Spot the pattern? Hint at the beginning! #shorts #maths #puzzle

(a) Look at the following matchstick pattern of squares (Fig 11.6). The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks in terms of the number of squares. (Hint : If you remove the vertical stick at the end, you will get a pattern of Cs.) (b) Fig 11.7 gives a matchstick pattern of triangles. As in Exercise 11 (a) above, find the general rule that gives the number of matchsticks in terms of the number of triangles.

Look at the following matchstick pattern of squares (see fig.). The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks in terms of the number of squares. (Hint: If you remove the vertical stick at the end, you will get a pattern of Cs.)

A rope is stretched between two stationary boats on the surface of a lake. A man in the first boat pulls the rope with a constant force of 100 N. The distance between the boats is 100 m in the beginning. The mass of the first boat with the man is 250 kg ,while the mass of the other is 500 kg. Find :(i) the velocity of approach of the two boats 15 s after the start,(ii) the time taken for the two boats to meet each other. [Hint: Consider relative acceleration and apply kinematic equations.]

Assertion : Newton's rings are formed in the reflected system. When the space between the lens and the glass plate is filled with a liquid of refractive index greater than that of glass, the central spot of the pattern is bright. Reason : This is because the reflections in these cases will be from a denser to a rarer medium and the two interfering rays are reflected under similar conditions.

Unscramble the following words using the hints given against them. (i) MATLICE (Hint: weather pattern in a region over a period of time) (ii) AROPL (Hint: coolest region on earth) (iii) TREHMEOMRET (Hint: used to measure temperature) (iv) UHIDYTMI (Hint: feature of weather)

In the context of India's Five Year Plans, a shift in the pattern of industrialization, with lower emphasis of heavy industries and move on infrastructure begins in :