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Day 124: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Binomial Theorem. This type asked 2 times: 25 Jun 2022, 27 Jun 2022. This one: 27 Jun 2022 See all 2 of this type

    174
    If the sum of the coefficients of all the positive powers of xx, in the binomial expansion of (xn+2x5)7\left( x^{n}+\frac{2}{x^{5}} \right)^{7} is 939, then the sum of all the possible integral values of nn is:

  2. Question 2

    Conic Sections. This type asked 2 times: 2021 Paper 13, 27 Jun 2022. This one: 27 Jun 2022 See all 2 of this type

    162
    The set of values of kk for which the circle C : 4x2+4y2−12x+8y+k=04x^{2}+ 4y^{2}- 12x + 8y + k = 0 lies inside the fourth quadrant and the point (1,−13)\left( 1, -\frac{1}{3} \right) lies on or inside the circle CC is :

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  3. Question 3

    Sequences and Series. This type asked 2 times: 2021 Paper 3, 27 Jun 2022. This one: 27 Jun 2022 See all 2 of this type

    63
    If x=∑n=0∞an,y=∑n=0∞bn,z=∑n=0∞cnx =\sum_{n = 0}^{\infty} a^{n},y =\sum_{n = 0}^{\infty} b^{n},z =\sum_{n = 0}^{\infty} c^{n}, where a,b,ca,b,c are in A.P. and ∣a∣<1,∣b∣<1,∣c∣<1,abc≠0|a| < 1,|b| < 1,|c| < 1,abc \neq 0, then

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  4. Question 4

    Straight Lines. This type asked 2 times: 2021 Paper 21, 14 Jun 2022. This one: 14 Jun 2022 See all 2 of this type

    160
    Let the area of the triangle with vertices A(1,α)A(1,\alpha), B(α,0)B(\alpha,0) and C(0,α)C(0,\alpha) be 4 sq. units. If the point (α,−α),(−α,α)(\alpha, - \alpha),( - \alpha,\alpha) and (α2,β)\left( \alpha^{2},\beta \right) are collinear, then β\beta is equal to

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  5. Question 5

    Conic Sections. This type asked 2 times: 2021 Paper 11, 2021 Paper 24. This one: 2021 Paper 24 See all 2 of this type

    73
    Consider the parabola with vertex (12,34)\left( \frac{1}{2},\frac{3}{4} \right) and the directrix y=12y=\frac{1}{2}. Let PP be the point where the parabola meets the line x=−12x = -\frac{1}{2}. If the normal to the parabola at PP intersects the parabola again at the point QQ, then (PQ)2(PQ)^{2} is equal to:

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