11.

If $\left|\mathrm{z} + 4\right| \ge 3$ then the greatest and the least value of $\left|\mathrm{z} + 1\right|$ are

• - 1, 6

• 6, 0

• 6, 3

• None of these

The angle between lines joining the origin to the point of intersection of the line $\sqrt{3}$x + y = 2 and the curve y² - x² = 4 is

• ${\tan }^{-1}\left(\frac{2}{\sqrt{3}}\right)$

• $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$6$}\right.$

• ${\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

• $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

If the area of the triangle on the complex plane formed by the points z, z + iz and iz is 200, then the value of 3lz I must be equal to

• 20

• 40

• 60

• 80

Equation of the chord of the hyperbola 25x²  - 16y² = 400 which is bisected at the point (6, 2), is

• 6x - 7y = 418

• 75x - 16y = 418

• 25x - 4y = 400

• None of these

A four-digit number is formed by the digits 1, 2, 3, 4 with no repetition. The probability that the number is odd, is

• zero

• $\frac{1}{3}$

• $\frac{1}{4}$

• None of these

The equation of normal to the curve y = (1 + x)^y +sin^-1(sin²(x)) at a = 0 is

• x + y = 1

• x - y = 1

• x + y = - 1

• x - y = - 1

The value of cfrom the Lagrange's mean value theorem for which f(x) = $\sqrt{25 - {\mathrm{x}}^2}$ in [1, 5], is

• 5

• 1

• $\sqrt{15}$

• None of these

If A = $\left[\begin{array}{cc}3& 4\\ 5& 7\end{array}\right]$ then A . (adj A) is equal to

• A

• $\left|\mathrm{A}\right|$

• $\left|\mathrm{A}\right| . \mathrm{I}$

• None of these

If there is an error of h % in measuring the edge of a cube, then the per cent error in estimating its volume is

• k

• 3k

• $\frac{\mathrm{k}}{3}$

• None of these

If the system of equations x + ky - z = 0, 3x - ky - z = 0 and x - 3y + z =0, has non-zero solution, then k is equal to

• - 1

• 0

• 1

• 2