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In a Plane there are 37 straight lines, of which 13 pass through the point A and 11 pass through the point B. Besides, no three lines pass through one point, no lines passes through both points A and B , and no two are parallel. Find the number of points of intersection of the straight lines.

Correct Answer: 535

The number of points of intersection of 37 lines is C237. But 13 straight lines out of the given 37 straight lines pass through the same point A.

 

Therefore instead of getting C213 points, we get only one point A. Similarly 11 straight lines out of the given 37 straight lines intersect at point B. Therefore instead of getting C211 points, we get only one point B.

 

 Hence the number of intersection points of the lines is C237-C213-C211 +2 = 535

 

 

 

 

 

 

 

  

Arrange the following stages in a sequence, such that they result in an ogee curve between two parallel lines AB and CD, such that they are the tangents to the arc. m) Join the adjacent ends B and C with a straight line. n) Divide the line BC into four parts using the points P1, P2, P3. o) Draw lines such that they pass through the points P1, P2, P3, and are perpendicular to the line BC. p) Draw the perpendicular lines through the points B and C such that they cut the lines passing through P1, P3 respectively at E and F. q) With the center E draw an arc BP2 and with center F draw an arc P2C, thus arc BP2C is required ogee curve.

Drawing straight lines on both the surfaces of solids and then pointing the points where they intersect and drawing lines which forms the line of intersection this process of finding the line of intersection is termed as _______ method.

Rahim has invited his three buddies over to watch the basketball game on his wide-screen television. They are all hungry, but no one wants to leave to get food. Just as they are arguing about who should make the food run, a commercial comes on for a local pizzeria that delivers. The phone number flashes on the screen briefly and they all try to remember it. By the time Zachary grabs a pen and paper, each of them recollects a different number.i. All of the men agree that the first three numbers are 995.ii. Three of them agree that the fourth number is 9.iii. Three agree that the fifth number is 2.iv. Three agree that the sixth number is 6; three others agree that the seventh number is also 6.Which of the numbers is most likely the telephone number of the pizzeria?

Zachary has invited his three buddies over to watch the basketball game on his wide-screen television. They are all hungry, but no one wants to leave to get food. Just as they are arguing about who should make the food run, a commercial comes on for a local pizze-ria that delivers. The phone number flashes on the screen briefly and they all try to remember it. By the time Zachary grabs a pen and paper, each of them recollects a different number.

#1 : All of the men agree that the first three numbers are 995.
#2 : Three of them agree that the fourth number is 9.
#3 : Three agree that the fifth number is 2.
#4 : Three agree that the sixth number is 6; three others agree that the seventh number is also 6.

Which of the numbers is most likely the telephone number of the pizzeria?

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Two circular dials of exactly the same size are mounted on a wall side by side in such a way that their perimeters touch at one point. Dial 1, which is on the left , spins clockwise around its center , and dial 2 , which is on the right spins counter clockwise around its center . (Assume that there is no friction at the point of contact between the dials.) Each dial is marked on its perimeter at three points that are at equale distances around the points arked ondial 1 are N, O, and P and the points marked on dial 2 are X, Y, and Z. If points O and Z are just meeting at the point of contact between the dials , and if dial 1 spins at the same speed as dial 2, what is the smallest number of revolutions of each dial that will bring O and Z together again?

To locate the point of intersection of two straight lines, we stretch a thread or string between two stakes, where line of sight cuts the string is over required point of intersection.

To draw an arc of given radius touching two straight lines at right angles with each other, we first draw ______ with centre at the intersection point of the two lines on both the lines.

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 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?