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Day 337: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 30 Jan 2024 (same type asked 9 times) See all 9 of this type

    62
    Let SnS_{n} denote the sum of first nn terms of an arithmetic progression. If S20=790S_{20}= 790 and S10=145S_{10}= 145, then S15−S_{15}- S5S_{5} is:

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  2. Question 2

    Sequences and Series. Asked once: 29 Jul 2022 (same type asked 9 times) See all 9 of this type

    84
    Let a1,a2,a3,…a_{1},a_{2},a_{3},\ldots be an A.P. If ∑r=1∞ar2r=4\sum_{r = 1}^{\infty} \frac{a_{r}}{2^{r}}= 4, then 4a24a_{2} is equal to

  3. Question 3

    Determinants. Asked once: 6 Apr 2023 (same type asked 9 times) See all 9 of this type

    158
    For the system of equations
    x+y+z=6x + y + z = 6
    x+2y+αz=10x + 2y + \alpha z = 10
    x+3y+5z=βx + 3y + 5z = \beta, which one of the following is NOT true?

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  4. Question 4

    Statistics. Asked once: 29 Jan 2023 (same type asked 8 times) See all 8 of this type

    175
    Let X={11,12,13,…,40,41}X = \{ 11,12,13,\ldots,40,41\} and Y={61,62,63,…,90,91}Y = \{ 61,62,63,\ldots,90,91\} be the two sets of observations. If xˉ\bar{x} and yˉ\bar{y} are their respective means and σ2\sigma^{2} is the variance of all the observations in X∪YX \cup Y, then ∣xˉ+yˉ−σ2∣\left| \bar{x}+\bar{y}-\sigma^{2} \right| is equal to

  5. Question 5

    Determinants. Asked once: 8 Apr 2023 (same type asked 8 times) See all 8 of this type

    157
    Let SS be the set of all values of θ∈[−π,π]\theta \in \lbrack - \pi,\pi\rbrack for which the system of linear equations
    x+y+3z=0x + y +\sqrt{3}z = 0
    −x+(tan⁡θ)y+7z=0- x + (\tan\theta)y +\sqrt{7}z = 0
    x+y+(tan⁡θ)z=0x + y + (\tan\theta)z = 0
    has non-trivial solution. Then 120π∑θ∈Sθ\frac{120}{\pi}\sum_{\theta \in S} \theta is equal to

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