The equation of straight line through the intersection of the lines x - 2y = 1 and x + 3y = 2 and parallel to 3x + 4y = 0 is

• 3x + 4y + 5 = 0

• 3x + 4y - 10 = 0

• 3x + 4y - 5 = 0

• 3x + 4y + 6 = 0

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

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 equation of straight line through the intersection of line 2x +y = 1 and 3x + 2y = 5 and passing through the origin is

• 7x + 3y = 0

• 7x - y = 0

• 3x + 2y = 0

• x + y = 0

The condition that the line lx + my = 1 may be normal to the curve y² = 4ax, is

• al³ - 2alm² = m²

• al² + 2alm³ = m²

• al³ + 2alm² = m³

• al³ + 2alm² = m²

If the lines $\frac{\mathrm{x} - 1}{2} = \frac{\mathrm{y} +\hspace{0.17em}1}{3} = \frac{\mathrm{z} - 1}{4}$ and $\frac{\mathrm{x} - 3}{2} = \frac{\mathrm{y} -\hspace{0.17em}\mathrm{k}}{3} = \frac{\mathrm{z}}{1}$ intersect, then the value of k, is

• $\frac{3}{2}$

• $\frac{9}{2}$

• $- \frac{2}{9}$

• - $\frac{3}{2}$

The area (in square unit) of the triangle formed by x + y + 1 = 0 and the pair of straight lines x² - 3xy + 2y² = 0 is

• $\frac{7}{12}$

• $\frac{5}{12}$

• $\frac{1}{12}$

• $\frac{1}{6}$

The pairs of straight lines x² - 3xy + 2y² = 0 and x² - 3xy + 2y² + x - 2 = 0 form a

• square but not rhombus

• rhombus

• parallelogram

• rectangle but not a square

The shortest distance between the straight lines through the points A₁ = (6, 2, 2) and A₂ = (- 4, 0, - 1) in the directions of (1, - 2, 2) and (3, - 2, - 2) is

• 6

• 8

• 12

• 9

The length of the straight line x - 3y = 1 intercepted by the hyperbola x² - 4y² = 1 is :

• $\sqrt{10}$

• $\frac{6}{5}$

• $\frac{1}{\sqrt{10}}$

• $\frac{6}{5}\sqrt{10}$