Questions from previous years' IIT-JEE (Indian Institute of Technology-Joint Entrance Examination)
1. Solve the equation:-
2. Prove that the cube roots of unity when represented on the Argand diagram form the vertices of an equilateral triangle.
3. Show that the area of the triangle on the Argand diagram formed by the complex numbers z, iz and z+iz is ½|z|².
4. Let -1 ≤ p ≤ 1. Show that the equation 4x³-3x-p=0 has a unique root in the interval[1/2, 1] and identify it.
5. Let a>0, b>0, c>0. Then prove that the roots of the equation ax²+bx+c=0 have negative and real parts.
7. For a ≥0, determine all roots of the equation
x²-2a|x-a|-3a² ≥ 0.
8. Find the set of all x for which
9. The interior angles of a polygon are in arithmetic progression. The smallest angle is 120° and the common difference is 5°. Find the number of sides of the polygon.
10. The sum of first 10 terms of an arithmetic progression is 155 and the sum of first two terms of a geometric progression is 9; the first term of the arithmetic progression is equal to the common ratio of the geometric progression and the first term of the geometric progression is equal to the common difference of the arithmetic progression. Find the two progressions.
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