Download App

Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
The values of $a$ and $b$ such that the function defined by
$f(x)=\left\{\begin{array}{cl}7 & , \text { if } x \leq 2 \\ax+b & , \text { if } 2 < x < 9 \text { is continuous on its } \\21 & , \text { if } x \geq 9\end{array}\right.$
domain are
  • A
    a = 3, b = 2
  • ✓
    a = 2, b = 3
  • C
    a = 7, b = 9
  • D
    None of these
✓

Answer

Correct option: B.
a = 2, b = 3
(B)
Since $f (x)$ is continuous on its domain.
$\therefore $ it is continuous at $x=2$ and $x=9$.
$\therefore \lim _{x \rightarrow 2^{+}} f (x)=\lim _{x \rightarrow 2^{-}} f (x)$
$\Rightarrow \lim _{x \rightarrow 2^{+}}( ax + b )=7$
$\Rightarrow 2 a+b=7$ $\quad\ldots(i)$
Also, $\lim _{x \rightarrow 9^{-}} f (x)=\lim _{x \rightarrow 9^{+}} f (x)$
$\Rightarrow \lim _{x \rightarrow 9^{-}}( ax + b )=21$
$\Rightarrow 9 a+b=21$ $\quad\ldots(ii)$
Solving (i) and (ii), we get $a=2, b=3$

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 "MCQ" from Continuity→Continuity — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

The function $f (x)=\sec \left[\log \left(x+\sqrt{1+x^2}\right)\right]$ is
→
The equation of a line, having inclination 120° with positive direction of X-axis, which is at a distance of 3 units from the origin is
→
There are 3 bags which are known to contain 2 white and 3 black balls; 4 white and 1 black balls and 3 white and 7 black balls respectively. A ball is drawn at random from one of the bags and found to be a black ball. Then the probability that it was drawn from the bag containing the most black balls is
→
If $\tan\alpha=\frac{1-\cos\beta}{\sin\beta},$ then :
→
The equation of the conic with focus at $(1, -1)$ directrix along $x - y + 1 = 0$ and eccentricity $\sqrt2$ is
→
The probability that in a throw of two dice we get, an even sum or sum less than 5 is,
→
The value of $\lim _{x \rightarrow \infty} \frac{1+2+3+\ldots+n}{n^2+100}$ is equal to
→
If $a, b, c$ are in $G.P$. is $2$ and $x, y$ are $AM\ '$s between $a, b$ and $b, c$ respectively, then :
→
The points on the X-axis whose perpendicular distance from the line $\frac{x}{a}+\frac{y}{b}=1$ is a, are
→
The argument of $\frac{1-\text{i}}{1+\text{i}}$ is :
→