The sum of the focal distances of a point on an ellipse is constant and equal to the

How far is point 'R' from Point 'T'? Statement (I): Point 'R' is 5 metres to the north of point 'M'. Point 'U' is 4 metres to the east of point 'R'. Point 'T' is to the west of point 'R' such that points 'U' 'R' and 'T' form a straight line of metres. Statement (II): Point 'Z' is metres to the south of point 'T'. Point 'U' is metres to the east of point 'T'. Point 'M' is metres to the east of point 'Z'. Point 'R' is metres to the north of point 'M'. Point 'R' lies on the line formed by joining points 'T' and 'U'.

A

Statement (I) and (III) are independently sufficient to answer the question.

B

Statement (I) and (II) are together required to answer the question.

C

Statement (I) alone is sufficient to answer the question while statement (II) is not sufficient to answer the question.

D

Statement (II) alone is sufficient to answer (I) is not sufficient to answer the question.

Point A is 3m in the north of point B. Point D is 2m in the east of point E. Point F is 9m in the west of point G. Point C is 4m in the west of point B. Point C is 3m in the south of point D. Point F is 5m in the south of point E. Point H is 5m in the north of point G. What is the shortest distance between point H and point A?

A

5m

B

4m

C

3m

D

6m

Point P is 4m in the west of point V. Point R is 6m in the north of point Q. Point T is 5m in the south of point S. Point V is in the middle of point R and Q. Point U is 5m in the east of point R. Point V is in north of point Q. Point S is 5m in the east of point V. What is the area of triangle formed by point P, R and Q?

A

14m²

B

15m²

C

16m²

D

12m²

Garima starts walking towards the south from point R. He walks for 5m to reach Point S then turns right and walks for 2m to reach point T from there he turns left and walks for 3m to reach Point Z. He then turns right from point Z and walks for 6m to reach point Y and then turns right and walks for 3m to reach point X. He then turns right from point X and walks for 4m to reach point W and then turns left and walks for 5m to reach point V and then turns left and walks for 4m till point U and stops. What is the shortest distance between point V and point R?

A

4m

B

3m

C

5m

D

8m

Study the following information and answer the questions. Point A is 8m to the west of Point B. Point C is 4m to the south of Point B. Point D is 4m to the east of Point C. Point F is 6m to the north of Point D. Point E is 8m to the west of Point F. Point G is 2m to the south of Point E. How far and in which direction is Point G from Point A?

A

4m to the east

B

8m to the west

C

4m to the west

D

8m to the east

Study the following information and answer the questions. Point A is 8m to the west of Point B. Point C is 4m to the south of Point B. Point D is 4m to the east of Point C. Point F is 6m to the north of Point D. Point E is 8m to the west of Point F. Point G is 2m to the south of Point E. If point G is 4m to the north of Point H, then what is the distance between H and D?

A

11m

B

8m

C

6m

D

4m

Steps are given to draw an ellipse by trammel method. Arrange the steps. i. Place the trammel so that R is on the minor axis CD and Q on the major axis AB. Then P will be on the ellipse. ii. Draw two axes AB and CD intersecting each other at O. iii. By moving the trammel to new positions, always keeping R on CD and Q on AB, obtain other points and join those to get an ellipse. iv. Along the edge of a strip of paper which may be used as a trammel, mark PQ equal to half the minor axis and PR equal to half of major axis.

A

i, ii, iii, iv

B

ii, iv, i, iii

C

iii, iv, i, ii

D

iv, i, ii, iii

Consider the following statements 1. The focal length of the eyepiece is larger than the focal length of the objective. 2. The focal length of the eyepiece is smaller than the focal length of the objective. 3. The aperture of the eyepiece lens is larger than the objective lens. Which of the following statements is/are INCORRECT about a compound microscope?

A

Only 1

B

Only 2

C

Only 3

D

1, 2 and 3

In case of compound microscope which of the following statements is/are correct? 1) The focal length of eye piece is larger than the focal length of the objective 2) The focal length of the eye piece is smaller than the focal length of the objective 3) The image produced in a normal optical microscope is real 4) The image produced in a normal optical microscope is virtual

A

1 only

B

1 and 4

C

2 and 3

D

2 and 4

In case of a compound microscope, which of the following statements is/are correct?
1. The focal length of the eyepiece is larger than the focal length of the objective.
2. The focal length of the eyepiece is smaller than the focal length of the objective.
3. The image produced in a normal optical microscope is real.
4. The image produced in a normal optical microscope is virtual.
Select the correct answer:

A

Only 1

B

1 and 4

C

2 and 3

D

2 and 4

The sum of the focal distances of a point on an ellipse is constant and equal to the

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