Dubey

Algebrathon The Last Word on Algebra By: Santosh Dubey

The function f(x) = log( x - 1) – log( x - 2), and g(x) = log(x-1/x-2) are identical when x lies in the interval ,[object Object],[object Object],[object Object],[object Object]

For n = 1,2,3…… the value of [(n +1)/2 ] + [ (n +2)/4 ] + [ (n +4)/8 ]+ [ (n +8)/16 ]+……… ∞ where [ . ] represents the greatest integer function ,[object Object],[object Object],[object Object],[object Object]

If x satisfies I x 2 – 3x + 2 I + I x-1 I = x – 3 then ,[object Object],[object Object],[object Object],[object Object]

Let f(x) = α x / (x +1) , x ≠ - 1, then for what values of α is f [ { f(x)} ] = x ,[object Object],[object Object],[object Object],[object Object]

Let g(x) = 1 + x – [x] and f(x)= -1 ,x < 0 0 ,x = 0 1, x > 0 then for all x f [g(x)] is ,[object Object],[object Object],[object Object],[object Object]

For real number x , [x] denotes the integral part of x then the value of [1/2] + [ (1/2) + (1/100)] + [(1/2) + (2/100)]….…[(1/2) + (99/100)] ,[object Object],[object Object],[object Object],[object Object]

If f(x) = ( a – x n ) 1/n then find f [f(x)] ,[object Object],[object Object],[object Object],[object Object]

If g(x) = 1 + √x and f[g(x)] = 3 + 2 √x + x then f(x) = ,[object Object],[object Object],[object Object],[object Object]

If f(x) = (2 x + 2 -x )/2 then f(x+y).f(x-y) = ,[object Object],[object Object],[object Object],[object Object]

If f(x) = log[(1-x)/(1+x)], then f [ 2x/(1+x 2 ) ] = ,[object Object],[object Object],[object Object],[object Object]

Which of the following is an even function ,[object Object],[object Object],[object Object],[object Object]

Let f(x) = x 2 + 1/x 2 and x ≠ 0 then f(x) is equal to ,[object Object],[object Object],[object Object],[object Object]

If 2f(x) – 3f(1/x) = x 2 and x ≠ 0 then f(2) is equal to ,[object Object],[object Object],[object Object],[object Object]

Range of (x 2 + x +2) / (x 2 +x +1) is ,[object Object],[object Object],[object Object],[object Object]

If s is the set of all real x such that (2x - 1) / (2x 3 +3x 2 + x) is positive then s contains ,[object Object],[object Object],[object Object],[object Object]

If f(x) = log[(1+x)/(1+x)], and g(x) = [ (3x + x 3 ) / (1+3x 2 ) ] then f [ g(x) ] = ,[object Object],[object Object],[object Object],[object Object]

If x ε R and P = x 2 / (x 4 - 2x 2 + 4) then P lies in the interval ,[object Object],[object Object],[object Object],[object Object]

The minimum value of (x 2 – 3) 3 +27 2 ,[object Object],[object Object],[object Object],[object Object]

If f(x) = 4 x / (4 x +2) then f(1/1997) + f(2/1997) + f(3/1997) + f(4/1997) ………f(1996/1997 ) ,[object Object],[object Object],[object Object],[object Object]

Let f(x) be a function defined on [-1 , 1].If the area of the equilateral triangle with two of its vertices at (0 , 0) and (x ,f(x)) is (√3)/4 then the function f(x) is ,[object Object],[object Object],[object Object],[object Object]

Let f(x) = 1 / (1- x) , g(x) = f { f(x)} and h(x) = f [ f { f(x)}] then f(x)g(x)h(x) is ,[object Object],[object Object],[object Object],[object Object]

If f(x + y) = f(x) + f(y) – xy – 1for all x,y ε R and f(1) = 1then the number of solutions to f(n) = n ,[object Object],[object Object],[object Object],[object Object]

Let f(x) = 64x 3 + 1/x 3 and a and b are the roots of equation (4x) + (1/x) = 3 then ,[object Object],[object Object],[object Object],[object Object]

If f( x+y , x-y) = xy ,then the arithmetic mean of f(x ,y) and f(y , x) is ,[object Object],[object Object],[object Object],[object Object]

If f(x) = (1- x)/(1+ x) x ≠ 0 then f[f(x)] + f[f(1/x)] ,[object Object],[object Object],[object Object],[object Object]

If f(n+1) = [2f(n) + 1]/2 , n = 1,2,3…… and f(1) = 2 then f(101) equals ,[object Object],[object Object],[object Object],[object Object]

a,b,c are three distinct real numbers in G.P.If a+b+c = xb, then ,[object Object],[object Object],[object Object],[object Object]

The sum of all numbers of the form n 3 which lie between 100 and 10,000 ,[object Object],[object Object],[object Object],[object Object]

If the first term of an infinite G.P series is 1 and its every term is the sum of next successive terms then its fourth term will be ,[object Object],[object Object],[object Object],[object Object]

Sum of n terms of 1.2.3 + 2.3.4 + 3.4.5……… will be ,[object Object],[object Object],[object Object],[object Object]

