Invertible Element Binary Operation

Q. $Let\text{'}*\text{'}beabinaryoperationonsetQ-\left\{1\right\}definedbya*b=a+b-abforalla,b\in Q-\left\{1\right\}.$
Then, which of the following statement(s) is/are true?

1. 0 is the identity element with respect to * on $Q-${1}.
2. Every element of $Q-$ {1} is invertible.
3. For any element $a\in Q-${1}, inverse of a is $\frac{a}{a-1}$
4. * is associative on $Q-$ {1}

Q. For any three sets A, B and C
(a) $A\cap \left(B-C\right)=\left(A\cap B\right)-\left(A\cap C\right)$
(b) $A\cap \left(B-C\right)=\left(A\cap B\right)-C$
(c) $A\cup \left(B-C\right)=\left(A\cup B\right)\cap \left(A\cup C\text{'}\right)$
(d) $A\cup \left(B-C\right)=\left(A\cup B\right)-\left(A\cup C\right).$

Q.

If a ${}^{\ast }$ b = a = b ${}^{\ast }$ a, then b is called the inverse of a under the operation ${}^{\ast }$

1. True

2. False

Q. Let $f$ be a twice differentiable function on $(1,6)$. If $f\left(2\right)=8,f^{\prime }\left(2\right)=5,f^{\prime }\left(x\right)\ge 1$ and $f^{\prime \prime }\left(x\right)\ge 4,$ for all $x\in (1,6),$ then

1. $f\left(5\right)+$$f^{\prime }\left(5\right)\ge 28$
2. $f^{\prime }\left(5\right)+f^{\prime \prime }\left(5\right)\le 20$
3. $f\left(5\right)\le 10$
4. $f\left(5\right)+f^{\prime }\left(5\right)\le 26$

Q.

$iff:N\to Nisdefinedbyf\left(n\right)=n-(-1{)}^n,then$

1. f is one-one but not onto

2. f is both one-one and onto

3. f is neither one-one nor onto

4. f is onto but not one-one