The sum of the real solutions of equation $2{\left|\mathrm{x}\right|}^2 + 51 = \left|1 + 20\mathrm{x}\right|$ is

• 5

• 24

• 0

• None of these

The quadratic equation whose roots are $\frac{1}{3 + \sqrt{2}} \mathrm{and} \frac{1}{3 - \sqrt{2}}$, will be

• 7x² - 6x + 1 = 0

• 6x² - 7x + 1 = 0

• x² - 6x + 7 = 0

• x² - 7x + 6 = 0

Who said, "Number of transistors per square inch on integrated circuits double every year, since their invention will continue to do so in the foreseable future"?

• Alan Turing

• Jon Von Neumann

• Herbert Simon

• Gorden Moore

4.

The point on the straight line y = 2x + 11 which is nearest to the circle 16(x² + y) + 32x - 8y - 50 = 0, is

• $\left(\frac{9}{2}, 2\right)$

• $\left(\frac{9}{2}, - 2\right)$

• $\left(- \frac{9}{2}, 2\right)$

• $\left(- \frac{9}{2}, - 2\right)$

The locus of the extrimities of the latusrectum of the family of ellipses b²x² + y² = a²b² having a given major axis, is

• ${\mathrm{x}}^2 \pm \mathrm{ay} = {\mathrm{a}}^2$

• ${\mathrm{y}}^2 \pm \mathrm{bx} = {\mathrm{a}}^2$

• ${\mathrm{x}}^2 \pm \mathrm{by} = {\mathrm{a}}^2$

• ${\mathrm{y}}^2 \pm \mathrm{ax} = {\mathrm{b}}^2$

In $∆\mathrm{ABC}$, if 3a = b + c, then value of $\cot \left(\frac{\mathrm{B}}{2}\right)\cot \left(\frac{\mathrm{C}}{2}\right)$ will be

• 1

• 2

• $\sqrt{3}$

• $\sqrt{2}$

API stands for

• Access Programming Interface

• Android Programming Interface

• Application Programming Interface

• None of the above

Let A and B be two events of an experiment $\mathrm{P}\left(\mathrm{A}\right) = \frac{1}{4}, \mathrm{P}\left(\mathrm{A} \cup \mathrm{B}\right) = \frac{1}{2}$, then the value of $\mathrm{P}\left(\frac{\mathrm{B}}{{\mathrm{A}}^{\mathrm{C}}}\right)$ is

• $\frac{2}{3}$

• $\frac{1}{3}$

• $\frac{5}{6}$

• $\frac{1}{2}$

If z = $\mathrm{ilog}\left(2 - \sqrt{3}\right)$, then the value of cos(Z) will be

• i

• 2i

• 1

• 2

Two lines of regressions are given by x + 2y - 5 = 0 and 2x + ky - 8 = 0. If ${{\mathrm{\sigma }}_{\mathrm{x}}}^2 = 12$ and ${{\mathrm{\sigma }}_{\mathrm{y}}}^2 = 4$, then the value of k is

• 1

• 2

• 3

• 4