Religions in Tulunadu

Q. Why did the Amarasulya rebellion break out?

Q. The kannada dictionary compiled by Ferdinand Kittel was printed at .

1. Mangaluru
2. Mandya
3. Kittur
4. Bengaluru

Q. Discussing about spirituality, Mohan states that Madhvacharya gave a famous theory and belonged to Tulunadu. Rishi adds about the philosophy that its followers worshiped Lord Vishnu. Aditya mentions that according to the philosophy individuals and gods exists as separate entities. Which philosophy are they talking about?

1. Hinduism
2. Adwaita
3. Dwaita
4. Islam

Q. Most of the people in Tulunadu were ____.

1. Buddhists
2. Christians
3. Muslims
4. Jains

Q. Which among the following religions were followed in Tulunadu?

1. Hinduism
2. Buddhism
3. Jainism
4. All of the above

Q. Find the number of points of intersection of the line $x+y-5=0$ and the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1.$

1. $0$
2. $2$
3. $1$
4. $3$

Q. Find the centre of the ellipse whose equation is $x^2+2xy+2y^2-1=0$. Also, find the length of the major and minor axes.

1. Centre: $(1,1)$
2. Length of major - axis $=\frac{2\sqrt{2}}{\sqrt{3-\sqrt{5}}}$
3. Length of minor - axis $=\frac{2\sqrt{2}}{\sqrt{3+\sqrt{5}}}$
4. Centre: $(0,0)$

Q.

Find the set of values of $\lambda$ for which the
line $3x-4y+\lambda =0$ intersects the ellipse
$\frac{x^2}{16}+\frac{y^2}{a}=1$ at 2 distinct point.

1. $(12,12\sqrt{2})$

2. $(-12,12)$

3. $(-12,12\sqrt{2})$

4. $(-12\sqrt{2},12\sqrt{2})$

Q. If the curve $x^2+2y^2=2$ intersects the line $x+y=1$ at two points $P$ and $Q,$ then the angle subtended by the line segment $PQ$ at the origin is:

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

Q. The value(s) of $\lambda$ for which the line $y=x+\lambda$ touches the ellipse
$9x^2+16y^2=144$ is/are:

1. $-10$
2. $10$
3. $-5$
4. $5$