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The right triangle ABC has legs of length AB = 2 and BC = 4. Point D is the foot of the perpendicular from B on the side AC. The altitude from D of triangle BDC meets the side BC at E. The altitude from E of triangle DEC meets DC at F......(as so forth). If the area of the shaded regions can be expressed in lowest rational equal to p/q , find (p + q).
If A.M., G.M. and H.M. of first and last terms of the series 100, 101, 102,…. n –1, n are the terms of the series it self then the value of n is (100 < n ≤ 500 )
If (1 – y) (1 + 2x + 4x^{2} + 8x^{3} + 16x^{4} + 32x5) = 1 – y6, (y ≠ 1), then a value y/x is 
If  a  <1 &  b  < 1 then sum of the series a (a + b) + a^{32} (a^{2}+ b^{2}) + a^{3} (a^{3}+ b^{3}) + ….. up to ∞ is
Consider an infinite G.P. with first term a and common ratio r. Its sum is 4 and the second term is 3/4, then
Let S_{1}, S_{2},… be squares such that for each n ≥ 1, the length of a side of S_{n} equals the length of a diagonal of S_{n+1}. If the length of a side of S_{1} is 10 cm, then the smallest value of n for which Area (S_{n}) < 1 is 
Let a, b be the roots of x^{2} –3x + p = 0 and let c, d be the roots of x^{2} –12x + q = 0, where a, b, c, d form an increasing G.P. Then the ratio of q + p : q – p is equal to
Sum of the series .5 + .55 + .555 + ………. upto n terms is
Suppose a, b, c are in A.P. and a^{2}, b^{2}, c^{2} are in G.P. If a < b < c and a + b + c =3/2, then the value of a is 
If the sixth term of an A.P. is equal to 2. the value of the common difference of the A.P. which makes the product a_{1} a_{4} a_{5} the greatest is
(the ith term is denoted by a)
If x, y, z are positive nos. minimum value of x^{lny –lnz} + y^{lnz}^{–lnx} + z^{lnx –lny }is –
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209 videos443 docs143 tests
