Mathematics questions
18011 published questions with worked solutions.
- The value of ( ^7C_0+ ^7C_1 )+ ( ^7C_1+ ^7C_2 )+ + ( ^7C_6+ ^7C_7 ) is
- If (1+x-2x^2 )^6=1+a_1x+a_2x^2+ +a_ 12 x^ 12 , then the value of a_2+a_4+ +a_ 12 is
- C_0 1+ C_2 3+ C_4 5+ C_6 7+ is equal to
- The binomial coefficients which are in decreasing order are
- If ^ n-1 C_r= (k^2-3 ) ^nC_ r+1 , then k
- Let S_1= _ j=1 ^ 10 j(j-1) , ^ 10 C_j, S_2= _ j=1 ^ 10 j , ^ 10 C_j and S_3= _ j=1 ^ 10 j^2 , ^ 10 C_j. Statement 1: S_3=55 2^9....
- The value of 1 81^n - 10 81^n , ^ 2n C_1+ 10^2 81^n , ^ 2n C_2- 10^3 81^n , ^ 2n C_3+ + 10^ 2n 81^n is
- ^ n-2 C_r+2 , ^ n-2 C_ r-1 + ^ n-2 C_ r-2 equals
- The value of ^ 50 C_0 1+ ^ 50 C_2 3+ ^ 50 C_4 5+ + ^ 50 C_ 50 51 is
- If C_0,C_1,C_2, ,C_n denote the binomial coefficient in the expansion of (1+x)^n, then C_0+ C_1 2+ C_2 3+ + C_n n+1 is equal to
- If n=5, then ( ^nC_0 )^2+ ( ^nC_1 )^2+ ( ^nC_2 )^2+ + ( ^nC_5 )^2 is equal to
- If (1+x)^n=C_0+C_1x+C_2x^2+ +C_nx^n. Then, C_0C_1+C_1C_2+ +C_ n-1 C_n is equal to
- If n is an integer greater than 1, then a- ^nC_1(a-1)+ ^nC_2(a-2)+ +(-1)^n(a-n) is equal to
- The value of ^ 15 C_8+ ^ 15 C_9- ^ 15 C_6- ^ 15 C_7 is
- ^ 15 C_0 ^5C_5+ ^ 15 C_1 ^5C_4+ ^ 15 C_2 ^5C_3+ ^ 15 C_3 ^5C_2+ ^ 15 C_4 ^5C_1 is equal to
- The value of the sum of the series 3 ^nC_0-8 ^nC_1+13 , ^nC_2-18 ^nC_3+ upto (n+1) terms is
- ^8C_0 6- ^8C_1+ ^8C_2 6- ^8C_3 6^2+ + ^8C_8 6^7 is equal to
- ^ 20 C_4+2 ^ 20 C_3+ ^ 20 C_2- ^ 22 C_ 18 is equal to
- In the expansion of (1+x)^ 30 , the sum of the coefficients of odd powers of x is
- For r=0, ,10 let A_r, B_r and C_r denote, respectively, the coefficient of x^r in (1+x)^ 10 , (1+x)^ 20 and (1+x)^ 30 . Then _...