MCQ
If $\text{y}=(\sin^{-1}\text{x})^2,$ then $(1-\text{x}^2)\text{y}_2$ is equal to:
- ✓$xy_1 + 2$
- B$xy_1 - 2$
- C$-xy_1 + 2$
- DNone of these
✓
Answer
Correct option: A.
$xy_1 + 2$
Here,
$\text{y}=(\sin^{-1}\text{x})\frac{1}{\sqrt{1-\text{x}^2}}$
$\Rightarrow\text{y}_2=\frac{2}{1-\text{x}^2}+\frac{2\text{x}\sin^{-1}\text{x}}{(1-\text{x}^2)^\frac{3}{2}}$
$\Rightarrow\text{y}_2=\frac{2}{1-\text{x}^2}+\frac{2\text{x}\sin^{-1}\text{x}}{(1-\text{x}^2)\sqrt{1-\text{x}^2}}$
$\Rightarrow\text{y}_2=\frac{2}{1-\text{x}^2}+\frac{\text{xy}_1}{(1-\text{x}^2)}$
$\Rightarrow\text{y}_2(1-\text{x}^2)=2+\text{xy}_1$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A rectangular parallelopiped is formed by planes drawn through the point (5, 7, 9) and (2, 3, 7) parallel to the coordinate planes. The length of an edge of this rectangular parallelopiped is:
- 2
- 3
- 4
- all of these
A line $\overrightarrow{O P}$ in space, represented by the figure below; has a magnitude of $2 \sqrt{2}$ units.
Which of these are the direction ratios of $\overrightarrow{O P}$ ?
→Which of these are the direction ratios of $\overrightarrow{O P}$ ?
The integrating factor of the differential equation$(1-\text{y}^{2})\frac{\text{dx}}{\text{dy}}+\text{yx}=\text{ay}(-1<\text{y}<1)$ is:
→-
$\frac{1}{\text{y}^{2}-1}$
-
$\frac{1}{\sqrt{\text{y}^{2}+1}}$
-
$\frac{1}{1-\text{y}^{2}}$
-
$\frac{1}{\sqrt{1-\text{y}^{3}}}$
A straight line passes through (1, -2, 3) and perpendicular to the plane 2x + 3y - z = 7. Find the direction ratios of normal to plane:
- < 2, 3, -1 >
- < 2, 3, 1 >
- < -1, 2, 3 >
- None of the above
Choose the correct answer from the given four options.
If $\text{P}(\text{B})=\frac{3}{5},\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\frac{1}{2}$ and $\text{P}(\text{A}\cup\text{B})=\frac{4}{5},$ then $\text{P}(\text{A}\cup\text{B})'+\text{P}(\text{A}'\cup\text{B})=$
→If $\text{P}(\text{B})=\frac{3}{5},\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\frac{1}{2}$ and $\text{P}(\text{A}\cup\text{B})=\frac{4}{5},$ then $\text{P}(\text{A}\cup\text{B})'+\text{P}(\text{A}'\cup\text{B})=$
A machine operates if all of its three components function. The probability that the first component fails during the year is $0.14$ , the second component fails is $0.10$ and the third component fails is $0.05$ . What is the probability that the machine will fail during the year?
→Choose the correct answer from the given four options.The value of $\sin^{-1}\bigg[\cos\Big(\frac{33\pi}{5}\Big)\bigg]$ is:
→- $\frac{3\pi}{5}$
- $\frac{-7\pi}{5}$
- $\frac{\pi}{10}$
- $\frac{-\pi}{10}$
The value of $\sin\big(2\big(\tan^{-1}0.75\big)\big)$ is equal to:
→The area bounded by the curve $y = x^4 - 2x^3 + x^2 + 3$ with x-axis and ordinates corresponding to the minima of $y$ is:
→Two events A and B will be independent, if
→- A and B are mutually exclusive
- $\text{P}(\text{A}'\text{B}')=\big[1-\text{P}(\text{A})\big]\big[1-\text{P}(\text{B})\big]$
- P(A) = P(B)
- P(A) + P(B) = 1