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Day 611: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 8 Apr 2024

    173
    Let SS be the focus of the hyperbola x23−y25=1\frac{x^{2}}{3}-\frac{y^{2}}{5}= 1, on the positive xx-axis. Let CC be the circle with its centre at A(6,5)A(\sqrt{6},\sqrt{5}) and passing through the point SS. if OO is the origin and SABSAB is a diameter of CC then the square of the area of the triangle OSB is equal to -

  2. Question 2

    Definite Integration. Asked once: 30 Jan 2023

    75
    If [t]\lbrack t\rbrack denotes the greatest integer ≤t\leq t, then the value of 3(e−1)e∫12x2e[x]+[x3]dx\frac{3(e - 1)}{e}\int_{1}^{2} x^{2}e^{\lbrack x\rbrack +\left\lbrack x^{3} \right\rbrack}dx is :

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  3. Question 3

    Matrices. Asked once: 2021 Paper 4

    65
    If for the matrix, A=[1−ααβ],AA⊤=I2A=\begin{bmatrix} 1 & -\alpha \\ \alpha & \beta \end{bmatrix},AA^{\top}=I_{2}, then the value of α4+β4\alpha^{4}+\beta^{4} is:

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  4. Question 4

    Sequences and Series. Asked once: 29 Jan 2023

    172
    Let a1=b1=1a_{1}=b_{1}= 1 and an=an−1+(n−1),bn=bn−1+an−1,∀n≥2a_{n}=a_{n - 1}+ (n - 1),b_{n}=b_{n - 1}+a_{n - 1},\forall n \geq 2. If S=∑n=110bn2nS =\sum_{n = 1}^{10} \frac{b_{n}}{2^{n}} and T=∑n=18n2n−1T =\sum_{n = 1}^{8} \frac{n}{2^{n - 1}}, then 27(2S−T)2^{7}(2S - T) is equal to

  5. Question 5

    Straight Lines. Asked once: 2021 Paper 9

    62
    The number of integral values of mm so that the abscissa of the point of intersection of the lines 3x+4y=93x + 4y = 9 and y=mx+1y = mx + 1 is also an integer, is:

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