Related InterviewSolutions

• In the expansion of `(5^(1//2)+7^(1//8))^(1024),`the number of integral terms is`128`b. `129`c. `130`d. `131`A. 128B. 129C. 130D. 131
• For natural numbers m, n if `(1-y)^(m)(1+y)^(n) = 1+a_(1)y+a_(2)y^(2) + "……."` and `a_(1) = a_(2) = 10`, then `(m,n)` is :A. (20, 45)B. (35, 20)C. `(45, 35)`D. (35, 45)
• If the expansion in power of x of the function `(1)/(( 1 - ax)(1 - bx)) is a_(0) + a_(1) x + a_(2) x^(2) + a_(3) a^(3) + …, ` then `a_(n)` isA. `(b^(n) - a^(n))/(b-a)`B. `(a^(n) - b^(n))/(b-a)`C. `(a^(n+1) - b^(n+1))/(b-a)`D. `(b^(n+1) - a^(n+1))/(b-a)`
• The value of `(30 0)(30 10)-(30 1)(30 11)+(30 2)(30 12)++(30 20)(30 30)=``^60 C 20`b. `^30 C 10`c. `^60 C 30`d. `^40 C 30`A. `""^(30)C_(11)`B. `""^(60)C_(10)`C. `""^(30)C_(10)`D. `""^(65)C_(55)`
• Which is larger : `(99^(50)+100^(50))` or `(101)^(50)`.A. `99^(50) + 100^(50)`B. both are equalC. ` (101)^(50)`D. none of these
• If w is a non-real cube root of unity, x is a real number and `n in N` such that first three terms in the binomial expansion of `(w + x)^n` are `1,12bar w and 69 w` respectively, thenA. ` n = 36, x = 1`B. n = 12, x=2C. ` n = 24, x = (1)/(2)`D. ` n = 18, x = (1)/(3)`
• The coefficient of `x^9` in the expansion of `(1 + x) (1 +x^2)(1 +x^3)...(1+x^(100))`isA. 2B. 6C. 9D. 8
• The power of x which has the greatest coefficient inthe expansion of `(1+x/2)^10`A. 2B. 3C. 4D. 5
• The coefficient of `x^2 y^5 z^3` in the expansion of `(2x + y + 3z)^10` isA. `(10!)/(2!3!5!)`B. `(10!)/(2!3!5!)xx2^(2) xx3^(3)`C. `(10!)/(2!3!5!)xx2^(3) xx3^(2)`D. `10! xx2^(2) xx3^(3)`
• The total number of terms in the expansion of `(2x - y + 4z)^(12)`,isA. 90B. 91C. 13D. none of these