If \(F=\alpha t^2-\beta t \) is the magnitude of the force acting on a particle at an instant \(t,\) then the time at which the force becomes constant is (where \(\alpha \) and \(\beta \) are constants):

1.	\(\dfrac{\beta}{\alpha}\)	2.	\(\dfrac{\beta}{2\alpha}\)
3.	\(\dfrac{2\beta}{\alpha}\)	4.	zero

The scalar and vector product of two vectors, $\overrightarrow{\mathrm{a}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\left(3\hat{\mathrm{i}}-4\hat{\mathrm{j}}+5\hat{\mathrm{k}}\right)$ and $\overrightarrow{\mathrm{b}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\left(-2\hat{\mathrm{i}}+\hat{\mathrm{j}}-3\hat{\mathrm{k}}\right)$ is equal to:

1. \(-25\) & $\left(7\hat{\mathrm{i}}-\hat{\mathrm{j}}-5\hat{\mathrm{k}}\right)$

2. \(25\) & $\left(-7\hat{\mathrm{i}}+\hat{\mathrm{j}}-5\hat{\mathrm{k}}\right)$

3. \(0\) & $\left(-7\hat{\mathrm{i}}+\hat{\mathrm{j}}+3\hat{\mathrm{k}}\right)$

4. \(-25\) & $\left(-7\hat{\mathrm{i}}+\hat{\mathrm{j}}+5\hat{\mathrm{k}}\right)$

For two vectors \(\vec A\) and \(\vec B\), |\(\vec A\)+\(\vec B\)|=|\(\vec A\) - \(\vec B\)| is always true when:

It is found that \(|\vec{A}+\vec{B}|=|\vec{A}|\). This necessarily implies:

The incorrect statement/s is/are:
1. (b), (d)
2. (a), (c)
3. (b), (c), (d)
4. (a), (b)

Consider the quantities of pressure, power, energy, impulse, gravitational potential, electric charge, temperature, and area. Out of these, the only vector quantities are:

The component of a vector \(\vec{r}\) along the X-axis will have maximum value if: