Question
Let × be a binary operation on Q, defined by $\text{a}\times\text{b}=\frac{3\text{ab}}{5}$ is:
  1. Commutative.
  2. Associative.
  3. Both (a) and (b).
  4. None of these.

Answer

  1. Both (a) and (b).

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

Similar questions

If $\vec{\text{a}}$ is any vector, then $\big(\vec{\text{a}}\times\hat{\text{i}}\big)^2+\big(\vec{\text{a}}\times\hat{\text{j}}\big)^2+\big(\vec{\text{a}}\times\hat{\text{k}}\big)^2=$
  1. $\vec{\text{a}}^2$
  2. $2\vec{\text{a}}^2$
  3. $3\vec{\text{a}}^2$
  4. $4\vec{\text{a}}^2$
The value of $\sin\bigg[\cos^{-1}\Big(\frac{7}{25}\Big)\bigg]$ is:
  1. $\frac{25}{24}$
  2. $\frac{25}{7}$
  3. $\frac{24}{25}$
  4. $\frac{7}{24}$
If the function $\text{f}(\text{x})=\frac{-\text{x}}{2}+\sin\text{x}$ defined on $\Big[\frac{-\pi}{3},\frac{\pi}{3}\Big]$ is:
  1. Increasing.
  2. Decreasing.
  3. Constant.
  4. None of these.
A line makes angles $\alpha, \beta$ and $\gamma$ with the co-ordinate axes. If $\alpha+\beta=90^{\circ}$, then the value of angle $\gamma$ is
The area bounded by the line y = 2x - 2, y = -x and x-axis is given by:
  1. $\frac{9}{2}\text{sq}.\text{units}$
  2. $\frac{43}{6}\text{sq}.\text{units}$
  3. $\frac{35}{6}\text{ sq}.\text{units}$
  4. $\text{None of these}$
The degree of the differntial equation $\left\{5+\Big(\frac{\text{dy}}{\text{dx}}\Big)^{2}\right\}^{\frac{5}{3}}=\text{x}^{5}\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}\Big)$ is:
  1. 4
  2. 2
  3. 5
  4. 10
The distance of the plane through the intersection of the planes ax + by + cz +d = 0 and lx + my + nz + P = 0 and parallel to the line y = 0, z = 0
  1. (bl - am)y + (cl - an)z + dl - ap = 0
  2. (am - bl)x + (mc - bn)z + md - bp = 0
  3. (na - cl)x + (bn - cm)y + nd - cp = 0
  4. None of these
If $\tan^{-1}(\cot\theta)=2\theta,$ then $\theta=$
  1. $\pm\frac{\pi}{3}$
  2. $\pm\frac{\pi}{4}$
  3. $\pm\frac{\pi}{6}$
  4. $\text{none of these}$
If $\begin{bmatrix} 1 & -\tan\theta \\ \tan\theta & 1 \end{bmatrix}\begin{bmatrix} 1 & \tan\theta \\ -\tan\theta & 1 \end{bmatrix}-1=\begin{bmatrix} \text{a} & -\text{b} \\ \text{b} & \text{a} \end{bmatrix},$ then:
  1. $\text{a}=1,\text{b}=1$
  2. $\text{a}=\cos2\theta,\text{b}=\sin2\theta$
  3. $\text{a}=\sin2\theta,\text{b}=\cos2\theta$
  4. None of these.
Choose the correct answer from given four options in each of the Exercise:
If $x, y, z$ are all different from zero and $\begin{vmatrix}1+\text{x}&1&1\\1&1+\text{y}&1\\1&1&1+\text{z}\end{vmatrix}=0,$ then the value of $x^{-1} + y^{-1} + z^{-1}$ is: