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 and B are two points and C is any point collinear with A and B. IF AB=10, BC=5, then AC is equal to:
- either 15 or 5
- necessarily 5
- necessarily 16
- none of these
Choose the correct answer from the given four options.
The vectors $\lambda\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}},\ \hat{\text{i}}+\lambda\hat{\text{j}}-\hat{\text{k}}$ and $2\hat{\text{i}}-\hat{\text{j}}+\lambda\hat{\text{k}}$ are coplanar if:
→The vectors $\lambda\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}},\ \hat{\text{i}}+\lambda\hat{\text{j}}-\hat{\text{k}}$ and $2\hat{\text{i}}-\hat{\text{j}}+\lambda\hat{\text{k}}$ are coplanar if:
- $\lambda=-2$
- $\lambda=0$
- $\lambda=1$
- $\lambda=-1$
If $A=\left[a_{i j}\right]$ is a square matrix of order 2 such that $a_{i j}=\left\{\begin{array}{ll}1, & \text { when } i \neq j \\ 0, & \text { when } i=j\end{array}\right.$ then $A^2$ is
→The vector equation of the plane passing through $\vec{\text{a}},\ \vec{\text{b}},\ \vec{\text{c}},$ is $\vec{\text{r}}=\alpha\vec{\text{a}}+\beta\vec{\text{b}}+\gamma\vec{\text{c}}$, provided that,
→- $\alpha+\beta+\gamma=0$
- $\alpha+\beta+\gamma=1$
- $\alpha+\beta=\gamma$
- $\alpha^2+\beta^2+\gamma^2=1$
A line makes an angle $\alpha,\beta,\gamma$ with the X, Y, Z axes. Then $\sin^2\alpha+\sin^2\beta+\sin^2\gamma=$
→If a line makes angles of $90^{\circ}, 135^{\circ}, 45^{\circ}$ with $x, y$ and $z$ axes, then its direction cosines will be :
→Area of the region bounded by the curve y = |x + 1| + 1, x = –3, x = 3 and y = 0 is:
- 8 sq units
- 16 sq units
- 32 sq units
- None of these
A die is thrown and a card is selected ar random from a deck pf $52$ playing cards. The probability of getting an even number of the die and a spade card is
→Choose the correct answer from the given four options.
Let F = 3x - 4y be the objective function. Maximum value of F is:
Let F = 3x - 4y be the objective function. Maximum value of F is:
If $\text{A}=\begin{bmatrix} 3 & 4 \\ 2 & 4 \end{bmatrix},\text{B}=\begin{bmatrix} -2 & -2 \\ 0 & -1 \end{bmatrix}$ then $(A + B)^{-1} =$
→