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Higher Order Derivatives MATHS - Higher Order Derivatives

Rajasthan Board (RBSE) - STD 12 Science - MATHS (Rajasthan - English Medium). 96 questions in this chapter.

Question types

Higher Order Derivatives question types

96 questions across 4 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

96
Questions
4
Question groups
5
Question types
Sample Questions

Higher Order Derivatives questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
If $\text{x}=\text{f}(\text{t})\cos\text{t}-\text{f}(\text{t})\sin\text{t}\ \text{and}\ \text{y}=\text{f}(\text{t})\sin\text{t}+\text{f}(\text{t})\cos\text{t},$ then $\Big(\frac{\text{dx}}{\text{dt}}\Big)^2+\Big(\frac{\text{dy}}{\text{dt}}\Big)^2=$
  1. $\text{f}(\text{t})-\text{f}(\text{t})$
  2. $\{\text{f}(\text{t})-\text{f}(\text{t})\}^2$
  3. $\{\text{f}(\text{t})+\text{f}(\text{t})\}^2$
  4. $\text{None of these}$
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Q 2M.C.Q (1 Marks)1 Mark
If $\text{y}=\text{a}+\text{bx}^2,\text{a,b}$ arbitrary constants, then
  1. $\frac{\text{d}^2\text{y}}{\text{dx}^2}=2\text{xy}$
  2. $\text{x}\frac{\text{d}^2\text{y}}{\text{dx}^2}=\text{y}_1$
  3. $\text{x}\frac{\text{d}^2\text{y}}{\text{dx}^2}-\frac{\text{dy}}{\text{dx}}+\text{y}=0$
  4. $\text{x}\frac{\text{d}^2\text{y}}{\text{dx}^2}=2\text{xy}$
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Q 3M.C.Q (1 Marks)1 Mark
If $\text{y}=\tan^{-1}\Big\{\frac{\log(\frac{\text{e}}{\text{x}})^2}{\log(\frac{\text{e}}{\text{x}})^2}\Big\}+\tan^{-1}\Big(\frac{3-2\log,\text{x}}{1-6\log,\text{x}}\Big)$ then $\frac{\text{d}^2\text{y}}{\text{dx}^2}=$
  1. 2
  2. 1
  3. 0
  4. -1
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Q 4M.C.Q (1 Marks)1 Mark
If $\text{y}=\text{x}^{\text{n}-1}\log\text{x}$ $\text{x}^2\text{y}_2+(3-2\text{n})\text{xy}_1$ is equals to:
  • ✓
    $-(n - 1)^2y$
  • B
    $(n - 1)^2y$
  • C
    $-n^2y$
  • D
    $n^2y$

Answer: A.

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Q 5M.C.Q (1 Marks)1 Mark
If $\text{y}=\frac{\text{ax}+\text{b}}{\text{x}^2+\text{c}},$ then $(2\text{xy}_1+\text{y})\text{y}_3=$
  • ✓
    $3(xy_2 + y_1) y_2$
  • B
    $3(xy_1 + y_2) y_2$
  • C
    $3(xy_1 + y_2) y_1$
  • D
    None of these

Answer: A.

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Q 102 Marks Questions2 Marks
If $\text{x}=2\text{ at},\text{y}=\text{at}^2,$ where a is a constant, then find $\frac{\text{d}^2\text{y}}{\text{dx}^2}\text{ at}\text{ x}=\frac{1}{2}.$
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Q 153 Marks Question3 Marks
If $\text{x}=\text{a}\cos\text{nt}-\text{b}\sin\text{nt}$ and $\frac{\text{d}^2\text{x}}{\text{dt}^2}=\lambda\text{x}$ then find the value of $\lambda.$
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Q 175 Marks Questions5 Marks
If $\text{x}=\text{a}(1-\cos^3\theta),\text{y}=\text{a}\sin^3\theta,$ Prove that $\frac{\text{d}^2\text{y}}{\text{dx}^2}=\frac{32}{27\text{a}}\text{ at}\ \theta=\frac{\pi}{6}$
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Q 185 Marks Questions5 Marks
If $\text{x}=\text{a}\sin\text{t}-\text{b}\cos\text{t},\text{y}=\text{a}\cos\text{t}+\text{b}\sin\text{t},$ Prove that $\frac{\text{d}^2\text{y}}{\text{dx}^2}=-\frac{\text{x}^2+\text{y}^2}{\text{y}^2}$ 
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Q 205 Marks Questions5 Marks
If $\text{x}=\cos\theta,\text{y}=\sin^3$ prove that $\text{y}\frac{\text{d}^2\text{y}}{\text{dx}^2}+\Big(\frac{\text{dy}}{\text{dx}^2}\Big)=3\sin^2\theta(5\cos^2\theta-1)$
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