1.

To the lines ax² + 2hxy + by² = 0, the lines a²x² + 2h(a + b) xy + b²y² = 0 are

• equally inclined

• perpendicular

• bisector of the angle

• None of these

If R be a realtion from A = {1, 2, 3, 4} to B = {1, 3, 5} such that (a, b) ∈R $\iff \mathrm{a} < \mathrm{b}$, then ROR^-1 is

• {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}

• {(3, 1), (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)}

• {(3, 3), (3, 5), (5, 3), (5, 5)}

• {(3, 3), (3, 4), (4, 5)}

If x + iy = ${\left(1 - \mathrm{i}\sqrt{3}\right)}^{100}$, then find (x, y).

• $\left(2^{99}, 2^{99}\sqrt{3}\right)$

• $\left(2^{99}, - 2^{99}\sqrt{3}\right)$

• $\left(- 2^{99}, 2^{99}\sqrt{3}\right)$

• None of these

For a GP, a_n = 3(2ⁿ), ∀ n ∈ N. Find the common ratio

• 2

• 1/2

• 3

• 1/3

If a, b, c are in HP, then $\frac{\mathrm{a}}{\mathrm{b} + \mathrm{c}}, \frac{\mathrm{b}}{\mathrm{c} + \mathrm{a}}, \frac{\mathrm{c}}{\mathrm{a} + \mathrm{b}}$ will be in

• AP

• GP

• HP

• None of these

If $\frac{{\mathrm{x}}^2 + 2\mathrm{x} + 7}{2\mathrm{x} + 3} < 6, \mathrm{x} \in \mathrm{R}$, then

• $\mathrm{x} > 11 \mathrm{or} \mathrm{x} = - \frac{3}{2}$

• x > 11 or x < - 1

• $- \frac{3}{2} < \mathrm{x} < - 1$

• $- 1 < \mathrm{x} < 11 \mathrm{or} \mathrm{x} < - \frac{3}{2}$

The number of ways of painting the faces of a cube of six different colours is

• 1

• 6

• 6!

• 36

A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. What is its y intercept

• 1/3

• 2/3

• 1

• 4/3

The number of common tangents to the circles x² + y² = 4 and x² + y² - 6x - 8y = 24 is

• 0

• 1

• 3

• 4

If D is the set of all real x such that 1 - e^{(1/x) - 1} is positive, then D is equal to

• $(- \infty , 1]$

• $\left(- \infty , 0\right)$

• $\left(1, \infty \right)$

• $\left(- \infty , 0\right) \cup \left(1, \infty \right)$