Download App

STD 12 - 5. continuity and differentiation — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 5. continuity and differentiation4 Marks
MCQ
A function $f$ satisfies the relation

$f(x) = f''(x) + f'''(x) + .......\infty $ where $f(x)$ is a differentiable function indefinitely. If $f(1) = 5$ , then the value of $f'(1) + f''(1)$ is equal to

  • A
    $0$
  • B
    $-5$
  • ✓
    $5$
  • D
    cannot be determined
✓

Answer

Correct option: C.
$5$
c
$f'(1) + f''(1) = f(1) = 5$

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 solution set of the constraints $x+2 y \leq 2000, x+y \leq 1500, y \leq 600$ and $x \geq 0$ does not include the point
→
The points of contact $Q$  and $R$  of tangent from the point $P (2, 3) $ on the parabola $y^2 = 4x$ are
→
The value of $\int\limits_{ - 7}^7 {\frac{{{5^x}}}{{{5^{[x]}}}}dx} $ is equal to (where $[.]$ denotes greatest integer function)
→
Let $P_m$ stand for $^nP_m$ . Then the expression $1 . P_1 + 2 . P_2 + 3 . P_3 + ..... + n . P_n =$
→
If the points with vectors $\alpha \hat{i}+10 \hat{j}+13 \hat{k}$, $6 \hat{i}+11 \hat{j}+11 \hat{k}, \frac{9}{2} \hat{i}+\beta \hat{j}-8 \hat{k}$ are collinear, then $(19 \alpha-6 \beta)^2$ is equal to $...........$.
→
If $f(t)=\int_0^\pi \frac{2 x d x}{1-\cos ^2 \sin ^2 x}, 0 < t < \pi$, then the value of $\int_0^{\frac{\pi}{2}} \frac{\pi^2 d t}{f(t)}$ equals..........
→
If $\vec a = \hat i + \hat j + \hat k,\,\,\vec b = \hat i - \hat j + \hat k,\,\,\vec c = \hat i + 2\hat j + \hat k$ ,  then the value of $\left| {\begin{array}{*{20}{c}}
  {\vec a.\vec a}&{\vec a.\vec b}&{\vec a.\vec c} \\ 
  {\vec b.\vec a}&{\vec b.\vec b}&{\vec b.\vec c} \\ 
  {\vec c.\vec a}&{\vec c.\vec b}&{\vec c.\vec c} 
\end{array}} \right|$ is
→
Let $A$ and $B$ be non empty sets in $R$ and $f : A \to B$ is a bijective function.
Statement $1$ : $f$ is an onto function .
Statement $2$ : There exists a function $g : B \to A$ such that $fog = I_B$
→
If $A(6,3),$ $B( - 3,5)$, $C(4, - 2)$ and $D(x,{\rm{ }}3x)$ are four points. If the ratio of area of $\Delta DBC$ and $\Delta ABC$ is $1 : 2$, then the value of $x$, will be
→
If the sum of the $n$ terms of $G.P.$ is $S$ product is $P$ and sum of their inverse is $R$, than ${P^2}$ is equal to
→