If _ x 2 (x - 2)( x^2 + (a - 2)x - 2a) ( x^2 - 4x + 4) = 7,then '… - Vidyadip

Question

If $\mathop {\lim }\limits_{x \to 2} \frac{{\tan (x - 2)({x^2} + (a - 2)x - 2a)}}{{({x^2} - 4x + 4)}} = 7$,then $'a'$ is -

✓

Answer

b
$\mathop {\lim }\limits_{x \to 2} \frac{{\tan (x - 2)({x^2} + (a - 2)x - 2a)}}{{{{(x - 2)}^2}}} = 7$

$\Rightarrow a+2=7 \Rightarrow a=5$

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

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

Similar questions

The least positive integral value of $\alpha$, for which the angle between the vectors $\alpha \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \mathrm{k}$ and $\alpha \hat{\mathrm{i}}+2 \alpha \hat{\mathrm{j}}-2 \mathrm{k}$ is acute, is

Let a ray of light passing through the point $(3,10)$ reflects on the line $2 x+y=6$ and the reflected ray passes through the point $(7,2)$. If the equation of the incident ray is $a x+b y+1=0$, then $a ^2+ b ^2+3 ab$ is equal to.

Number of values of $ x \in \left[ {0,2\pi } \right]$ satisfying the equation $cotx - cosx = 1 - cotx. cosx$

The derivative of $f(x) = |x{|^3}$ at $x = 0$ is

Let the area of the region $\left\{(x, y):|2 x-1| \leq y \leq\left|x^2-x\right|, 0 \leq x \leq 1\right\}$ be $A$. Then $(6 A +11)^2$ is equal to $.......$.

$\operatorname{Lim}_{n \rightarrow \infty}\left\{\left(2^{\frac{1}{2}}-2^{\frac{1}{3}}\right)\left(2^{\frac{1}{2}}-2^{\frac{1}{5}}\right) \ldots \ldots\left(2^{\frac{1}{2}}-2^{\frac{1}{2 n+1}}\right)\right\}$ is equal to

If $A = \left[ {\begin{array}{*{20}{c}}{ab}&{{b^2}}\\{ - {a^2}}&{ - ab}\end{array}} \right]$ and ${A^n} = O$, then the minimum value of $n$ is

Let $A=\left[\begin{array}{lll}1 & a & a \\ 0 & 1 & b \\ 0 & 0 & 1\end{array}\right], a, b \in R$. If for some $n \in N$, $A ^{ n }=\left[\begin{array}{ccc}1 & 48 & 2160 \\ 0 & 1 & 96 \\ 0 & 0 & 1\end{array}\right]$ then $n + a + b$ is equal to $\dots\dots$

If $\omega $ is the cube root of unity, then $\left| {\begin{array}{*{20}{c}}1&\omega &{{\omega ^2}}\\\omega &{{\omega ^2}}&1\\{{\omega ^2}}&1&\omega \end{array}} \right|$=

Six ‘$+$’ and four ‘$-$’ signs are to placed in a straight line so that no two ‘$-$’ signs come together, then the total number of ways are