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Day 296: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 1 Feb 2024 (same type asked 9 times) See all 9 of this type

    160
    Let SnS_{n} denote the sum of the first nn terms of an arithmetic progression. If S10=390S_{10}= 390 and the ratio of the tenth and the fifth terms is 15:715:7, then S15−S5S_{15}-S_{5} is equal to:

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  2. Question 2

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

    174
    If (20)19+2(21)(20)18+3(21)2(20)17+(20)^{19}+ 2(21)(20)^{18}+ 3(21)^{2}(20)^{17}+ +20(21)19=k(20)19+ 20(21)^{19}= k(20)^{19}, then kk is equal to

  3. Question 3

    Determinants. Asked once: 10 Apr 2023 (same type asked 9 times) See all 9 of this type

    71
    For the system of linear equations
    2x−y+3z=52x - y + 3z = 5
    3x+2y−z=73x + 2y - z = 7
    4x+5y+αz=β4x + 5y + \alpha z = \beta
    Which of the following is NOT correct?

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  4. Question 4

    Statistics. Asked once: 31 Jan 2023 (same type asked 8 times) See all 8 of this type

    159
    Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and α\alpha ( >> 0)0), and the mean and standard deviation of marks of class B of nn students be respectively 55 and 30 −α- \alpha. If the mean and variance of the marks of the combined class of 100+n100 + n students are respectively 50 and 350, then the sum of variances of classes AA and BB is :

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  5. Question 5

    Determinants. Asked once: 4 Apr 2024 (same type asked 8 times) See all 8 of this type

    67
    If the system of equations
    x+(2sin⁡α)y+(2cos⁡α)z=0x + (\sqrt{2}\sin\alpha)y + (\sqrt{2}\cos\alpha)z = 0
    x+(cos⁡α)y+(sin⁡α)z=0x + (\cos\alpha)y + (\sin\alpha)z = 0
    x+(sin⁡α)y−(cos⁡α)z=0x + (\sin\alpha)y - (\cos\alpha)z = 0
    has a non-trivial solution, then α∈(0,π2)\alpha \in\left( 0,\frac{\pi}{2} \right) is equal to:

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