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1990 (AIEEE / IIT-JEE, in the JEE Main bank) questions

7 questions, by subject. Each opens with its options and answer.

Mathematics

  1. The equation (cos p - 1)x^2 + (cos p)x + sin p = 0 in the variable x, has real roots. Then, p can take any value in the interval

    Complex Numbers and Quadratic Equations

  2. Let f(x) be a quadratic expression which is positive for all real values of x. If g(x) = f(x) + f'(x) + f''(x), then for any real x

    Complex Numbers and Quadratic Equations

  3. Let f: R → R be a differentiable function and f(1) = 4. Then, the value of lim_x → 1 int_4^f(x) 2t/(x-1) dt is

    Definite Integrals and Areas · with solution

  4. In a triangle ABC, angle A is greater than angle B. If the measures of angles A and B satisfy the equation 3sin x - 4sin^3 x - k = 0, 0 < k < 1, then the measure of ∠ C is

    Trigonometry · with solution

  5. Line L has intercepts a and b on the coordinate axes. When, the axes are rotated through a given angle, keeping the origin fixed, the same line L has intercepts p and q, then

    Straight Lines and Pair of Lines · with solution

  6. Let f: R → R and g: R → R be continuous functions. Then, the value of the integral int_-π/2^π/2 [f(x) + f(-x)][g(x) - g(-x)] dx

    Definite Integrals and Areas

Chemistry

  1. The volume strength of 1.5 N H_2O_2 is

    Some Basic Concepts of Chemistry · with solution

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