Mathematics questions
18011 published questions with worked solutions.
- If the sum of the first 20 terms of the series _ (7^ 1/2 ) x+ _ (7^ 1/3 ) x+ _ (7^ 1/4 ) x+ is 460, then x is equal to
- The common difference of the A.P. b_1,b_2, ,b_m is 2 more than the common difference of A.P. a_1,a_2, ,a_n. If a_ 40 =-159, a_...
- Let a,b,c be in arithmetic progression. Let the centroid of the triangle with vertices (a,c), (2,b) and (a,b) be ( 10 3, 73 ). If...
- If 0< , < 2, x= _ n=0 ^ ^ 2n , y= _ n=0 ^ ^ 2n and z= _ n=0 ^ ^ 2n ^ 2n then
- The minimum value of f(x)=a^ a^x +a^ 1-a^x , where a,x R and a>0, is equal to
- In an increasing geometric series, the sum of the second and the sixth term is 25 2 and the product of the third and fifth term...
- The sum of infinite series 1+ 23+ 7 3^2 + 12 3^3 + 17 3^4 + 22 3^5 + is equal to
- If , , are natural numbers such that 100^ -199 =(100)(100)+(99)(101)+(98)(102)+ +(1)(199), then the slope of the line passing...
- Let S_1 be the sum of first 2n terms of an arithmetic progression. Let S_2 be the sum of first 4n terms of the same arithmetic...
- Let S_n denote the sum of first n -terms of an arithmetic progression. If S_ 10 =530, S_5=140, then S_ 20 -S_6 is equal to
- Let S_n be the sum of the first n terms of an arithmetic progression. If S_ 3n =3S_ 2n , then the value of S_ 4n S_ 2n is
- If [x] be the greatest integer less than or equal to x, then _ n=8 ^ 100 [ (-1)^nn 2 ] is equal to
- If ( 9 ),x, ( 7 18 ) are in arithmetic progression and ( 9 ),y, ( 5 18 ) are also in arithmetic progression, then |x-2y| is equal...
- If the sum of an infinite GP a,ar,ar^2,ar^3, is 15 and the sum of the squares of its each term is 150, then the sum of...
- _ x 2 ( _ n=1 ^9 x n(n+1)x^2+2(2n+1)x+4 ) is equal to
- Let A B = (A-C) (C-B) , where A,B,C are angles of a triangle ABC. If the lengths of the sides opposite to these angles are a,b,c...Not in JEE syllabus
- If 0<x<1, then 32x^2+ 53x^3+ 74x^4+ , is equal to
- Three numbers are in an increasing geometric progression with common ratio r. If the middle number is doubled, then the new...
- The sum of 10 terms of the series 3 1^2 2^2 + 5 2^2 3^2 + 7 3^2 4^2 + is
- Let a_1,a_2,a_3, be an A.P. If a_1+a_2+ +a_ 10 a_1+a_2+ +a_p = 100 p^2 , p 10, then a_ 11 a_ 10 is equal to