Download App

STD 12 - 1. relation and function — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 1. relation and function4 Marks
MCQ
$f : R \to R$ is defined as

$f(x) = \left\{ {\begin{array}{*{20}{c}}
{{x^2} + 2mx - 1\,,}&{x \leq 0}\\
{mx - 1\,\,\,\,\,\,\,\,\,\,\,\,\,,}&{x > 0}
\end{array}} \right.$

 If $f (x)$ is one-one then the set of values of $'m'$ is

  • ✓
    $( - \infty ,0)$
  • B
    $\left( { - \infty ,0} \right]$
  • C
    $\left( {0,\infty } \right)$
  • D
    $\left[ {0,\infty } \right)$
✓

Answer

Correct option: A.
$( - \infty ,0)$
a
For $f$ to be one - one vertex must lie on or to the right of $y -$ axis.

$\therefore  - m \ge 0 \Rightarrow m \le 0$

for $m = 0,\,\,f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}
{{x^2} - 1,}&{x \le 0}\\
{ - 1,}&{x > 0}
\end{array}} \right.$           which is not

one - one

$\therefore m \in \left( { - \infty ,0} \right)$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into $n $determinants, where $ n$  has the value
→
If $x + y + z = {180^o},$ then $\cos 2x + \cos 2y - \cos 2z$ is equal to
→
The expression ${[x + {({x^3} - 1)^{1/2}}]^5} + {[x - {({x^3} - 1)^{1/2}}]^5}$ is a polynomial of degree
→
If $y =\frac{{{x^4} - {x^2} + 1}}{{{x^2} + \sqrt 3 x + 1}}$ and $\frac{{dy}}{{dx}} = ax + b$ then the value of $a + b$ is equal to
→
If the point of intersections of the ellipse $\frac{ x ^{2}}{16}+\frac{ y ^{2}}{ b ^{2}}=1$ and the circle $x ^{2}+ y ^{2}=4 b , b > 4$ lie on the curve $y^{2}=3 x^{2},$ then $b$ is equal to:
→
Fifteen football players of a club-team are given $15$ T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least $3$ players pick the correct $T$-shirt is
→
In a tournament there are twelve players $P_1, P_2, P_3,........ P_{12}$ and divided into six pairs at random. From each game a winner is decided on the basis of game played between the two players of the pair. Assuming each player is of equal strength, then the probability that exactly one out of $P_1$ and $P_2$ is among the losers is
→
Number of values of $m \in N$ for which $y = e^{mx} $ is a solution of the differential equation $D^3y - 3D^2y - 4Dy + 12y = 0,$ is
→
The value of the integral $\int_{ - \pi }^\pi {{{(\cos ax - \sin bx)}^2}dx} $, ($a$ and $b$ are integer) is
→
A line $l$ passing through the origin and perpendicular to the lines

${l_1} = \left( {3 + t} \right)\hat i + \left( { - 1 + 2t} \right)\hat j + \left( {4 + 2t} \right)\hat k,\, - \infty  < t < \infty $

${l_2} = \left( {3 + 2s} \right)\hat i + \left( {3 + 2s} \right)\hat j + \left( {2 + s} \right)\hat k,\, - \infty  < s < \infty $

Statement $1$ : Line $l$ and $l_2$ are coplaner lines

Statement $2$ : Line $l$ and $l_2$ are intersecting lines

→