If G is the centroid of the $∆$ABC, then GA + BG + GC is equal

• 2GB

• 2GA

• 0

• 2BG

If the vectors $\hat{\mathrm{i}} + 3\hat{\mathrm{j}} + 4\hat{\mathrm{k}}, \mathrm{\lambda }\hat{\mathrm{i}} - 4\hat{\mathrm{j}} + \hat{\mathrm{k}}$ are orthogonal to each other, then $\mathrm{\lambda }$ is equal to

• 5

• - 5

• 8

• - 8

The vector c . (b + c) x (a + b + c) is equal to

• c . b x a

• 0

• c . a x b

• a . c x b

$\mathrm{If} 3\hat{\mathrm{i}} + 3\hat{\mathrm{j}} + \sqrt{3}\hat{\mathrm{k}}, \sqrt{3}\hat{\mathrm{i}} + \sqrt{3}\hat{\mathrm{j}} + \mathrm{\lambda }\hat{\mathrm{k}} \mathrm{are} \mathrm{coplaner}, \mathrm{then} \mathrm{\lambda } \mathrm{is} \mathrm{equal} \mathrm{to}$

• 1

• 2

• 3

• 4

If X is a poisson variate with P(X = 0) = 0.8, then the variance of X is

• ${\log }_{\mathrm{e}}\left(20\right)$

• ${\log }_{10}\left(20\right)$

• ${\log }_{\mathrm{e}}\left(\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\right)$

• 0

If the direction ratio of two lines are given by l + m + n = 0, mn - 2ln + lm = 0, then the angle between the lines is

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{2}$

• 0

If (2, - 1, 3) is the foot of the perpendicular drawn from the origin to the plane, then the equation of the plane is

• 2x + y - 3z + 6 = 0

• 2x - y + 3z - 14 = 0

• 2x - y + 3z - 13 = 0

• 2x + y + 3z - 10 = 0

If the plane 3x - 2y - z - 18 = 0 meets the coordinate axes in A, B, C then the centroid of $∆\mathrm{ABC}$ is

• (2, 3, - 6)

• (2, - 3, 6)

• (- 2, - 3, 6)

• (2, - 3, - 6)

69.

$\mathrm{If} \mathrm{f}\left(\mathrm{x}\right) = \frac{1}{{\mathrm{x}}^2}{\int }_3^{\mathrm{x}}\left(2\mathrm{t} - 3\mathrm{f}\text{'}\left(\mathrm{t}\right)\right)\mathrm{dt}, \mathrm{then} \mathrm{f}\text{'}\left(\mathrm{t}\right), \mathrm{then} \mathrm{f}\text{'}\left(3\right) \mathrm{is} \mathrm{equal} \mathrm{to}$

• $\frac{- 1 }{2}$

• $\frac{- 1}{3}$

• $\frac{1}{2}$

• $\frac{1}{3}$

$\int \frac{\mathrm{dx}}{\left(\mathrm{x} + 100\right)\sqrt{\mathrm{x} + 99}} = \mathrm{f}\left(\mathrm{x}\right) + \mathrm{c} \Rightarrow \mathrm{f}\left(\mathrm{x}\right)$

• 2(x + 100)^1/2

• 3(x + 100)^1/2

• $2{\tan }^{-1}\left(\sqrt{\mathrm{x} + 99}\right)$

• $2{\tan }^{-1}\left(\sqrt{\mathrm{x} + 100}\right)$