For the curve xy = c², the subnormal at any point varies as

• x³

• x²

• y³

• $\infty$

The function f(x) = $\left|\mathrm{x}\right| + \frac{\left|\mathrm{x}\right|}{\mathrm{x}}$ is

• discontinuous at origin because $\left|\mathrm{x}\right|$ is discontinuous there

• continuous at origin

• discontinuous at origin because both $\left|\mathrm{x}\right|$ and $\raisebox{1ex}{$\left|\mathrm{x}\right|$}\!\left/ \!\raisebox{-1ex}{$\mathrm{x}$}\right.$ are discontinuous there

• discontinuous at the origin because $\raisebox{1ex}{$\left|\mathrm{x}\right|$}\!\left/ \!\raisebox{-1ex}{$\mathrm{x}$}\right.$ is discontinuous there

If ${\cos }^{-1}\left(\mathrm{x}\right) + {\cos }^{-1}\left(\mathrm{y}\right) + {\cos }^{-1}\left(\mathrm{z}\right) = 3\mathrm{\pi }$, then xy + yz + zx is equal to

• 1

• 0

• - 3

• 3

14.

In three element group {e, a, b} where e is the identity a⁵b⁴ is equal to

• a

• e

• ab

• b

The relation R = {(1, 1), (2, 2), (3, 3)} on the set { 1, 2, 3} is

• symmetric only

• reflexive only

• an equivalence relation

• transitrve only

If the vectors $4\hat{\mathrm{i}} + 11\hat{\mathrm{j}} + \mathrm{m}\hat{\mathrm{k}}$, $7\hat{\mathrm{i}} + 2\hat{\mathrm{j}} + 6\hat{\mathrm{k}}$ and $\hat{\mathrm{i}} + 5\hat{\mathrm{j}} + 4\hat{\mathrm{k}}$ are coplanar, then m is equal to

• 0

• 38

• - 10

• 10

If $\left|\mathrm{a} \times \mathrm{b}\right| = 4 \mathrm{and} \left|\mathrm{a} . \mathrm{b}\right| = 2, \mathrm{then} {\left|\mathrm{a}\right|}^2{\left|\mathrm{b}\right|}^2$ is equal to

• 6

• 2

• 20

• 8

The angle between the vectors a + b and a - b when a = (1, 1, 4) and b = (1, - 1, 4) is

• 45°

• 90°

• 15°

• 30°

The angle between the lines in

x² - xy - 6y² - 7x + 31y - 18 = 0 is

• 60°

• 45°

• 30°

• 90°

${\int }_0^{2\mathrm{\pi }}\left(\sin \left(\mathrm{x}\right) +\hspace{0.17em}\left|\sin \left(\mathrm{x}\right)\right|\right)\mathrm{dx}$ is equal to

• 4

• 0

• 1

• 8