Download App

STD 11 - basic of algoritham — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - basic of algoritham4 Marks
MCQ
The equation ${4^{({x^2} + 2)}} - {9.2^{({x^2} + 2)}} + 8 = 0$ has the solution
  • A
    $x = 1$
  • B
    $x = - 2$
  • C
    $x = \sqrt 2 $
  • ✓
    (a) and (b) both
✓

Answer

Correct option: D.
(a) and (b) both
d
(d) ${4^{({x^2} + 2)}} - {9.2^{({x^2} + 2)}} + 8 = 0$

$ \Rightarrow {\left( {{2^{({x^2} + 2)}}} \right)^2} - {9.2^{({x^2} + 2)}} + 8 = 0$

Put ${2^{({x^2} + 2)}}^2 = y$. Then ${y^2} - 9y + 8 = 0$, which gives $y = 8,y = 1$.

when $y = 8\,\, \Rightarrow \,\,{2^{{x^2} + 2}} = 8$ ==> ${2^{{x^2} + 2}} = {2^3}$ ==> ${x^2} + 2 = 3$

==> ${x^2} = 1$ ==>$x = 1, - 1$.

when $y = 1$ ==> ${2^{{x^2} + 2}} = 1$ ==> ${2^{{x^2} + 2}} = {2^o}$

==> ${x^2} + 2 = 0$ ==>${x^2} = - 2$, which is not possible.

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

Let $\mathrm{f}: R \rightarrow R$ and $\mathrm{g}: R \rightarrow R$ be defined as $f(x)=\left\{\begin{array}{lll}\log _e x & , & x>0 \\ e^{-x} & , & x \leq 0\end{array}\right.$ and $g(x)=\left\{\begin{array}{lll} x & , & x \geq 0 \\ e^{x} & , & x <  0\end{array}\right.$ Then $gof:R \to R$ is $. . . . $
→
Let $x$ and $y$ be distinct integers where $1 \leq x \leq 25$ and $1 \leq y \leq 25$. Then, the number of ways of choosing $x$ and $y$, such that $x + y$ is divisible by $5$ , is $.........$.
→
If coefficients of $2^{nd}$, $3^{rd}$ and $4^{th}$ terms in the binomial expansion of ${(1 + x)^n}$ are in $A.P.$, then ${n^2} - 9n$ is equal to
→
$\tan 20^\circ \tan 40^\circ \tan 60^\circ \tan 80^\circ = $
→
Let the eleven letters $A,B.....,K$ denote an arbitrary permutation of the integers $(1, 2,.....11)$, then $(A - 1)(B - 2)(C - 3).....(K - 11)$
→
If $n$ positive integers are taken at random and multiplied together, the probability that the last digit of the product is $2, 4, 6$ or $8$, is
→
The conditions that $ax + by + c = 0$ is tangent to the parabola $y^2 = 4ax$, is
→
A bag has $13$ red, $14$ green and $15$ black balls. The probability of getting exactly $2$ blacks on pulling out $4$ balls is ${P_1}$. Now the number of each colour ball is doubled and $8$ balls are pulled out. The probability of getting exactly $4$ blacks is ${P_2}.$ Then
→
The value of $tan^{-1} (\frac{sin2 -1}{cos2})$ is equal to:-
→
A bag contains $4$ white, $5$ red and $6$ green balls. Three balls are picked up randomly. The probability that a white, a red and a green ball is drawn is
→