JEE Main 2008 Mathematics — Questions with Solutions

The vector a=α i+2 j+β k lies in the plane of the vectors b=i+j and c=j+k and bisects the angle between b and c. Then w…

If the straight lines (x-1)/(k)=(y-2)/(2)=(z-3)/(3) and (x-2)/(3)=(y-3)/(k)=(z-1)/(2) intersect at a point, then the in…

The line passing through the points (5,1, a) and (3, b, 1) crosses the y z- plane at the point (0, (17)/(2), (-13)/(2)…

Suppose the cube x³-p x+q has three distinct real roots where p>0 and q>0. Then which one of the following holds?

How many real solutions does the equation x⁷+14 x⁵+16 x³+30 x-560=0 have?

The differential equation of the family of circles with fixed radius 5 units and centre on the line y=2 is

The solution of the differential equation (d y)/(d x)=(x+y)/(x) satisfying the condition y(1)=1 is

The statement p →(q → p) is equivalent to

Let p be the statement " x is an irrational number", q be the statement " y is a transcendental number", and r be the s…

Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity matrix. Denote by tr(A), the sum of diagonal ent…