JEE Main entrance exam Question Bank Solutions for Mathematics (JEE Main)

If the shortest distance between the lines `(x - 1)/2 = (y - 2)/3 = (z - 3)/λ` and `(x - 2)/1 = (y - 4)/4 = (z - 5)/5` is `1/sqrt(3)`, then the sum of all possible values of λ is ______.

The shortest distance between the z-axis and the line x + y + 2z – 3 = 0 = 2x + 3y + 4z – 4, is ______.

The line segment joining the points (1, 2) and (−2, 1) is divided by the line 3x + 4y = 7 in the ratio ______.

The foot of the perpendicular drawn from the origin, on the line, 3x + y = λ(λ ≠ 0) is P. lf the line meets x-axis at A and y-axis at B, then the ratio BP : PA is ______.

Choose the correct alternative:
If one of the lines given by 6x² – xy – 4cy² = 0 is 3x + 4y = 0, then c equals to ______.

The distance between the two points A and A' which lie on y = 2 such that both the line segments AB and A'B (where B is the point (2, 3)) subtend angle `π/4` at the origin, is equal to ______.

If `"z"^2/(("z" - 1))` is always real, then z, can lie on ______.

Let the equation of the pair of lines, y = px and y = qx, can be written as (y – px) (y – qx) = 0. Then the equation of the pair of the angle bisectors of the lines x² – 4xy – 5y² = 0 is ______.

The pair of lines represented by 3ax² + 5xy + (a² – 2)y² = 0 are perpendicular to each other for ______.

A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point ______.

If the length of the chord of the circle, x + y² = r²(r > 0) along the line, y – 2x = 3 is r, then r² is equal to ______.

If the line 3x + 4y = m touches the circle x² + y² = 10x, then m is equal to ______.

The abscissae of two points A and B are the roots of the equation x² + 2ax – b² = 0, and their ordinates are the roots of the equation x² + 2px – q² = 0. The radius of the circle with AB as diameter is ______.

Length of intercept made by line x + y = 2 on the circle x² + y² – 4x – 6y – 3 = 0 is ______.

If the angle between the tangent t The circle x² + 4² + 2x + 4y – 11 = 0 from p(3, 3) is  `tan^-1(a/b)` where a and b are relatively prime then the value of a – 3b is ______.

The equation of a circle passing through (3, –6) and touching both the axes is ______.

The value of p so that the straight line xcosα + ysinα – p = 0 may touch the circle x² + y² – 2ax cosα – 2by sinα – a²sin²α = 0 is ______.

If two circles `x^2 + y^2 + 2n_1x + 2y + 1/2` = 0 and `x^2 + y^2 + n_2x + n_2y + n_1 = 1/2`, intersect each other orthogonally where n₁, n₂ ∈ I, then number of possible of ordered pairs (n₁, n₂) is ______.