Download App

Binary Operations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsBinary Operations1 Mark
MCQ
The binary operation $^*$ is defined by $a ^* b = a^2 + b^2 + ab + 1,$ then $(2 ^* 3) ^* 2$ is equal to:
  • A
    $20$
  • B
    $40$
  • C
    $400$
  • ✓
    $445$
✓

Answer

Correct option: D.
$445$
Given: $a ^* b = a^2 + b^2 + ab + 1$
$2 ^* 3 = 2^2 + 3^2 + 2 \times 3 + 1$
$= 4 + 9 + 6 + 1$
$= 20$
$(2 ^* 3) ^* 2 = 20 ^* 2$
$= 20^2 + 2^2 + 20 \times 2 + 1$
$= 400 + 4 + 40 + 1$
$= 445$

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 Binary Operations→Binary Operations — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The area bounded by the curve $y = f(x),$ the $x-$axis and $x = 1$ and $x = b$ is $(b – 1)$ sin $(3b + 4).$ Then$, f(x)$ is:
→
The distance of the line $\vec{\text{r}}=2\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}+\lambda(\hat{\text{i}}-\hat{\text{j}}+4\hat{\text{k}})$ from the plane $\vec{\text{r}}.(\hat{\text{i}}+5\hat{\text{j}}+\hat{\text{k}})=5$ is:
→
Let $h(x) = \min \{ x,\,{x^2}\} ,$ for every real number of $x$. Then
→
Choose the correct answer from the given four options:The area of the region bounded by the curve $x = 2y + 3$ and the $y$ lines$. y = 1$ and $y = -1$ is:
→
Choose the correct answer from the given four options.The domain of the function defined by $\text{f}(\text{x})=\sin^{-1}\sqrt{\text{x}-1}$ is:
→
If $f(x)=\int \frac{5 x^{8}+7 x^{6}}{\left(x^{2}+1+2 x^{7}\right)^{2}} d x,(x \geq 0), f(0)=0$ and $f(1)=\frac{1}{K},$ then the value of $K$ is
→
The equations of tangent at those points where the curve $y = x^2 - 3x + 2$ meets $x-$ axis are :
→
Let $f: \mathrm{R} \rightarrow \mathrm{R}$ be a function given by

$f(x)= \begin{cases}\frac{1-\cos 2 x}{x^2} & , x<0 \\ \alpha & , x=0, \text { where } \alpha, \beta \in R \text {. If } \\ \frac{\beta \sqrt{1-\cos x}}{x} & , x>0\end{cases}$

$f$ is continuous at $\mathrm{x}=0$, then $\alpha^2+\beta^2$ is equal to :

→
The differential equation of all circles having centre lies on $x$ -axis and touches the $y$ -axis at origin is-
→
$\int_{}^{} {({{\sin }^{ - 1}}x + {{\cos }^{ - 1}}x)\;dx = } $
→