Download App

CONTINUITY AND DIFFERENTIABILITY — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSCONTINUITY AND DIFFERENTIABILITY1 Mark
MCQ
If $\text{y}=\text{ax}^{\text{n+1}}+\text{bx}^{-\text{n}}$ Then $\text{x}^2\frac{\text{d}^2\text{y}}{\text{dx}^2} =$
  • A
    $n(n - 1) y$
  • ✓
    $n(n + 1) y$
  • C
    $ny$
  • D
    $n^2y$
✓

Answer

Correct option: B.
$n(n + 1) y$
Here
$\text{y}=\text{ax}^{\text{n}+1}+\text{bx}^{\text{-n}}$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\text{a}(\text{n}+1)\text{x}^\text{n}-\text{bn}\text{x}^{-\text{n}-1}$
$\Rightarrow\frac{\text{d}^2\text{y}}{\text{dx}^2}=\text{an}(\text{n}+1)\text{x}^{\text{n}-1}+\text{bn}(\text{n}+1)\text{x}^{-\text{n}-2}$
$\therefore\text{x}^2\frac{\text{d}^2\text{y}}{\text{dx}^2}=\text{x}^2\{\text{an}(\text{n}+1)\text{x}^{\text{n}-1}+\text{bn}(\text{n}+1)\text{x}^{-\text{n}-2}\}$
$=\text{n}(\text{n}+1)(\text{ax}^{\text{n}+1}+\text{b x}^{-\text{n}})$
$=\text{n}(\text{n}+1)\text{y}$

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 "M.C.Q (1 Marks)" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If x > a, $\int\frac{\text{dx}}{\text{x}^2-\text{a}^2}=$
  1. $\frac{2}{2\text{a}}\text{log }\frac{\text{x-a}}{\text{x+a}}+\text{k}$
  2. $\frac{2}{2\text{a}}\text{log }\frac{\text{x+a}}{\text{x-a}}+\text{k}$
  3. $\frac{1}{\text{a}}\text{log}(\text{x}^2-\text{a}^2)+\text{k}$
  4. $\log(\text{x}+\sqrt{\text{x}^2-\text{a}^2}+\text{k})$
→
Let R be the relation on the set A = {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Then,
  1. R is reflexive and symmetric but not transitive.
  2. R is reflexive and transitive but not symmetric.
  3. R is symmetric and transitive but not reflexive.
  4. R is an equivalence relation.
→
The value of the integral $\int\limits^2_{-2}\big|1-\text{x}^2\big|\text{dx}$ is:
  1. 4
  2. 2
  3. -2
  4. 0
→
The cosines of the angle between any two diagonals of a cube is:
→
If $|\vec{a}-\vec{b}|=|\vec{a}+\vec{b}|$ then the angle between $\vec{a}$ and $\vec{b}$ will be -
→
Let $f(x) = x^2 – x + 1, \text{x}\geq\frac{1}{2},$ then the solution of the equation $f(x) = f^{-1}(x)$ is:
→
$\int\frac{\cos2\text{x}-\cos2\theta}{\cos\text{x}-\cos\theta}\text{ dx}$ is equal to:
  1. $2(\sin\text{x}+\text{x}\cos\theta)+\text{C}$
  2. $2(\sin\text{x}-\text{x}\cos\theta)+\text{C}$
  3. $2(\sin\text{x}+2\text{x}\cos\theta)+\text{C}$
  4. $2(\sin\text{x}-2\text{x}\cos\theta)+\text{C}$
→
The function $\text{f(x)}=\tan\text{x}-\text{x}$
→
The area enclosed by the curve $\frac{\text{x}^2}{25}+\frac{\text{y}^2}{9}=1\text{ is:}$
  1. $10\pi\text{sq.}\text{units}$
  2. $15\pi\text{sq.}\text{units}$
  3. $5\pi\text{sq.}\text{units}$
  4. $4\pi\text{sq.}\text{units}$
→
Fifteen coupons are numbered $1$ to $15.$ Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is $9$ is$:$
→