Algebraic Expression

Q. If $T_0,T_1,\cdots ,T_n$ represent the terms in the expansion of $(x+a{)}^n$, then the value of $(T_0-T_2+T_4-\cdots {)}^2+(T_1-T_3+T_5-\cdots {)}^2$ is

1. $a^{2n}$
2. $(x+a{)}^{2n}$
3. $(x^2+a^2{)}^n$
4. $a^{2n}$

Q. Let the function $f:R-\{-b\}\to R-\left\{1\right\}$ be defined by $f\left(x\right)=\frac{x+a}{x+b},a\ne b.$ Then

1. 𝑓 is neither one–one nor onto function
2. 𝑓 is onto but not one–one function
3. 𝑓 is one–one but not onto function
4. 𝑓 is bijective function

Q. The total number of two digit numbers $n$, such that $3^n+7^n$ is a multiple of $10$, is

Q.

If x, y, z are positive, and x + y + z = 1, then the maximum value of xyz is

1. $\frac{1}{3}$

2. $\frac{1}{5}$

3. $\frac{1}{25}$

4. $\frac{1}{27}$

Q.

$1+2^1+2^2+2^3.........{.2}^{1999}$ =

1. $2^{2000}$

2. $2^{2000}-1$

3. $2^{2001}-2$

4. $2^{2001}-1$

Q. If a, b, c are the positive integers, then (a+b)(b+c)(c+a) is

1. = 8 abc
2. < 8 abc
3. None of these
4. > 8 abc

Q. If the arithmetic mean and geometric mean of the $p^{th}$ and $q^{th}$ terms of the sequence $-16,8,-4,2,...$ satisfy the equation $4x^2-9x+5=0$, then $p+q$ is equal to