Mathematics questions
18011 published questions with worked solutions.
- If the sum and product of the first three terms in an A.P. are 42 and 2394, then find the 15^ th term. [Common difference (d)>0]
- Find the least value of k for which 3^ 1+x +3^ 1-x , k2, 9^x+9^ -x are three consecutive terms of an A.P.
- If the sum of 1^ st term, 9^ th term and 23^ rd term of an A.P. is 69, then find the sum of first 21 terms.
- If 3^ 2 2 -1 , 14 and 3^ 4-2 2 are the first three terms of an A.P., then find its 7^ th term.
- If p=e^ ( ^2x+ ^4x+ ^6x+ ) _e2 , 0<x< 2, satisfies the equation x^2-17x+16=0, find x+ x x- x .
- Find the value of 1 17 - 16 - 1 18 - 17 + 1 19 - 18 - - 1 144 - 143 .
- If the sum of the first 12 terms of the series 1+6+ 9 (1^2+2^2+3^2 ) 7+ 12 (1^2+2^2+3^2+4^2 ) 9+ is 259m 3, then find the value...
- If the sum of the series 1+ 23+ 69+ 10 27 + 14 81 + is 2m-5 then find the value of m.
- If the A.M. of two numbers is greater than G.M. by 2 and the ratio of the numbers is 4:1, then find the sum of two numbers.
- The product of three consecutive terms of a G.P. is 216. If 3 is added to each of the first and the second of these terms, the...
- Let a be the arithmetic mean of two positive numbers and b,c be the two geometric means between them. Find the value of b^3+c^3...
- If x>0 and _2x+ _2 x+ _2 [4]x+ =4, find x+4.
- The sum of three consecutive terms in a geometric progression is 14. If 1 is added to each of the first and second terms and 1 is...
- If the sum of an infinite geometric series is 3 and the sum of the cubes of its terms is 27 19 , then find the first term of the...
- Let a_1,a_2,a_3, be the terms of an A.P. If a_1+a_2+ +a_p a_1+a_2+ +a_q = p^2 q^2 , p q and a_6 a_ 21 = mn, where G.C.D. (m,n)=1,...
- Find the value of _ r=1 ^ (4r+5)5^ -r r(5r+5) .
- If 11 A.M.'s are inserted between 28 and 10, then find the number of integral A.M.'s.
- Let a_1,a_2,a_3, be in A.P. and g_1,g_2,g_3, be in G.P. If a_1=g_1=3 and a_8=g_4=24, then find g_7 a_4 .
- For three positive integers p,q,r, x^ pq^2 =y^ qr =z^ p^2r and r=pq+1 such that 3,3 _yx,3 _zy,7 _xz are in A.P. with common...
- If a_n= -2 4n^2-16n+15 , then a_1+a_2+ +a_ 25 is equal to