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prove that am n am - n 2amans a m n a1 m n - 1 da m-n a1 m - n -1 dam a1 m-1 dadd 1 amp 2a mn a m-n a1mn-1 d
raghav buys a shop for rs120000he pays half the balance of the amount in cash and agrees to pay the balance in 12 annual instalments of rs5000 each
find the value of x if 2x 1 x2 x 1 3x2 - 3x 3 are consecutive terms of an apans a2 -a1 a3 -a2rarr x2 x 1-2x - 1 3x2 - 3x 3-
find the sum of all 3 digit numbers which leave remainder 3 when divided by 5ans 103 108998 a n-1d998rarr103 n-15998rarrn180s180
a man arranges to pay a debt of rs3600 in 40 monthly instalments which are in a ap when 30 instalments are paid he dies leaving one third of the debt
find the sum of first 40 positive integers divisible by 6 also find the sum of first 20 positive integers divisible by 5 or
if the pth qth amp rth term of an ap is x y and z respectively show that xq-r yr-p zp-q 0ans pth term rarr x a p-1 dqth term rarr y
find the 20th term from the end of the ap 3 8 13253ans 3 8 13 253last term 253 a20 from end l - n-1d253 - 20-1 5253 - 95
arithmetic progressions one of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a
if the roots of the equation a-bx2 b-c x c - a 0 are equal prove that 2abcans a-bx2 b-c x c - a 0tp 2a b cb2 - 4ac 0b-c2 - 4a-b c -
a pole has to be erected at a point on the boundary of a circular park of diameter 13m in such a way that the differences of its distances from two
a teacher on attempting to arrange the students for mass drill in the form of a solid square found that 24 students were left over when he increased
the positive value of k for which x2 kx 64 0 amp x2 - 8x k 0 will have real roots ans x2 kx 64 0rarr b2 -4ac gt 0k2 - 256 gt 0k gt 16 or k
the hypotenuse of a right triangle is 20m if the difference between the length of the other sides is 4m find the sidesans apqx2 y2 202 x2 y2
a lotus is 2m above the water in a pond due to wind the lotus slides on the side and only the stem completely submerges in the water at a distance of
a dealer sells a toy for rs24 and gains as much percent as the cost price of the toy find the cost price of the toyans let the cp be
the sum of areas of two squares is 468m2 if the difference of their perimeters is 24cm find the sides of the two squaresans let the
1abx 1a1b1x ab ne 0ans 1abx 1a1b1xgt 1abx -1x 1a 1brarr x - a b xxa b x a b abrarrabxabxab0rarrxabxab0rarrx2
solve by factorizationx2 aab abax1 0x2 aab abax1gt x2 aab x abax aab abagt xxaab abaaaab 0gt x -aab x -aba ab ne
quadratic equations for the things of this world cannot be made known without a knowledge of mathematicssolve
the population of the village is 5000 if in a year the number of males were to increase by 5 and that of a female by 3 annually the population
a cyclist after riding a certain distance stopped for half an hour to repair his bicycle after which he completes the whole journey of 30km at half
when the son will be as old as the father today their ages will add up to 126 years when the father was old as the son is today their ages add upto
when 6 boys were admitted amp 6 girls left the percentage of boys increased from 60 to 75 find the original no of boys and girls in the classans let
in an election contested between a and b a obtained votes equal to twice the no of persons on the electoral roll who did not cast their votes amp