CLASS-IX MOCK TEST (06-08-2021)

The expansion of (x + y)ⁿ where x and y any two real numbers and n is any positive integer, maybe stated as follows

• ⁿC₀ xⁿ - ⁿC₁ x^n-1 y + ⁿC₂ x^n-2 y² - ⁿC₃ x^n-3 y³ … + ⁿC_n yⁿ

• ⁿC₀ xⁿ + ⁿC₁ x^n-2 y + ⁿC₂ x^n-1 y² + ⁿC₃ x^n-3 y³ … + ⁿC_n yⁿ

• ⁿC₀ xⁿ + ⁿC₁ x^n-1 y + ⁿC₂ x^n-2 y² + ⁿC₃ x^n-3 y³ … (-1)ⁿ yⁿ

• ⁿC₀ xⁿ + ⁿC₁ x^n-1 y + ⁿC₂ x^n-2 y² + ⁿC₃ x^n-3 y³ … + ⁿC_n yⁿ

The expansion of (x - y)ⁿ where x and y any two real numbers and n is any positive integer, maybe stated as follows

• ⁿC₀ xⁿ - ⁿC₁ x^n-1 y + ⁿC₂ x^n-2 y² - ⁿC₃ x^n-3 y³ … + ⁿC_n yⁿ

• ⁿC₀ xⁿ - ⁿC₁ x^n-1 y + ⁿC₂ x^n-2 y² - ⁿC₃ x^n-3 y³ … (-1)^{n n}c_n x⁰ yⁿ

• ⁿC₀ xⁿ - ⁿC₁ x^n-1 y + ⁿC₂ x^n-2 y² + ⁿC₃ x^n-3 y³ … (-1)ⁿ yⁿ

• ⁿC₀ xⁿ + ⁿC₁ x^n-1 y + ⁿC₂ x^n-2 y² + ⁿC₃ x^n-3 y³ … + ⁿC_n yⁿ

The total number of terms that comes in the expansion of (x+y)ⁿ is

• n

• n-1

• n+1

• none of thse

T_{r + 1} =

• ⁿC_r x^n-r . y^r

• x^n-r . y^r

• nC0 xn + nC1 xn-1 . y + nC2 xn-2 . y2 + … + nCn yn

• ⁿC₀ xⁿ - ⁿC₁ x^n-1 . y + ⁿC₂ x^n-2. y² + … + ⁿC_n yⁿ

The middle term in  $\left(x+y\right)^n$  is

•  

   $\frac{n}{2}+1$ where n is odd

•    $\frac{n+1}{2}\ where\ n\ is\ even$ 

•  $\frac{n}{2}+\ 1\ where\ n\ is\ even$ 

• both 1 & 2

The greatest binomial co-efficient in (x+a)ⁿ is

• $n_{c_{n+\frac{1}{2}}}\$ when n is odd

• $n_{c_{\frac{n+1}{2\ }}}\$ when n is even

• $n_{c_{\frac{n}{2}}}\$ when n is even

• $n_{c_{\frac{n}{2}+1}\ }$

The middle term in (x+y)ⁿ is ______

• $\frac{n+1}{2}\$ when n is odd

• $\frac{n+3}{2}\$ when n is even

• $\frac{n+3}{2\ }\$ when n is odd

• both 1 & 3

The greatest binomial co-efficient in (x+a)ⁿ is

• $n_{c_{\frac{n}{2}}}$ when n is odd
  

• $n_{c_{\frac{n+1}{2}}}$ when n is odd

• $n_{c_{\frac{n-1}{2}}}$ when n is even

• $n_{c_{\frac{n-1}{2}}}$ when n is odd

• Both 2 & 4

Numerically greatest integer in the expansion of (x+a)^n if $\frac{\left(n+1\right)\left|x\right|}{1+\left|x\right|}=\ p$  is

•  $t_p$  

•  $t_{p-1}$  

•  $T_{\frac{p+1}{ }}$  

• both 1 & 3

Numerically greatest integer in the expansion of (x+a)^n if $\frac{\left(n+1\right)\left|x\right|}{1+\left|x\right|}=\ p+f$  and 0<f<1 is

•  $t_p$  

•  $t_{p-1}$  

•  $T_{\frac{p+1}{ }}$  

• both 1 & 3