Mathematics Test

Result

Mathematics Test - 9

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Question 1
1 / -0

A

B

C

D

Solution
Question 2
1 / -0

A
1/2

B
2/3

C
3/2

D
2

Solution

Concept 2 :
Basics of Ellipse(1)   Focus : The fixed point is called the focus of the ellipse.

(2)   Directrix : The fixed straight line is called the directrix of the ellipse.

(3)   Eccentricity : The constant ratio is called the eccentricity of the ellipse and is denoted by e.

(4)   Axis : The straight line passing through the focus and perpendicular to the directrix is called the axis of the ellipse.

(5)   Vertex : The points of intersection of the ellipse and the axis are called vertices of ellipse

(6)   Centre : The point which bisects every chord of the ellipse passing through it, is called the centre of ellipse.

(7)   Latus - rectum : The latus - rectum of a ellipse is the chord passing through the focus and perpendicular to the axis.

(8)   Double ordinate : The double ordinate of a ellipse is a chord perpendicular to the axis.

(9)   Focal chord : A chord passing through the focus of the ellipse is called a focal chord.

(10)   Focal distance : The distance of any point on the ellipse from the focus is called the focal distance of the point.
Question 3
1 / -0

A

B

C

D

Solution
Question 4
1 / -0

In a cricket championship there are 36 matches. The number of teams, if each plays 1 match with other are

A
9

B
10

C
$8$

D
12

Solution
Question 5
1 / -0

A
(-4, 12)

B
(5, 0)

C
(3, 4)

D
(2, 4)

Solution
Question 6
1 / -0

A
Both S and R are wrong

B
Both S and R are correct but R is not the correct explanation for S

C
S is correct and R is the correct explanation for S

D
S is correct, R is wrong

Solution
Question 7
1 / -0

Direction cosines of the line that makes equal angles with the three axes in a space are

A
$\pm \frac{1}{3}, \pm \frac{1}{3}, \pm \frac{1}{3}$

B
$\pm \frac{6}{7}, \pm \frac{2}{3}, \pm \frac{3}{7}$

C
$\pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}$

D
$\pm \sqrt{\frac{1}{7}}, \pm \sqrt{\frac{3}{14}}, \pm \sqrt{\frac{1}{14}}$

Solution
Question 8
1 / -0

A hyperbola whose transverse axis is along the major axis of the conic, and has vertices at the foci of this conic. If the eccentricity of the hyperbola is 3/2, then which of the following points does not lie on it?

A

B

C

D

Solution

Main Concept :
Basics of Hyperbola A plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant.

The point on each branch closest to the centre is that branch's "vertex". The vertices are some fixed distance a from the centre. The line going from one vertex, through the center, and ending at the other vertex is called the "transverse" axis. The "foci" of a hyperbola are "inside" each branch, and each focus is located some fixed distance c from the centre. (This means that a < c for hyperbolas.) The values of a and c will vary from one hyperbola to another, but they will be fixed values for any given hyperbola.

Other Concepts :

Concept 1 :
Basics of Ellipse(1)   Focus : The fixed point is called the focus of the ellipse.

(2)   Directrix : The fixed straight line is called the directrix of the ellipse.

(3)   Eccentricity : The constant ratio is called the eccentricity of the ellipse and is denoted by e.

(4)   Axis : The straight line passing through the focus and perpendicular to the directrix is called the axis of the ellipse.

(5)   Vertex : The points of intersection of the ellipse and the axis are called vertices of ellipse

(6)   Centre : The point which bisects every chord of the ellipse passing through it, is called the centre of ellipse.

(7)   Latus - rectum : The latus - rectum of a ellipse is the chord passing through the focus and perpendicular to the axis.

(8)   Double ordinate : The double ordinate of a ellipse is a chord perpendicular to the axis.

(9)   Focal chord : A chord passing through the focus of the ellipse is called a focal chord.

(10)   Focal distance : The distance of any point on the ellipse from the focus is called the focal distance of the point.
Question 9
1 / -0

A

B

C

D

Solution