Download App

STD 12 - 1. relation and function — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 1. relation and function1 Mark
MCQ
Let $f(x)=\left\{\begin{array}{l}x-1, x \text { is even, } \\ 2 x, x \text { is odd, }\end{array}\right.$. If for some $a \in N, f(f(f(a)))=21$, then $\lim _{x \rightarrow a^{-}}\left\{\frac{|x|^3}{a}-\left[\frac{x}{a}\right]\right\}$, where $[t]$ denotes the greatest integer less than or equal to $t$, is equal to :
  • A
    $121$
  • ✓
    $144$
  • C
    $169$
  • D
    $225$
✓

Answer

Correct option: B.
$144$
b
$f(x)=\left\{\begin{array}{cc}x-1 ; & x=\text { even } \\ 2 x ; & x=\text { odd }\end{array}\right.$
$ f(f(\mathrm{a})))=21 $
$ \text { C-1: If } a=\text { even } $
$ f(\mathrm{a})=\mathrm{a}-1=\text { odd } $
$ f(a))=2(a-1)=\text { even } $
$ f(f(f(a)))=2 a-3=21 \Rightarrow a=12 $
$ \text { C-2: If } a=\text { odd } $
$ f(\mathrm{a})=2 \mathrm{a}=\text { even } $
$ f(f(\mathrm{a}))=2 \mathrm{a}-1=\text { odd } $
$ f(f(f(a)))=4 a-2=21 \text { (Not possible) } $
Hence $\mathrm{a}=12$
Now
$ \lim _{x \rightarrow 12^{-}}\left(\frac{|x|^3}{12}-\left[\frac{x}{12}\right]\right) $
$ =\lim _{x \rightarrow 12^{-}} \frac{|x|^3}{12}-\lim _{x \rightarrow 12^{-}}\left[\frac{x}{12}\right] $
$ =144-0=144 .$

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 STD 12 - 1. relation and function→STD 12 - 1. relation and function — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If the rate of change of area of a circle is equal to the rate of change of its diameter, then its radius is equal to:
→
The length of the perpendicular drawn from the point $(4, -7, 3)$ on the $y-$axis is:
→
If $f(x)=|x|+|x-2|$, then
→
Let $f ( x )= x \cdot\left[\frac{ x }{2}\right],$ for $-10< x <10,$ where $[ t ]$ denotes the greatest integer function. Then the number of points of discontinuity of $f$ is equal to
→
If $a,b$ and $c$ are perpendicular to $b + c,c + a$and $a + b$ respectively and if $|a + b| = 6,|b + c| = 8$ and $|c + a| = 10$ then $|a + b + c| = $
→
The inverse of the function $f(x) = \frac{{{e^x} - {e^{ - x}}}}{{{e^x} + {e^{ - x}}}} + 2$ is given by
→
The area $($sq. units$)$ bounded by the parabola $y^2 = 4ax$ and the line $x = a$ and $x = 4a$ is:
→
Let $R= \{(3, 3) (5, 5), (9, 9), (12, 12), (5, 12), (3, 9), (3, 12), (3, 5)\}$ be a relation on the set $A= \{3, 5, 9, 12\}.$ Then, $R$ is
→
If $a = 3i - j + 2k,$ $b = 2i + j - k$ and $c = i - 2j + 2k,$then $(a \times b) \times c$ is equal to
→
Simplify $ {\cot ^{ - 1}}\frac{1}{{\sqrt {{\text{x}^2} - 1} }} $ for $\text{ x} < - 1$:
→