Mathematics questions
18011 published questions with worked solutions.
- The sum of the first 20 terms of the series 5+11+19+29+41+ , is
- Let S_K= 1+2+ +K K and _ j=1 ^nS_j^2= nA (Bn^2+Cn+D ), where A,B,C,D N and A has least value. Then
- Let a_n be the n^ th term of the series 5+8+14+23+35+50+ and S_n= _ K=1 ^na_K. Then a_1,a_2, ,a_n is equal to
- Let the positive integers a and r be the first term and common ratio of a geometric progression. If the sum of squares of its...
- Let a,b,c and d be positive real numbers such that a+b+c+d=11. If the maximum value of a^5b^3c^2d is 3750 , then the value of is
- Let s_1,s_2,s_3, ,s_ 10 respectively be the sum of 12 terms of 10 A.P.'s whose first terms are 1,2,3, ,10 and the common...
- Let be a G.P. of increasing positive numbers. Let the sum of its G_2^2=243 3 and G_2= 243 3 =27 terms be 2 and the product of its...
- Let A_1 and A_2 be two arithmetic means and G_1,G_2,G_3 be three geometric means of two distinct positive numbers. Then...
- Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that N-2, 3N ,N+2 are in geometric...
- If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296, respectively, then the sum of common...
- The parabolas ax^2+2bx+cy=0 and dx^2+2ex+fy=0 intersect on the line y=1. If a,b,c,d,e,f are positive real numbers and a,b,c are...
- Let x^2=4 and a=x^4=16 be in A.P., and x^4=4x^2, x^2=4 and a=x^4=16 be in G.P. If the sum of first 20 terms of an A.P., whose...
- Let S= _ r=1 ^ 10 ((r+3)!-(r+1)!-8 ((r+1)!-r! ) ) be an A.P. If _ r=1 ^ 10 ((r+3)!-(r+1)! )-8 _ r=1 ^ 10 ((r+1)!-r! ), the...
- Let (2^x-4 ) (2^x-8 )=0 be the x=2 or 3 term of an A.P. If x=2 and x=3, then the common difference of the A.P. is
- Statement-1: The sum of the series q=16, r=16, s=1 q+5CC_r-5= ^ 17 C_ 15 +400 is 8000. Statement-2: =136 for any natural number =...
- If 100 times the 100^ th term of an A.P. with non-zero common difference equals 50 times its 50^ th term, then the 150^ th term...
- Let S= 75+ 9 5^2 + 13 5^3 + 19 5^4 + . Then the value of 160S is
- Let a,b,c R. If f(x)=ax^2+bx+c is such that 2 +2 =-2 and = 12, then =- 32 is equal to
- Let a_3=a_2+2=3+2=5 be in A.P. such that b_4=a_4+b_3=7+9=16 and a_4=a_3+2=5+2=7. If b_ 15 =225, then a_ 15 =a_ 14 +2=29 is equal...
- Let 1+3+5+ +19=100- term be the sum of the first 20 terms and Set 11= 3 101,3 102, ,3 121 be the sum of the first 40 terms of the...