AILET entrance exam Question Bank Solutions for Mathematics

The equation of a st-line passing through the point (1,2) and making equal angles to with axes, will be:

The pole of the straight line 9x + y – 28 = 0 w.r.t. the circle x² + y² = 16 will be: 

The equation of line which os parallel to the straight line 3x + 4y – 7 = 0 and passing through (1, 2) is:

The equation of the tangent from origin to the circle x² + y² – 2rx – 2hy + h² = 0 is: 

If αα and ββ are the roots of the equation 1 (1 + n² + n⁴) = 0 then α² α +β² β is equal to:

f (x) = 2x3 – 9x2 + 12x + 29 is a monotonic decreasing function when:

If x = t² y = 2t, then the normal at t = 1 is: 

Find the equation of the straight line perpendicular to the line `"x"/"a" - "y"/"b" = 1` and passes through the point where the given st –line cuts the x – axis:

The equation of the polar line w.r.t. the pole (1, -2) to the arile x² + y² -2x – 6y + 5 = 0 is: 

The radical axis of the circles 2x² + 2y² – 7x = 0 and x² + y² – 4y – 7 = 0 is: 

The equation of the normal at a point of intersection of line 2x + y = 3 and curve yx² + y² = 5 is: 

If α and β are the roots of the equation x² + px + q = 0 then the value of α 3α + β 2β = 0 will be:

If α and β are the roots of the equation whose roots are `1/(alpha alpha) , 1/(beta beta)` is :

If the cube roots of unity are 1, ω, ω² , then the roots of the equation (x – 1)³ + 8 = 0 are 

Variables of linear equation is implicitly raised to

Axes in three dimension coordinate system divide plane in three spaces called

Slope intercept form of linear equation is

Number of ordered pair values (x,y) to satisfy linear equation ax + by = c are

In linear equation 'x = c ⁄ a' with undefined slope, slope is represented with

Example of linear equation involving two variables is