The value of the integral of the function g(x, y) = 4x3 + 10y4 along the straight line segment from the point (0, 0) to the point (1, 2) in the x - y plane is

The value of the integral of the function g(x, y) = 4x<sup>3</sup> + 10y<sup>4</sup> along the straight line segment from the point (0, 0) to the point (1, 2) in the x - y plane is

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.

The letters P, Q, R, S, T and U are to be placed one per vertex on a regular convex hexagon, but not necessarily in the same order. Consider the following statements: The line segment joining R and S is longer than the line segment joining P and Q. The line segment joining R and S is perpendicular to the line segment joining P and Q. The line segment joining R and U is parallel to the line segment joining T and Q. Based on the above statements, which one of the following options is CORRECT?

A

The line segment joining R and T is parallel to the line segment joining Q and S

B

The line segment joining T and Q is parallel to the line joining P and U

C

The line segment joining R and P is perpendicular to the line segment joining U and Q

D

The line segment joining Q and S is perpendicular to the line segment joining R and P

Segment CD is shorter than Segment MN, Segment MN is shorter than Segment TR, Segment AB is shorter than Segment CD and Segment MN is shorter than Segment PQ. Which segment is the shortest?

A

CD

B

MN

C

PQ

D

AB

A line of 12 cm length is perpendicular to profile plane and the least distance from this line to profile plane is 6 cm. This is at a distance of 4 cm from the vertical plane and 5 cm from the horizontal plane. What is distance from the point on line far away from the profile plane to profile plane?

A

12 cm

B

9 cm

C

18 cm

D

6 cm

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

Choose the sentence (s) in which the word 'straight means 'honest or frank'. (1) Draw a straight line through the two points. (2) You are not being straight with me, even though you know that I like straight answers. (3) It was a straight choice between taking or leaving the offer of friendship.

A

(1)

B

(3)

C

(1) and (2)

D

1) and (3)

A line is perpendicular to profile plane, the perpendicular distance from 1st end of the line to vertical plane is 20 cm and perpendicular distance of 2nd end of line to horizontal plane is 10 cm. What is the distance from 1st end of line to vertical plane?

A

15 cm

B

20 cm

C

10 cm

D

Can’t say

A line of 12 cm length is perpendicular to profile plane and the least distance from this line to profile plane is 6 cm. This is at a distance of 4 cm from vertical plane and 5 cm from the horizontal plane. What is distance from the line to xy reference line in top view?

A

6 cm

B

4 cm

C

5 cm

D

0 cm

A line of 12 cm length is perpendicular to profile plane and the least distance from this line to profile plane is 6 cm. This is at a distance of 4 cm from vertical plane and 5 cm from the horizontal plane. What is the distance from the line to xy reference line in front view?

A

0 cm

B

6 cm

C

4 cm

D

5 cm

The value of the integral of the function g(x, y) = 4x³ + 10y⁴ along the straight line segment from the point (0, 0) to the point (1, 2) in the x - y plane is

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