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Question 9
Question: Answer: ..
Question: Answer: ..Question 9
Question: Find the number of triangles that can be drawn through 12 distinct points, no three of which are collinear. Answer: To draw a triangle, we require three non-collinear points. Hence, the number of triangles that can be drawn is ..
Question: Find the number of triangles that can be drawn through 12 distinct points, no three of which are collinear. Answer: To draw a triangle, we require three non-collinear points. Hence, the number of triangles that can be drawn is ..
To find the sum of a number of terms in Arithmetical Progression:
Let a=first term, d = common difference, l=t n =last term, s = required sum. Then, Writing the series in the reverse order, Adding together the two series, ..
Let a=first term, d = common difference, l=t n =last term, s = required sum. Then, Writing the series in the reverse order, Adding together the two series, ..Examples:
Each one of the following series form an A.P. i) 1, 3, 5, 7, ii) 3, 7, 11, 15, iii) 15, 12, 9, iv) x, x - d, x - 2d, ..... The common difference is found by subtracting any term of the series from the immediate succeeding term. In the above example, common difference in the first is..
Each one of the following series form an A.P. i) 1, 3, 5, 7, ii) 3, 7, 11, 15, iii) 15, 12, 9, iv) x, x - d, x - 2d, ..... The common difference is found by subtracting any term of the series from the immediate succeeding term. In the above example, common difference in the first is..Examples:
i) 1 + 4 + 7 + 10 + ... is a series in which first term is 1, second term is 4, third term is 7 and so on. ii) 3 - 9 + 27 - 81 + ... is also a series in which the first term is 3, second term is -9, third term is 27 and so ..
Factorising a3
b3
The product of a + b and a 2 - ab + b 2 is a 3 + b 3 . Hence when a 3 + b 3 is factorised, we get: a 3 + b 3 = (a + b) (a 2 - ab + b 2 ) Similarly, a 3 - b 3 = (a - b) (a 2 + ab + b 2 ) Factorise: x 3 + 8 x 3 + 8 = (x) 3 + (2) 3 = (x + 2) (x 2 - 2x + 4) Factorise 64x 3 - 125. ..
b3 The product of a + b and a 2 - ab + b 2 is a 3 + b 3 . Hence when a 3 + b 3 is factorised, we get: a 3 + b 3 = (a + b) (a 2 - ab + b 2 ) Similarly, a 3 - b 3 = (a - b) (a 2 + ab + b 2 ) Factorise: x 3 + 8 x 3 + 8 = (x) 3 + (2) 3 = (x + 2) (x 2 - 2x + 4) Factorise 64x 3 - 125. ..Question 1
Question: Find n. Answer: i) ii..
Question: Find n. Answer: i) ii..Question 4
Question: Answer: Aliter: ..
Question: Answer: Aliter: ..Example:
Find the adjoint of the matrix. ..
Find the adjoint of the matrix. ..See what our Users say :
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