Define the collections E 1 , E 2 , E 3 , . . . . of ellipses and R 1 , R 2 , R 3 , . . . . of rectangles as follows: E 1 : x 2 9 + y 2 4 = 1 ; R 1 : rectangle of largest area, with sides parallel to the axes, inscribed in E 1 ; E n : ellipse x 2 a n 2 + y 2 b n 2 = 1 of largest area inscribed in R n - 1 , n > 1 ; R n : rectangle of largest area, with sides parallel to the axes, inscribed in E n , n > 1 . Then which of the following options is/are correct?

∑ n = 1 N a r e a o f R n < 24 , for each positive integer N

The eccentricities of E 18 and E 19 are NOT equal

The distance of a focus from the centre in E 9 is 5 32

EASY

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ABC समकोणीय त्रिभुज है। B समकोण है। BC और AC के मध्यबिन्दु क्रमश: $ {B}' $ और $ {A}' $ हैं। $ \triangle\;{A}'{B}'C $ का क्षेत्रफल कितना है?

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Important Questions on Basic Geometrical Ideas

EASY

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

Read the given question and decide which of the following information is sufficient to answer the question.

What is the value of 0?

Information :

Question Image

(II) 0 < q < 90°

MEDIUM

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

The exterior angle of a regular polygon is

72 °

. What would be the sum of all its interior angles?

MEDIUM

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

∆ A B D

C

is the midpoint of

B D

. If

A B

= 10

cm, AD

= 12

cm and

A C

= 9

cm, then

B D = ?

EASY

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

If the distance between the foci of an ellipse is

6

and the distance between its directrix is

12,

then the length of its latus rectum is

MEDIUM

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

If a point

P (x, y)

moves along the ellipse

\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1

and if

C

is the centre of the ellipse, then the sum of maximum and minimum values of

C P

HARD

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

Define the collections

\{E_{1}, E_{2}, E_{3}, . . . .\}

of ellipses and

\{R_{1}, R_{2}, R_{3}, . . . .\}

of rectangles as follows:

E_{1} : \frac{x^{2}}{9} + \frac{y^{2}}{4} = 1;

R_{1} :

rectangle of largest area, with sides parallel to the axes, inscribed in

E_{1};

E_{n} :

ellipse

\frac{x^{2}}{a_{n}^{2}} + \frac{y^{2}}{b_{n}^{2}} = 1

of largest area inscribed in

R_{n - 1}, n > 1;

R_{n} :

rectangle of largest area, with sides parallel to the axes, inscribed in

E_{n}, n > 1 .

Then which of the following options is/are correct?

MEDIUM

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

$5 : 18$ is the ratio of the length and perimeter of a rectangle. What would be the ratio of its length and breadth?

EASY

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

Find the perimeter (in

c m

) of a semicircle of radius

7 c m

EASY

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

A hall is

15 m

long and

12 m

broad. The sum of the areas of the floor and the ceiling is?(in square meters).

EASY

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

If the interior angle of a regularpolygon is $108 °$ , then it is a-

1. Octagon

2. Hexagon

3. Pentagon

4. Tetragon

EASY

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

The distance between the centres of two circles having radii

5 c m

and

6 c m

\sqrt{10} c m

. Find the length (in

c m

) of direct common tangent.

HARD

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is:

EASY

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

How many tangents can be drawn to two circles, whose radii are equal to

4 c m

and

5 c m

respectively and the distance between the two centres is

5 c m

EASY

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

In the given diagram, point R and Q are on PS. ÐPQT = x°, ÐRQT = (x – 50)° and ÐTUR = (x + 25°). find the value of ÐURS.

Question Image

EASY

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

The length of one side and the diagonal of a rectangle are

10 cm

and

26 cm

respectively. Find the length of the other side (in

cm

EASY

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

The area of an equilateral triangle is

18 \sqrt{3}

sq. units. Find the value of the side (in units) of the triangle.

EASY

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

An arc length of

16 π

units subtends an angle of

240

degrees. Find the radius (in unit) of the circle.

MEDIUM

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

If the length of a rectangle is decreased by

5

metres and breadth increased by

3

metres, its area decreases by

9 m^{2}

. If its length is increased by

3 m

and breadth by

2 m

, its area increases by

67

m^{2}

. What is the length of the rectangle ?

HARD

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

In a circle of radius

17 c m,

two parallel chords are drawn on opposite side of a diameter. The distance between the chords is

23 c m .

If the length of one chord is

16 c m,

then the length of the other chord is

MEDIUM

Mathematics>Geometry>Basic Geometrical Ideas>Introduction to Geometry

The equation of the circle passing through the foci of the ellipse

\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1

, and having centre at

(0, 3)

ABC समकोणीय त्रिभुज है। B समकोण है। BC और AC के मध्यबिन्दु क्रमश: \( {B}' \) और \( {A}' \) हैं। \( \triangle\;{A}'{B}'C \) का क्षेत्रफल कितना है?

Important Questions on Basic Geometrical Ideas

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