Mathematics questions
18011 published questions with worked solutions.
- Statement 1: For each natural number n, (n+1)^7-n^7-1 is divisible by 7. Statement 2: For each natural number n, n^7-n is...Not in JEE syllabus
- If n is a positive integer, then ( 3+1 )^ 2n - ( 3-1 )^ 2n is
- Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A B having 3 or more elements...
- The sum of the co-efficients of all odd degree terms in the expansion of (x+ x^3-1 )^5+ (x- x^3-1 )^5, (x>1) is
- The coefficient of t^4 in the expansion of ( 1-t^6 1-t )^3 is
- If _ i=1 ^ 20 ( ^ 20 C_ i-1 ^ 20 C_i+ ^ 20 C_ i-1 )^3= k 21 , then k equals
- The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is
- If the third term in the binomial expansion of (1+x^ _2x )^5 equals 2560, then a possible value of x is
- Consider the statement: "P(n):n^2-n+41 is prime." Then which one of the following is true?Not in JEE syllabus
- The positive value of for which the co-efficient of x^2 in the expression x^2 ( x+ x^2 )^ 10 is 720, is
- The sum of the real values of x for which the middle term in the binomial expansion of ( x^3 3+ 3x )^8 equals 5670 is
- Let (x+10)^ 50 +(x-10)^ 50 =a_0+a_1x+a_2x^2+ +a_ 50 x^ 50 , for all x R; then a_2 a_0 is equal to
- A ratio of the 5^ th term from the beginning to the 5^ th term from the end in the binomial expansion of (2^ 13 + 1 2(3)^ 13 )^...
- The total number of irrational terms in the binomial expansion of (7^ 1/5 -3^ 1/10 )^ 60 is
- The sum of the co-efficients of all even degree terms in x in the expansion of (x+ x^3-1 )^6+ (x- x^3-1 )^6, (x>1) is equal to
- If the fourth term in the Binomial expansion of ( 2x+x^ _8x )^6 (x>0) is 20 8^7, then a value of x is
- If some three consecutive coefficients in the binomial expansion of (x+1)^n in powers of x are in the ratio 2:15:70, then the...
- If the coefficients of x^2 and x^3 are both zero, in the expansion of the expression (1+ax+bx^2 )(1-3x)^ 15 in powers of x, then...
- The smallest natural number n, such that the coefficient of x in the expansion of (x^2+ 1 x^3 )^n is ^nC_ 23 , is
- The coefficient of x^ 18 in the product (1+x)(1-x)^ 10 (1+x+x^2 )^9 is