Let R and let the equation E be | x |^2-2| x |+| -3|=0. Then the … - Vidyadip

MCQ

Let $\lambda \in R$ and let the equation $E$ be $| x |^2-2| x |+|\lambda-3|=0$. Then the largest element in the set $S =$ $\{ x +\lambda: x$ is an integer solution of $E \}$ is $..........$

A
$4$
B
$3$
✓
$5$
D
$2$

✓

Answer

Correct option: C.

$5$

c
$| x |^2-2| x |+|\lambda-3|=0$

$| x |^2-2| x |+|\lambda-3|-1=0$

$(| x |-1)^2+|\lambda-3|=1$

At $\lambda=3, x =0$ and 2 ,

at $\lambda=4$ or 2, then

$x =1 \text { or }-1$

So maximum value of $x+\lambda=5$

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 4.2 Quadratic equations and inequations→4.2 Quadratic equations and inequations — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {1 - {x^2}} - \sqrt {1 + {x^2}} }}{{{x^2}}}$ is equal to

Five numbers are in $A.P.$, whose sum is $25$ and product is $2520 .$ If one of these five numbers is $-\frac{1}{2},$ then the greatest number amongst them is

If ${^\text{m}}\text{C}_{\text{1}}={^\text{n}}\text{C}_{\text{2}},$ is then:

Find the sum to n terms of the series whose nth term is n (n-2).

$\sec {50^o} + \tan {50^o}$ is equal to

The mean of two samples of size $200$ and $300$ were found to be $25, 10$ respectively their $S.D.$ is $3$ and $4$ respectively then variance of combined sample of size $500$ is :-

If the circles $(x+1)^2+(y+2)^2=r^2$ and $x^2+y^2-4 x-4 y+4=0$ intersect at exactly two distinct points, then

The smallest value of ${x^2} - 3x + 3$ in the interval $( - 3,\,3/2)$ is

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after:

If $\left| {\,a\,{{\sin }^2}\theta + b\sin \theta \cos \theta + c\,{{\cos }^2}\theta - \frac{1}{2}(a + c)\,} \right|\, \le \frac{1}{2}k,$ then ${k^2}$ is equal to