JEE Advanced questions
3844 published questions with worked solutions.
- Let a_1, a_2, a_3, be in AP and a_p, a_q, a_r be in GP. Then a_q : a_p is equal to
- If a, b, c are in GP then a + b, 2b, b + c are in
- If a, b, c, d are nonzero real numbers such that (a^2 + b^2 + c^2)(b^2 + c^2 + d^2) (ab + bc + cd)^2 then a, b, c, d are in
- If a, b, c are in AP then a bc , 1 c , 2 b are in
- If in an AP, t_1 = _ 10 a, t_ n+1 = _ 10 b and t_ 2n+1 = _ 10 c then a, b, c are in
- If n!, 3 n! and (n+1)! are in GP then n!, 5 n! and (n+1)! are in
- In an AP, the pth term is q and the (p+q)th term is 0. Then the qth term is
- In a sequence of (4n+1) terms the first (2n+1) terms are in AP whose common difference is 2, and the last (2n+1) terms are in GP...
- If x^2 + 9y^2 + 25z^2 = xyz ( 15 x + 5 y + 3 z ) then x, y, z are in
- If a, b, c, d and p are distinct real numbers such that (a^2 + b^2 + c^2)p^2 - 2(ab + bc + cd)p + (b^2 + c^2 + d^2) 0 then a, b,...
- The largest term common to the sequences 1, 11, 21, 31, to 100 terms and 31, 36, 41, 46, to 100 terms is
- The interior angles of a convex polygon are in AP, the common difference being 5^ . If the smallest angle is 2 /3 then the number...
- The minimum number of terms of 1 + 3 + 5 + 7 + that add up to a number exceeding 1357 is
- In the value of 100! the number of zeros at the end is
- The sum of all the proper divisors of 9900 is
- The sum of all odd proper divisors of 360 is
- In the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, , where n consecutive terms have the value n, the 150th term is
- In the sequence 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, , where n consecutive terms have the value n, the 1025th term is
- Let t_n be a sequence of integers in GP in which t_4 : t_6 = 1 : 4 and t_2 + t_5 = 216. Then t_1 is
- If ( 5c a ), ( 3b 5c ) and ( a 3b ) are in AP, where a, b, c are in GP, then a, b, c are the lengths of sides of