Question

24. साबित करें कि बिनदु (0, 7, 10), (-1, 6, 6) तथा (-4, 9, 6) समद्विबाहु समकोण त्रिभुज बनाते हैं ।
(Show that the points (0, 7, 10), (-1, 6, 6) and (-4, 9, 6) from a right angled isosceles triang!
25. श्रेणी के n पदों का योगफल निकालें (Find the surn to n terms of the series.)
13 + (1 + 23) + (12 + 22 + 33) + ......... पदों तक (terms)
26. निम्नलिखित आँकड़ों का माध्य विचलन ज्ञात करें । (Find the mean deviation of the following data
प्राप्तांक (Marks obtained) | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60
बारंबारता (Frequency) । 4 । 7 । 15 । 12 । 7 । 5
27. प्रथम सिद्धांत से (find the derivative of cosx form first principle) अवकलन ज्ञात करें ।
28. यदि (if y = Inxcox तो (then) = ?
29. आंकड़ों के लिए माध्य के सापेक्ष विचलन ज्ञात करे । (Find the mean deviation about the mean f
38, 70, 48, 40, 42, 55, 63, 46, 54, 44 ।
30. एक सिक्का दो बार उछाला जाता है । कम से कम एक पट् प्राप्त होने की क्या प्रायिकता है ।
(A coin is tossed twice, what is the probality that at least one tail occurs ?)
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Answer 1

Answer:

points are from a right angled isosceles triangle.

probability that at least one tail occurs  =  3/4

Step-by-step explanation:

Show that the points (0, 7, 10), (-1, 6, 6) and (-4, 9, 6) from a right angled isosceles triangle

Let say A =  (0, 7, 10)  B = (-1, 6, 6) C =  (-4, 9, 6)

AB² = (-1-0)² + (6-7)² + (6-10)² = 1 + 1 + 16 = 18

AC² = (-4-0)² + (9-7)² + (6-10)² = 16 + 4 + 16 = 36

BC² = (-4-(-1))² + (9-6)² + (6-6)² = 9 + 9 + 0 = 18

AB² = BC² = 18

=> AB = BC = √18  ( isosceles)

36 = 18 + 18

AC² = AB² + BC² ( right angle )

=> points are from a right angled isosceles triangle.

A coin is tossed twice, what is the probability that at least one tail occurs

= 1  -  Probability no tail occurs

Probability of No tails =   Probability of both heads

=>Probability of No tails = (1/2)(1/2) = 1/4

=>probability that at least one tail occurs  = 1  - 1/4 = 3/4