The point on the curve y = 2x² - 4x + 5, at which the tangent is parallel to x-axis, will be

• (1, 3)

• (- 1, 3)

• (1, - 3)

• (- 1, - 3)

The interval, inwhich the function f(x) = x²e^-x is an increasing function, will be

• $\left(- \infty , \infty \right)$

• (- 2, 0)

• $\left(2, \infty \right)$

• (0, 2)

Let f(x) = $$\begin{gathered} \left\{{\mathrm{x}}^{\mathrm{n}} . \sin \left(\frac{1}{\mathrm{x}}\right), \mathrm{x} \ne 0 \\ 0 , \mathrm{x} = 0\right\} \end{gathered}$$ Then, f(x) is differentiable at x = 0, if

• $\mathrm{n} \in \left(0, 1\right)$

• $\mathrm{n} \in \left(1, 2\right)$

• $\mathrm{n} \in \left(1, \infty \right)$

• $\mathrm{n} \in \left(- \infty , \infty \right)$

In which interval the function $\mathrm{f}\left(\mathrm{x}\right) = \sqrt{{\log }_{10}\left(\frac{5\mathrm{x} - {\mathrm{x}}^2}{4}\right)}$ is defined ?

• [1, 4]

• [0, 5)

• (0, 1)

• (- 1, $\infty$)

The probability that at least one ofthe events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then $\mathrm{P}\left(\overline{\mathrm{A}}\right) + \mathrm{P}\left(\overline{\mathrm{B}}\right)$ will be

• 1.5

• 1.3

• 1.2

• 0.8

The vector of magnitude 9 unit perpendicular to the vectors $4\hat{\mathrm{i}} - \hat{\mathrm{j}} + 3\hat{\mathrm{k}}$ and $- 2\hat{\mathrm{i}} + \hat{\mathrm{j}} - 2\hat{\mathrm{k}}$ will be

• $3\hat{\mathrm{i}} + 6\hat{\mathrm{j}} - 6\hat{\mathrm{k}}$

• $- 3\hat{\mathrm{i}} + 6\hat{\mathrm{j}} + 6\hat{\mathrm{k}}$

• $3\hat{\mathrm{i}} - 6\hat{\mathrm{j}} + 6\hat{\mathrm{k}}$

• $3\hat{\mathrm{i}} + 6\hat{\mathrm{j}} + 6\hat{\mathrm{k}}$

If $\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}} = \overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{b}} \ne \overrightarrow{0}$, then $\overrightarrow{\mathrm{a}} - \overrightarrow{\mathrm{c}}$ will be equal to

• $\mathrm{k}\overrightarrow{\mathrm{b}}$

• $\mathrm{k}\overrightarrow{\mathrm{a}}$

• $\mathrm{k}\overrightarrow{\mathrm{c}}$

• $\mathrm{k}\left(\overrightarrow{\mathrm{a}} + \overrightarrow{\mathrm{b}}\right)$

38.

The value of $\text{'}\mathrm{\lambda }\text{'}$, so that the vectors $\hat{\mathrm{i}} - 3\hat{\mathrm{j}} + \hat{\mathrm{k}}$, $2\hat{\mathrm{i}} + \mathrm{\lambda }\hat{\mathrm{j}} + \hat{\mathrm{k}}$ and $3\hat{\mathrm{i}} + \hat{\mathrm{j}} - 2\hat{\mathrm{k}}$ are coplanar, will be

• 0

• 2

• $- \frac{1}{2}$

• - 4

The line passing through the point (- 1, 2 3) and perpendicular to the plane x - 2y + 3z+ 5 = 0 will be

• $\frac{\mathrm{x} + 1}{1} = \frac{\mathrm{y} - 2}{3} = \frac{\mathrm{z} - 3}{5}$

• $\frac{\mathrm{x} + 1}{1} = \frac{\mathrm{y} - 2}{3} = \frac{\mathrm{z} + 3}{3}$

• $\frac{\mathrm{x} + 1}{1} = \frac{\mathrm{y} - 2}{3} = \frac{\mathrm{z} - 3}{2}$

• $\frac{\mathrm{x} + 1}{1} = \frac{\mathrm{y} - 2}{- 2} = \frac{\mathrm{z} - 3}{3}$

The value of k, if the line $\frac{\mathrm{x} - 4}{1} = \frac{\mathrm{y} - 2}{1} = \frac{\mathrm{z} - \mathrm{k}}{1}$ lies on the plane 2x - 4y + z = 7, will be

• 5

• 7

• 9

• 11