CDS MATHEMATICS CO ORDINATE GEOMETRY QUIZ 19

Question 1:

Find the polar co-ordinate of a point $(\sqrt{3}, 1)$.

$\left(2 \sin 60^{\circ}, 2 \cos 60^{\circ}\right)$

$\left(2 \cos 30^{\circ}, 2 \sin 30^{\circ}\right)$

$\left(2 \sin 30^{\circ}, 2 \cos 30^{\circ}\right)$

None of these

Question 2:

The equation of circle with centre $(3,1)$ and radius is $4 \mathrm{~cm}$ is:

$x^{2}+y^{2}-6 x-2 y-6=0$

$x^{2}-y^{2}+3 y-5 y+6=0$

$x^{2}+y^{2}-8 y-2 y+7=0$

$x^{2}-y^{2}+6 x-2 y+6=0$

Question 3:

The graphs of the equation $3 x-10 y-2=0$ and $2 x-3 y+4=0$. Intersect at $\mathrm{P}(\mathrm{a}, \mathrm{b})$. What is the value of $(a-b)$.

$\frac{-15}{11}$

$\frac{-30}{11}$

$\frac{15}{13}$

$\frac{-15}{11}$

Question 4:

$\left[(3)^{3} \times(5)^{4}\right] \div(3)^{5}=?$

$30.44$

$39.55$

$35.44$

$69.44$

Question 5:

The graphs of the linear equation $5 x-2 y=$ 9 and $x+y=6$ interesect at the point $P(\alpha, \beta)$ then what is the value of $(2 \alpha+3 \beta)$ is.

12

14

15

18

Question 6:

Find the distance between the points $(7 \mathrm{k}+$ $2,5-3 \mathrm{k})$ and $(-3+7 \mathrm{k},-7-3 \mathrm{k})$

12

13

15

18

Question 7:

In what ratio does the point $(-4,6)$ divide the line segment joining the points $\mathrm{A}(-6,10)$ and $\mathrm{B}(3,-8)$

$3: 5$

$5: 6$

$2: 1$

$1: 2$

Question 8:

Find centroid of the triangle then the vertex of triangle is $(3,8)(5,6)$ and $(7,4)$.

$(5,6)$

$(3,8)$

$(6,5)$

$(8,3)$

Question 9:

Find the circum - centre, of the triangle whose vertices are $(-2,5)(-3,0),(9,-6)$.

$\left({5}{}, {}{1}\right)$

$\left({4}{}, {}{1}\right)$

$\left({5}{}, {}{3}\right)$

None of these

Question 10:

Find the intercepts made by line $7 x+8 y-56=0$ on the axis.

$(5,6)$

$(8,7)$

$(7,8)$

none of these