Mathematical Induction and Binomial Theorem - Class 11 (HSSC-I) Mathematics

Q1

The coefficient of the 3rd term of the expression $(1-2x)^6$ will be

Q2

Which of the following conditions is valid for the convergence of $(2+5x)^{-2}$?

Q3

If the statement $x^{2k} - y^{2k}$ is true for $(k+1)$ terms, then it must be divisible by
I. $x+y$
II. $x-y$
III. $x^2+y^2$

Q4

The general term of the binomial expansion of $(3x+7y)^{10}$ is

Q5

The value of $b$ in the expansion of $(1-x)^{-5} = 1 + 5x + bx^2 + \ldots$ will be

Q6

In the binomial expansion of $\left(x - \dfrac{y}{4}\right)^5$, the sum of the coefficients of the first and second term is

Q7

The value of $p$ in the binomial expansion $(1+px)^3 = 1 + 12x + 48x^2 + 64x^3$ is

Q8

$1^3 + 2^3 + 3^3 + \ldots + K^3 = \dfrac{K^2(K+1)^2}{4}$ is true for the $(K+1)$th term, the term that should be added to both sides is

Q9

Fill in the blank:

Q10

Fill in the following blanks:

Q11

If the square and higher powers of $x$ are neglected, then the approximate form of the binomial expression $(1+7x)^{\dfrac{1}{2}}(1-3x)^{\dfrac{1}{2}}$ will be

Q12

The general term in the binomial expansion of $(3x+7y)^{10}$ is

Q13

If $(1-x)^{-5}=1+5x+bx^2+\dots$, then the value of $b$ will be

Q14

The third term in the expansion of $(a-2b)^6$ is