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Day 234: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. Asked once: 3 Apr 2025 (same type asked 8 times) See all 8 of this type

    148
    If Limx→0(tan⁡xx)1x2=p{Lim}_{x \rightarrow 0}\left( \frac{\tan x}{x} \right)^{\frac{1}{x^{2}}} = p, then 96log⁡ep96\log_{e}p is equal to.

  2. Question 2

    Binomial Theorem. Asked once: 8 Apr 2024 (same type asked 8 times) See all 8 of this type

    87
    Let α=∑r=0n(4r2+2r+1) nCr\alpha =\sum_{r = 0}^{n} \left( 4r^{2}+ 2r + 1 \right)\ ^{n}C_{r} and β=(∑r=0n nCrr+1)+1n+1\beta =\left( \sum_{r = 0}^{n} \frac{\ ^{n}C_{r}}{r + 1} \right)+\frac{1}{n + 1}. If 140<2αβ<281140 <\frac{2\alpha}{\beta}< 281, then the value of nn is

  3. Question 3

    Quadratic Equations. Asked once: 9 Apr 2024 (same type asked 8 times) See all 8 of this type

    169
    Let α,β;α>β\alpha,\beta;\alpha > \beta, be the roots of the equation x2−2x−3=0x^{2}-\sqrt{2}x -\sqrt{3}= 0. Let Pn=αn−βn,n∈NP_{n}=\alpha^{n}-\beta^{n},n \in N. Then (113−102)P10+(112+10)P11−11P12(11\sqrt{3}- 10\sqrt{2})P_{10}+ (11\sqrt{2}+ 10)P_{11}- 11P_{12} is equal to:

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  4. Question 4

    Sequences and Series. Asked once: 9 Apr 2024 (same type asked 8 times) See all 8 of this type

    72
    If the sum of series
    11⋅(1+d)+1(1+d)(1+2 d)+…...+1(1+9 d)(1+10 d)\frac{1}{1 \cdot (1 + d)}+\frac{1}{(1 + d)(1 + 2\text{ }d)}+ \ldots... +\frac{1}{(1 + 9\text{ }d)(1 + 10\text{ }d)}
    is equal to 5, then 50 d50\text{ }d is equal to:

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  5. Question 5

    Application of Integrals. Asked once: 8 Apr 2024 (same type asked 8 times) See all 8 of this type

    161
    The area of the region in the first quadrant inside the circle x2+y2=8x^{2}+y^{2}= 8 and outside the parabola y2=2xy^{2}= 2x is equal to :

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