1985 (AIEEE / IIT-JEE, in the JEE Main bank) questions
8 questions, by subject. Each opens with its options and answer.
Mathematics
- If f(x) = x (√(x) + √(x+1) ), then
Limits Continuity and Differentiability · with solution
- If a, b, c and u, v, w are the complex numbers representing the vertices of two triangles such that c = (1-r)a + rb and w = (1-r)u + rv, where r is a complex number, then the two triangles
Complex Numbers and Quadratic Equations
- If a, b, c are in GP, then the equations ax^2 + 2bx + c = 0 and dx^2 + 2ex + f = 0 have a common root, if d/a, e/b, f/c are in
Sequences and Series
- If f(x) = begincases (sin[x])/([x]), & [x] ≠ 0 \ 0, & [x] = 0 endcases where, [x] denotes the greatest integer less than or equal to x, then lim_x → 0 f(x) equals hspace2cm
Limits Continuity and Differentiability · with solution
- For any integer n, the integral int_0^π e^cos^2 x cos^3(2n+1)x dx has the value
Definite Integrals and Areas
Chemistry
- The radius of an atomic nucleus is of the order of
Atomic Structure · with solution
- Bohr's model can explain
Atomic Structure · with solution
- Electromagnetic radiation with maximum wavelength is
Atomic Structure · with solution
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