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Find the length of the altitude of an equilateral triangle with side length 12 cm.

A4*sqrt(3) cm

B6*sqrt(3) cm

C8*sqrt(3) cm

D9 cm

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If 30% of (A + B) = 50% of (A – B), find the ratio A:B.

A2:1

B3:1

C4:1

D5:1

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A vertical pole 12 m long casts a shadow 8 m long on the ground. At the same time, a tower casts a shadow 40 m long. Find the height of the tower.

A45 m

B50 m

C60 m

D75 m

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How many two-digit numbers are divisible by 7?

A12

B13

C14

D15

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If the roots of the equation x^2 – kx + 16 = 0 are equal, find the value of k.

A±4

B±6

C±8

D±12

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If cos(theta) = 3/5, what is the value of (1 + tan^2(theta))?

A16/9

B25/9

C25/16

D9/16

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A person travels from city A to city B at 40 km/h and returns at 60 km/h. What is his average speed for the whole journey?

A48 km/h

B50 km/h

C52 km/h

D54 km/h

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What is the fourth proportional to 4, 9, and 12?

A18

B24

C27

D36

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The mean of 100 observations was calculated as 40. It was later found that an observation 53 was misread as 83. Find the correct mean.

A39.3

B39.7

C40.3

D40.7

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A solid copper sphere of radius 6 cm is melted and recast into a wire of radius 0.1 cm. Find the length of the wire.

A144 m

B288 m

C360 m

D576 m

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