1993 (AIEEE / IIT-JEE, in the JEE Main bank) questions

Mathematics

1. Let [.] denotes the greatest integer function and f(x) = [tan^2 x], then

   Limits Continuity and Differentiability

2. Number of solutions of the equation tan x + sec x = 2cos x lying in the interval [0, 2π] is

   Trigonometry · with solution

3. The locus of the centre of a circle, which touches externally the circle x^2 + y^2 - 6x - 6y + 14 = 0 and also touches the Y-axis, is given by the equation

   Circles

4. Let a, b, c be distinct non-negative numbers. If the vectors ai + aj + ck, i + k and ci + cj + bk lie in a plane, then c is

   Vector Algebra · with solution

5. The value of int_0^π/2 dx/(1+tan^3 x) is

   Definite Integrals and Areas · with solution