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.

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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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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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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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:
  1. -(n - 1)2y
  2. (n - 1)2y
  3. -n2y
  4. n2y
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If $\text{y}=\frac{\text{ax}+\text{b}}{\text{x}^2+\text{c}},$ then $(2\text{xy}_1+\text{y})\text{y}_3=$
  1. 3(xy2 + y1) y2
  2. 3(xy1 + y2) y2
  3. 3(xy1 + y2) y1
  4. None of these
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Q 72 Marks2 Marks
If $\text{x}=\text{f}(\text{t})$ and $\text{y}=\text{g}(\text{t}),$ then write the value of $\frac{\text{d}^2\text{y}}{\text{dx}^2}.$
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Q 92 Marks2 Marks
Find $\frac{\text{d}^2\text{y}}{\text{dx}^2},$ where $\text{y}=\log\Big(\frac{\text{x}^2}{\text{e}^2}\Big)$
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Q 113 Marks3 Marks
If $\text{y}=2\sin\text{x}+3\cos\text{x}$ Prove that $\frac{\text{d}^2\text{y}}{\text{dx}^2}+\text{y}=0$
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Q 123 Marks3 Marks
If $\text{y}=\log(\sin\text{x})$ Prove that $\frac{\text{d}^3\text{y}}{\text{dx}^3}=2\cos\text{x}\ \text{cosec}^3\text{x}$
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Q 143 Marks3 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 153 Marks3 Marks
If $\text{y}=\text{x}+\tan\text{x},$ show that $\cos^2\text{x}\frac{\text{d}^2\text{y}}{\text{dx}^2}-2\text{y}+2\text{x}=0$
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Q 164 Marks4 Marks
If $\text{x}=\text{a}(\theta-\sin\theta),\text{y}=\text{a}(1+\cos\theta)$ find $\frac{\text{d}^2\text{y}}{\text{dx}^2}$
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Q 184 Marks4 Marks
If $\text{y}=\text{x}^3\log\text{x},$ Prove that $\frac{\text{d}^4\text{y}}{\text{dx}^4}=\frac{6}{\text{x}}$
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Q 194 Marks4 Marks
If $\text{x}=3\cot-2\cos^3\text{t},\text{y}=3\sin\text{t}-2\sin^3\text{t}$ find $\frac{\text{d}^2\text{y}}{\text{dx}^2}.$
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Q 204 Marks4 Marks
If $\text{y}=\text{x}^\text{n}\{\text{a}\cos(\log\text{x})+\text{b}\sin(\log\text{x})\},$ prove that $\text{x}^2\frac{\text{d}^2\text{y}}{\text{dx}^2}+(1-2\text{n})\frac{\text{dy}}{\text{dx}}+(1+\text{n}^2)\text{y}=0.$
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