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Day 258: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 23 Jan 2026 S2 (same type asked 4 times) See all 4 of this type

    70
    Let ∑k=1nak=αn2+βn\sum_{k = 1}^{n} a_{k}= \alpha n^{2}+ \beta n. If a10=59a_{10}= 59 and a6=7a1a_{6}= 7a_{1} then α+β\alpha + \beta is equal to

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  2. Question 2

    Straight Lines. Asked once: 26 Jun 2022 (same type asked 4 times) See all 4 of this type

    71
    Let RR be the point (3,7)(3,7) and let PP and QQ be two points on the line x+y=5x + y = 5 such that PQRPQR is an equilateral triangle. Then the area of △PQR\bigtriangleup PQR is:

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  3. Question 3

    Three Dimensional Geometry. Asked once: 22 Jan 2025 (same type asked 4 times) See all 4 of this type

    134
    The perpendicular distance, of the line x−12=y+2−1=z+32\frac{x - 1}{2}=\frac{y + 2}{- 1}=\frac{z + 3}{2} from the point P(2,−10,1)P(2, - 10,1), is:

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  4. Question 4

    Trigonometric Equations. Asked once: 29 Jan 2023 (same type asked 4 times) See all 4 of this type

    153
    The set of all values of λ\lambda for which the equation cos⁡22x−2sin⁡4x−2cos⁡2x=λ\cos^{2}2x - 2\sin^{4}x - 2\cos^{2}x = \lambda has a real solution xx, is

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  5. Question 5

    Binomial Theorem. Asked once: 26 Jun 2022 (same type asked 4 times) See all 4 of this type

    175
    If ( 40C0)+( 41C1)+( 42C2)+…+( 60C20)=mn 60C20, m\left( \ ^{40}C_{0} \right)+\left( \ ^{41}C_{1} \right)+\left( \ ^{42}C_{2} \right)+ \ldots +\left( \ ^{60}C_{20} \right)=\frac{m}{n}\ ^{60}C_{20},\text{ }m and nn are coprime, then m+nm + n is equal to