1.

What is the maximum number of points of intersection of 5 non-overlapping circles ?

• 10

• 15

• 20

• 25

What is the number of ways in which the letters of the word ‘ABLE’ can be arranged So that the Vowels occupy even places ?

• 2

• 4

• 6

• 8

Let $\mathrm{A} = \left[\begin{array}{ccc}\mathrm{a}& \mathrm{h}& \mathrm{g}\\ \mathrm{h}& \mathrm{b}& \mathrm{f}\\ \mathrm{g}& \mathrm{f}& \mathrm{c}\end{array}\right] \mathrm{and} \mathrm{B} = \left[\begin{array}{c}\mathrm{x}\\ \mathrm{y}\\ \mathrm{z}\end{array}\right] \mathrm{then} \mathrm{what} \mathrm{is} \mathrm{AB} = ?$

• $\left[\begin{array}{c}\mathrm{ax} + \mathrm{hy} + \mathrm{gz}\\ \mathrm{y}\\ \mathrm{z}\end{array}\right]$

• a + b

• $\left[\begin{array}{c}\mathrm{ax} + \mathrm{hy} + \mathrm{gz}\\ \mathrm{hx} + \mathrm{by} + \mathrm{fz}\\ \mathrm{gx} + \mathrm{fy} +\hspace{0.17em}\mathrm{cz}\end{array}\right]$

• $\left[\begin{array}{ccc}\mathrm{ax} + \mathrm{hy} +\mathrm{gz}& \mathrm{hz} + \mathrm{by} + \mathrm{fz}& \mathrm{gx} + \mathrm{fy} + \mathrm{cz}\end{array}\right]$

What is the value of the determinant $\left|\begin{array}{ccc}\mathrm{i}& {\mathrm{i}}^2& {\mathrm{i}}^3\\ {\mathrm{i}}^4& {\mathrm{i}}^6& {\mathrm{i}}^8\\ {\mathrm{i}}^9& {\mathrm{i}}^{12}& {\mathrm{i}}^{15}\end{array}\right|$

• 0

•  - 2

• 4i

• - 4i

Let S = {1, 2, 3, ...}. A relation R on S × S is defined by x Ry if log_a(x) > log_a(y) when $\mathrm{a} = \frac{1}{2}$, Then the relation is

• reflexive only

• symmetric only

• transitive only

• both symmetric and transitive

If 1.5 ≤ x ≤ 4.5, then which one of the following is correct ?

• (2x – 3) (2x – 9) > 0

• (2x – 3) (2x – 9) < 0

• (2x – 3) (2x – 9) ≥ 0

• (2x – 3) (2x – 9) ≤ 0

Let $\mathrm{A} = \left[\begin{array}{cc}\mathrm{x} + \mathrm{y}& \mathrm{y}\\ 2\mathrm{x}& \mathrm{x} - \mathrm{y}\end{array}\right], \mathrm{B} = \left[\begin{array}{c}2\\ - 1\end{array}\right] \mathrm{and} \mathrm{C} = \left[\begin{array}{c}3\\ 2\end{array}\right]$ If AB = C, then what is the value of the determinant of the matrix A ?

•  - 10

•  - 14

•  - 24

•  - 34

If, x = log_c (ab), y = log_a(bc), z = log_b(ca), then which of the following is correct ?

• xyz = 1

• x + y + z = 1

• (1 + x)^-1 + (1 + y)^-1 + (1 + z)^-1 = 1

• (1 + x)^-2 + (1 + y)^-2 + (1 + z)^-2 = 1

What is the value of $\frac{1}{10}{\log }_5\left(1024\right) - {\log }_5\left(10\right) + \frac{1}{5}{\log }_5\left(3125\right) ?$

• 0

• 1

• 2

• 3

The number (1101101 + 1011011)₂ can be written in decimal system as

• (198)₁₀

• (199)₁₀

• (200)₁₀

• (201)₁₀