In a G.P (m +n) th term is 9 and (m-n) th term is 4 then m th term ,[object Object],[object Object],[object Object],[object Object]

If each term of a G.P is positive and each term is sum of its two succeeding terms , then common ratio of the G.P ,[object Object],[object Object],[object Object],[object Object]

The product of (32)(32) 1/6 (32) 1/36 … ∞ ,[object Object],[object Object],[object Object],[object Object]

Sum of all terms of a G.P is five times the sum of the odd terms.The common ratio is ,[object Object],[object Object],[object Object],[object Object]

The sum of the series 1 + 2.2 + 3.2 2 + 4.2 3 + 5.2 4 +….+100.2 99 ,[object Object],[object Object],[object Object],[object Object]

The 20 th term of the series 2x4 + 4x6 + 6x8……………………. ,[object Object],[object Object],[object Object],[object Object]

The sum of the first n terms of 1 + 2.2 2 + 3 2 + 2.4 2 + 5 2 + 5.6 2 ………..is n(n+1) 2 when n is even what is the sum when n is odd ,[object Object],[object Object],[object Object],[object Object]

In a G.P the (p + q) th term is m and (p - q) th term is n, then what is the p th term ,[object Object],[object Object],[object Object],[object Object]

Let Tr be the r th term of an A.P, for r = 1,2,3……..If for some positive integer m , n we have Tm = 1/m and Tn = 1/n then Tmn = ,[object Object],[object Object],[object Object],[object Object]

If a 1 ,a 2 ,a 3 are three consecutive terms of a G.P with common ratio k.find the values of k for which the inequality a 3 > 4a 2 – 3a 1 is satisfied

If x = 1+ a + a 2 + a 3 + a 4 …..and y = 1+ b + b 2 + b 3 + b 4 …..then the value of 1 + ab + a 2 b 2 + a 3 b 3 + a 4 b 4 ….. if 0 < a < 1 and 0 < b <1 ,[object Object],[object Object],[object Object],[object Object]

Find the sum of the product of every pair of first n natural number

Sum to n terms of the series [1/(1 + 1 2 + 1 4 ) ] + [2/(1 + 2 2 + 2 4 )] + [3/(1 + 3 2 +3 4 )]…………….

Three successive terms of a G.P will form a triangle if the common ratio lies between

Two consecutive numbers from 1,2,3 ………..n are removed, arithmetic mean of the remaining numbers is 105/4. Find the removed numbers

Let s k be the sum of the first k terms of an arithmetic progression. What must this progression be for s kx /s x to be independent of x

100 th term of he series 1 + 3 + 7 + 15……. ,[object Object],[object Object],[object Object],[object Object]

Sum to 20 terms of series 1.3 2 +2.5 2 + 3.7 2 …………….. ,[object Object],[object Object],[object Object],[object Object]

Sum to 16 terms of (1 3 /1) + (1 3 + 2 3 )/3 + (1 3 + 2 3 + 3 3 )/1 + 3 + 5 ……………… ,[object Object],[object Object],[object Object],[object Object]

The largest value of positive integer k for which n k + 1 divides 1 + n + n 2 + ………..+ n 127 is divisible by ,[object Object],[object Object],[object Object],[object Object]

If x + y + z = 1 and x,y,z are positive numbers such that (1 – x) (1 – y) (1 – z) ≥ kxyz then k = ,[object Object],[object Object],[object Object],[object Object]

Number of terms in the sequence 1,3,6,10,15……………5050 ,[object Object],[object Object],[object Object],[object Object]

If a + b + c = 3 a > 0 , b >0 , c > 0 then the greatest value of a 2 b 3 c 2 ,[object Object],[object Object],[object Object],[object Object]

The largest term in the sequence (1/503) , (4/524) , (9/581), (16/692) ………….is ,[object Object],[object Object],[object Object],[object Object]

If T n = n x n! then Σ T n (n = 1 to20) is equal to ,[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object]

[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object]

If a,b,c & d are real numbers such that 2ac = b+d, then how many of the following statements are necessary true. x 2 + 2ax + b has real roots X 2 + 2cx + d has real roots

[object Object],[object Object],[object Object],[object Object]

How many ordered pair of Positive integers satisfy the condition p+q+12 =pq

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

If p + q + r = 7, p 2 + q 2 + r 2 = 35, and p 3 + q 3 + r 3 = 151, then Find the value of pq + qr + rp Find the value of pqr Find the value of p 4 + q 4 + r 4

If a, b, c are positive numbers satisfying a 2 + b 2 + c 2 = 12, then find the max/min value of a + b +c

NUMBER SYSTEMS PROBLEM SOLVING SESSION - 1

.abcabcabcabc…….=pq/rs.How many possible pairs of two digit numbers pq and rs are possible such that they are coprime to each other?????

Dubey

Recomendados

Recomendados

Más contenido relacionado

La actualidad más candente

La actualidad más candente (18)

Similar a Dubey

Similar a Dubey (20)

Último

Último (20)

Dubey

Notas del editor