Download App

RELATIONS AND FUNCTIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSRELATIONS AND FUNCTIONS1 Mark
Question
Let * be a binary operation on N defined by a * b = a + b + 10 for all a, b ∈ N. The identity element for * in N is:
  1. −10
  2. 0
  3. 10
  4. Non-existent.
✓

Answer

  1. Non-existent.
Solution:
Given a * b = a + b + 10
Let the identity element be e, then
a * e = a
⇒ a + e + 10 = a
⇒ e = -10
But the operation is defined on the set of natural numbers.
So, the identity element doesn't exist.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from RELATIONS AND FUNCTIONS→RELATIONS AND FUNCTIONS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

The vector equation of the plane containing the line $\vec{\text{r}}=(-2\hat{\text{i}}-3\hat{\text{j}}+\hat{\text{k}})+\lambda(3\hat{\text{i}}-2\hat{\text{j}}-\hat{\text{k}})$ and the point $\hat{\text{i}}+2\hat{\text{j}}+3\hat{\text{k}}$ is:
  1. $\vec{\text{r}}.(\hat{\text{i}}+3\hat{\text{k}})=10$
  2. $\vec{\text{r}}.(\hat{\text{i}}-3\hat{\text{k}})=10$
  3. $\vec{\text{r}}.(3\hat{\text{i}}+\hat{\text{k}})=10$
  4. $\text{None of these}$
→
If $\text{S}=\begin{bmatrix}\text{a} & \text{b} \\ \text{c} & \text{d} \end{bmatrix},$ then adj A is:
  1. $\begin{bmatrix} -\text{d} & -\text{b} \\ -\text{c} & \text{a} \end{bmatrix}$
  2. $\begin{bmatrix} \text{d} & -\text{b} \\ -\text{c} & \text{a} \end{bmatrix}$
  3. $\begin{bmatrix} \text{d} & \text{b} \\ \text{c} & \text{a} \end{bmatrix}$
  4. $\begin{bmatrix} \text{d} & \text{c} \\ \text{b} & \text{a} \end{bmatrix}$
→
Let us define a relation R in R as aRb if a ≥ b. Then R is:
  1. An equivalence relation.
  2. Reflexive, transitive but not symmetric.
  3. Symmetric, transitive but not reflexive.
  4. Neither transitive nor reflexive but symmetric.
→
The normal to the curve $x^2 = 4y$ passing through $(1, 2)$ is:
→
$\int\limits^1_{-1}|1-\text{x}|\text{dx}$ is equal to:
  1. -2
  2. 2
  3. 0
  4. 4
→
Mark the correct alternative in the following question for the binary operation * on Z defined by a * b = a + b + 1, the identity element is:
  1. 0
  2. -1
  3. 1
  4. 2
→
The domain of function $f(x)=\sin ^{-1} x+\cos x$ is-
→
A constraint in an LP model becomes redundant because:
→
Which of the following term is used in a linear programming problem?
→
If $A=\left[\begin{array}{ccc}-2 & 0 & 0 \\ 1 & 2 & 3 \\ 5 & 1 & -1\end{array}\right]$, then the value of $|A(\operatorname{adj} . A)|$ is:
→