Mathematics Syllabus (JEE Main)
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Q. Find the real part of the complex number z = 4(cos(π/3) + i sin(π/3)).
Q. Find the real part of the complex number z = 5 - 2i.
Q. Find the roots of the equation x^2 + 4x + 4 = 0.
Q. Find the scalar product of A = (1, 2, 3) and B = (4, 5, 6).
Q. Find the scalar product of the vectors (3, -2, 5) and (1, 4, -1).
Q. Find the scalar product of the vectors (4, 5) and (1, 2).
Q. Find the scalar product of the vectors (7, 8, 9) and (0, 1, 2).
Q. Find the scalar product of the vectors A = (2, 3) and B = (4, -1).
Q. Find the scalar product of the vectors A = 5i + 12j and B = 3i - 4j.
Q. Find the scalar product of the vectors G = (2, -3, 1) and H = (4, 0, -2).
Q. Find the scalar product of the vectors G = (5, -3, 2) and H = (1, 1, 1).
Q. Find the scalar projection of vector A = (3, 4) onto vector B = (1, 0).
Q. Find the scalar triple product of vectors A = (1, 2, 3), B = (4, 5, 6), and C = (7, 8, 9).
Q. Find the second derivative of f(x) = e^x at x = 0.
Q. Find the second derivative of f(x) = ln(x^2 + 1).
Q. Find the second derivative of f(x) = x^3 - 6x^2 + 9x.
Q. Find the second derivative of f(x) = x^4 - 4x^3 + 6x^2.
Q. Find the slope of the line passing through the points (2, 3) and (4, 7).
Q. Find the slope of the line represented by the equation 2x - 3y + 6 = 0.
Q. Find the slope of the line that passes through the points (0, 0) and (5, 5).
Q. Find the slope of the tangent line to the curve y = sin(x) at x = π/4.
Q. Find the slopes of the lines represented by the equation 5x^2 + 6xy + 2y^2 = 0.
Q. Find the slopes of the lines represented by the equation 6x^2 - 5xy + y^2 = 0.
Q. Find the solution for the inequality 2(x - 1) ≥ 3.
Q. Find the solution for the inequality 2x + 3 ≤ 5.
Q. Find the solution for the inequality 2x + 5 > 3x - 1.
Q. Find the solution for the inequality 3x + 2 ≥ 11.
Q. Find the solution for the inequality 3x - 5 ≥ 4.
Q. Find the solution for the inequality 6x - 4 ≤ 2x + 8.
Q. Find the solution for the inequality: -x + 4 ≤ 2.
