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Day 466: JEE Mains Maths

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

  1. Question 1

    Application of Integrals. Asked once: 24 Jan 2026 S1

    69
    Let A1A_{1} be the bounded area enclosed by the curves y=x2+2,x+y=8y =x^{2}+ 2,x + y = 8 and yy-axis that lies in the first quadrant. Let A2A_{2} be the bounded area enclosed by the curves y=x2+2,y2=x,x=2y =x^{2}+ 2,y^{2}= x,x = 2, and yy-axis that lies in the first quadrant. Then A1−A2A_{1}-A_{2} is equal to

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  2. Question 2

    Binomial Theorem. Asked once: 28 Jan 2025

    72
    If α=1+∑r=16(−3)r−1 12C2r−1\alpha= 1 +\sum_{r = 1}^{6} ( - 3)^{r - 1}\ ^{12}C_{2r - 1}, then the distance of the point (12,3)(12,\sqrt{3}) from the line αx−3y+1=0\alpha x-\sqrt{3}y+ 1 = 0 is.....

  3. Question 3

    Complex Numbers. Asked once: 21 Jan 2026 S2

    69
    Let zz be the complex number satisfying ∣z−5∣≤3|z - 5| \leq 3 and having maximum positive principal argument. Then 34∣5z−125iz+16∣234\left| \frac{5z - 12}{5iz + 16} \right|^{2} is equal to:

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  4. Question 4

    Conic Sections. Asked once: 6 Apr 2026 S1

    61
    If the eccentricity e of the hyperbola x2a2−y2 b2=1\frac{x^{2}}{a^{2}}-\frac{y^{2}}{{\text{ }b}^{2}}= 1, passing through (6,43)(6,4\sqrt{3}), satisfies 15(e2+1)=34e15\left( e^{2}+ 1 \right)= 34e, then the length of the latus rectum of the hyperbola x2 b2−y22(a2+1)=1\frac{x^{2}}{{\text{ }b}^{2}}-\frac{y^{2}}{2\left( a^{2}+ 1 \right)}= 1 is:

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  5. Question 5

    Definite Integration. Asked once: 4 Apr 2026 S2

    54
    If α=1\alpha= 1 and β=1+i2\beta= 1 + i\sqrt{2}, where i=−1i=\sqrt{- 1} are two roots of the equation x3+ax2+bx+c=0,a,b,c∈Rx^{3}+ax^{2}+ bx + c = 0,a,b,c \in\mathbb{R}, then ∫−11(x3+ax2+bx+c)dx\int_{- 1}^{1} \left( x^{3}+ax^{2}+bx+c \right)dx is equal to :

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