Subnormal

Q. For the curve $b{y}^2=(x+a{)}^3$ the square of subtangent is proportional to
[RPET 1999]

1. $ta{n}^{-1}\left(3\right)$
2. $ta{n}^{-1}\left(2\right)$
3. $\frac{\pi }{2}$
4. $\frac{\pi }{4}$

Q.

The sub-normal at any point of the curve $x^2{y}^2=a^2(x^2-a^2)$ varies as

1. $(Abcissa{)}^{-3}$

2. $(Abcissa{)}^3$

3. $(Ordinate{)}^{-3}$
4. $(Ordinate{)}^3$

Q. For the curve $b{y}^2=(x+a{)}^3$ the square of subtangent is proportional to
[RPET 1999]

1. $ta{n}^{-1}\left(3\right)$
2. $ta{n}^{-1}\left(2\right)$
3. $\frac{\pi }{2}$
4. $\frac{\pi }{4}$

Q. If A =$\{x|\frac{\pi }{6}\le x\le \frac{\pi }{3}\}$ and $f\left(x\right)=\cos x-x(1+x)$, then $f\left(A\right)$ is equal to

1. $[\frac{\pi }{6},\frac{\pi }{3}]$
2. $[-\frac{\pi }{3},-\frac{\pi }{6}]$
3. $[\frac{1}{2}-\frac{\pi }{3}(1+\frac{\pi }{3}),\frac{\sqrt{3}}{2}-\frac{\pi }{6}(1+\frac{\pi }{6})]$
4. $[\frac{1}{2}+\frac{\pi }{3}(1-\frac{\pi }{3}),\frac{\sqrt{3}}{2}+\frac{\pi }{6}(1-\frac{\pi }{6})]$

Q.

The sub-normal at any point of the curve $x^2{y}^2=a^2(x^2-a^2)$ varies as

1. $(Abcissa{)}^{-3}$

2. $(Abcissa{)}^3$

3. $(Ordinate{)}^{-3}$
4. $(Ordinate{)}^3$

Q. For the curve $xy=c^2$ the subnormal at any point varies as
[Karnataka CET 2003]

1. $x^2$
2. $x^3$
3. $y^2$
4. $y^3$

Q. If $f\left(x\right)={\cos }^{-1}\left(\frac{1-4^x}{1+4^x}\right),$ then $f^{\prime }\left(0\right)=$

1. $\frac{2}{5}\log 2$
2. $\frac{4}{5}\log 2$
3. $2\log 2$
4. $\log 2$

Q. For the curve $xy=c^2$ the subnormal at any point varies as
[Karnataka CET 2003]

1. $x^2$
2. $x^3$
3. $y^2$
4. $y^3$

Q. For the curve $b{y}^2=(x+a{)}^3$ the square of subtangent is proportional to
[RPET 1999]

1. $ta{n}^{-1}\left(3\right)$
2. $ta{n}^{-1}\left(2\right)$
3. $\frac{\pi }{2}$
4. $\frac{\pi }{4}$

Q.

The sub-normal at any point of the curve $x^2{y}^2=a^2(x^2-a^2)$ varies as

1. (Abcissa)^-3

2. (Abcissa)³

3. (Ordinate)^-3

4. None of these

Q. For the curve $xy=c^2$ the subnormal at any point varies as
[Karnataka CET 2003]

1. $x^2$
2. $x^3$
3. $y^2$
4. $y^3$

Q. Let $f$ be a real valued continuous function on $[0,1]$ and $f\left(x\right)=x+{\int }_0^1(x-t)f\left(t\right)dt$. Then, which of the following points $(x,y)$ lies on the curve $y=f\left(x\right)?$

Q. The angle made by the tangent of the curve $x=a(t+\sin t\cos t);y=a(1+\sin t{)}^2$ with the x-axis at any point on it is

1. $\frac{1}{4}(\pi +2t)$
2. $\frac{1-\sin t}{\cos t}$
3. $\frac{1}{4}(2t-\pi )$
4. $\frac{1+\sin t}{\cos 2t}$