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Day 440: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 6 Apr 2026 S1

    52
    Let one root of the quadratic equation in x : (k2−15k+27)x2+9(k−1)x+18=0\left( k^{2}- 15k+ 27 \right)x^{2}+ 9\left( k- 1 \right)x+ 18 = 0 be twice the other. Then the length of the latus rectum of the parabola y2=6kxy^{2}= 6kx is equal to:

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  2. Question 2

    Relations and Functions. Asked once: 8 Apr 2026 S2

    51
    Consider the relation R on the set {−2,−1,0,1,2}\mathbf{\{ - 2, - 1,0,1,2\}} defined by (a,b)∈R(a,b) \in R if and only if 1+ab>01 + ab > 0. Then among the statements : (I) The number of elements in R is 17 (II) R is an equivalence relation

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  3. Question 3

    Sequences and Series. Asked once: 8 Apr 2026 S2

    55
    Let α=3+4+8+9+13+14+…\alpha= 3 + 4 + 8 + 9 + 13 + 14 + \ldots.. upto 40 terms. If (tan⁡β)α1020(\tan\beta)^{\frac{\alpha}{1020}} is a root of the equation x2+x−2=0,β∈(0,π2)x^{2}+x- 2 = 0,\beta\in\left( 0,\frac{\pi}{2} \right), then sin⁡2β+3cos⁡2β\sin^{2}\beta+ 3\cos^{2}\beta is equal to :

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  4. Question 4

    Statistics. Asked once: 5 Apr 2026 S2

    60
    A variable XX takes values 0,0,2,6,12,20,…,n(n−1)0,0,2,6,12,20,\ldots,n(n - 1) with frequencies  nC0, nC1, nC2, nC3, nC4\ ^{n}C_{0},\ ^{n}C_{1},\ ^{n}C_{2},\ ^{n}C_{3},\ ^{n}C_{4},  nC5,….. nCn\ ^{n}C_{5},\ldots..\ ^{n}C_{n}, respectively. If the mean of this data is 60 , then its median is:

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  5. Question 5

    Straight Lines. Asked once: 5 Apr 2026 S2

    72
    From the point (−1,−1)( - 1, - 1), two rays are sent making angles of 45∘45^{\circ} with the line x+y=0x + y = 0. These rays get reflected from the mirror x+2y=1x + 2y = 1. If the equations of the reflected rays are ax+by=9ax + by = 9 and cx+dy=7,a,b,c,d∈Zcx + dy = 7,a,b,c,d \in Z, then the value of ad+bcad + bc is ____\_\_\_\_