7}+\frac{\pi}{2},\ \text{n}\in\text{Z}$

  2. $\text{x}=\frac{\text{n}\pi}{7}+\frac{\pi}{3},\ \text{n}\in\text{Z}$

  3. $\text{x}=\frac{\text{n}\pi}{7}+\frac{\pi}{14},\ \text{n}\in\text{Z}$

  4. $\text{x}=\frac{\text{n}\pi}{7}=\frac{\pi}{14},\ \text{n}\in\text{Z}$

→
The product of r consecutive positive integers is divisible by:
→
1 + 2 + 3 + 4 or 10 is a series?
→
The value of (8)1/3 is [RPET 2003]
→
The probability of any sure event is :
→
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{ae}^\text{x}+\text{b}\cos\text{x}+\text{c.e}^\text{x}}{\sin^2\text{x}}=4\text{ then}\text{ b:}$
→