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If a, b, c are in A.P., show that: (b + ...

If a, b, c are in A.P., show that: (b + c), (c + a) and (a + b) are also in A.P.

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If a, b, c are in A.P., prove that: (i) 1/(bc) , 1/(ca), 1/(ab) are in A.P. (ii) (b+c)^2- a^2 ,(a+c)^2- b^2 , (b+a)^2- c^2 are in A.P.

If a, b, c are in A.P., prove that: (i) 1/(bc) , 1/(ca), 1/(ab) are in A.P. (ii) (b+c)^2- a^2 ,(a+c)^2- b^2 , (b+a)^2- c^2 are in A.P.

If a,b,c are in A.P., then show that (i) a^2(b+c), b^2(c+a), c^2(a+b) are also in A.P.

If a ,b ,c are in A.P., prove that 1/(b c),1/(c a),1/(a b), is also in A.P.

If a, b, c are in A.P., then prove that : (i) b+c,c+a,a+b" are also in A.P." (ii) (1)/(bc),(1)/(ca),(1)/(ab)" are also in A.P." (iii) (a(b+c))/(bc),(b(c+a))/(ca),(c(a+b))/(ab)" are also in A.P."

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If (b+c)^(-1), (c+a)^(-1), (a+b)^(-1) are in A.P. then show that (a)/(b+c) , (b)/(c+a) , (c)/(a+b) are also in A.P.

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ICSE-MIXED PRACTICE -SET B
  1. If for two matrices M and N, N =[(3,2),(2,-1)] and product MxxN = [-1...

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  2. If the sum of first 20 terms of an A.P. is same as the sum of its firs...

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  3. If a, b, c are in A.P., show that: (b + c), (c + a) and (a + b) are al...

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  4. If a, b, c are in G.P. and also a, b, c are in A.P. Prove that: 1/a+...

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  5. Evaluate : 9 + 99 + 999 + ........... upto n terms.

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  6. Find the point on the y-axis whose distances from the points (3, 2) an...

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  7. In what ratio does the point P (a, 2) divide the line segment joining ...

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  8. A straight line makes on the co-ordinate axes positive intercepts whos...

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  9. The line 3x - 4y + 12 = 0 meets x-axis at point A and y-axis at point ...

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  10. The line 3x - 4y + 12 = 0 meets x-axis at point A and y-axis at point ...

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  11. In a triangle PQR, L and M are two points on the base QR, such that an...

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  12. In a triangle PQR, L and M are two points on the base QR, such that an...

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  13. In a triangle PQR, L and M are two points on the base QR, such that an...

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  14. In a rectangle ABCD, its diagonal AC = 15 cm and angleACD = alpha If ...

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  15. The given figure shows, AB is a diameter of the circle. Chords AC and ...

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  16. Use ruler and compasses for this question. Construct an isosceles tr...

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  17. Use ruler and compasses for this question. Draw AD, the perpendicula...

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  18. Use ruler and compasses for this question. Draw a circle with centre...

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  19. In triangle ABC, angleBAC = 90^@, AB = 6 cm and BC = 10 cm. A circle ...

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  20. A conical vessel of radius 6 cm and height 8 cm is completely filled w...

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