Length of Normal

Q. The length of normal to the curve $x=a\left(\theta +\sin \theta \right),y=a\left(1-\cos \theta \right)\mathrm{at}\theta =\frac{\pi }{2}$ is .

1. $2\left(a\right|$
2. $\sqrt{2}\left(a\right|$
3. $\frac{\left(}{a}$
4. $\frac{\left(}{a}$

Q. The length of the normal at point ‘t’ of the curve x = a(t + sin t), y = a (1 - cos t) is
[RPET 2001]

1. a sin t
2. $2asi{n}^3\left(t/2\right)sec\left(t/2\right)$
3. 2a sin(t / 2) tan(t/2)
4. 2a sin (t / 2)

Q. The length of normal to the curve x = $a(\theta +sin\theta )$ at the point $\theta =\pi /2$ is
[RPET 1999]

1. 2a
2. a/2
3. $\sqrt{2}a$
4. $a/\sqrt{2}$

Q. The length of normal to the curve x = $a(\theta +sin\theta )$ at the point $\theta =\pi /2$ is
[RPET 1999]

1. 2a
2. a/2
3. $\sqrt{2}a$
4. $a/\sqrt{2}$

Q. The length of the normal at point ‘t’ of the curve x = a(t + sin t), y = a (1 - cos t) is
[RPET 2001]

1. a sin t
2. $2asi{n}^3\left(t/2\right)sec\left(t/2\right)$
3. 2a sin(t / 2) tan(t/2)
4. 2a sin (t / 2)