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Day 383: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. Asked once: 28 Jul 2022 (same type asked 8 times) See all 8 of this type

    89
    lim⁡x→0((x+2cos⁡x)3+2(x+2cos⁡x)2+3sin⁡(x+2cos⁡x)(x+2)3+2(x+2)2+3sin⁡(x+2))100x\underset{x\rightarrow 0}{\lim} \left( \frac{(x+ 2\cos x)^{3}+ 2(x+ 2\cos x)^{2}+ 3\sin(x+ 2\cos x)}{(x+ 2)^{3}+ 2(x+ 2)^{2}+ 3\sin(x+ 2)} \right)^{\frac{100}{x}}is equal to

  2. Question 2

    Quadratic Equations. Asked once: 29 Jul 2022 (same type asked 8 times) See all 8 of this type

    172
    Let α,β(α>β)\alpha,\beta(\alpha > \beta) be the roots of the quadratic equation x2−x−4=0x^{2}- x - 4 = 0. If Pn=αn−βn,n∈NP_{n}=\alpha^{n}-\beta^{n},n \in N, then P15P16−P14P16−P152+P14P15P13P14\frac{P_{15}P_{16}-P_{14}P_{16}-P_{15}^{2}+P_{14}P_{15}}{P_{13}P_{14}} is equal to

  3. Question 3

    Sequences and Series. Asked once: 2021 Paper 24 (same type asked 8 times) See all 8 of this type

    78
    Let a1,a2,……,a21a_{1},a_{2},\ldots\ldots,a_{21} be an AP such that ∑n=1201anan+1=49\sum_{n= 1}^{20} \frac{1}{a_{n}a_{n+ 1}}=\frac{4}{9}. If the sum of this AP is 189, then a6a16a_{6}a_{16} is equal to:

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  4. Question 4

    Application of Integrals. Asked once: 27 Jul 2022 (same type asked 8 times) See all 8 of this type

    69
    The area of the smaller region enclosed by the curves y2=8x+4y^{2}= 8x + 4 and x2+y2+43x−4=0x^{2}+y^{2}+ 4\sqrt{3}x - 4 = 0 is equal to

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  5. Question 5

    Binomial Theorem. Asked once: 27 Jun 2022 (same type asked 7 times) See all 7 of this type

    85
    If the coefficient of x10x^{10} in the binomial expansion of (x514+5x13)60\left( \frac{\sqrt{x}}{5^{\frac{1}{4}}}+\frac{\sqrt{5}}{x^{\frac{1}{3}}} \right)^{60} is 5kl5^{k}l, where l,k∈Nl,k \in N and ll is coprime to 5 , then kk is equal to