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Day 213: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 27 Jan 2024 (same type asked 2 times) See all 2 of this type

    64
    If (a,b)(a,b) be the orthocentre of the triangle whose vertices are (1,2),(2,3)(1,2),(2,3) and (3,1)(3,1), and I1=∫abxsin(4x−x2)dx, I2=∫absin⁡(4x−x2)dxI_{1}=\int_{a}^{b} xsin\left( 4x -x^{2} \right)dx,\ I_{2}=\int_{a}^{b} \sin\left( 4x -x^{2} \right)dx , then 36I1I236\frac{I_{1}}{I_{2}} is equal to :

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  2. Question 2

    Straight Lines. Asked once: 29 Jan 2024 (same type asked 2 times) See all 2 of this type

    161
    The distance of the point (2,3)(2,3) from the line 2x−3y+28=02x-3y+ 28 = 0, measured parallel to the line 3x−y+1=0\sqrt{3}x-y+ 1 = 0, is equal to

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  3. Question 3

    Relations and Functions. Asked once: 30 Jan 2023 (same type asked 2 times) See all 2 of this type

    89
    Let S={1,2,3,4,5,6}\mathbf{S = \{ 1,2,3,4,5,6\}}. Then the number of one-one functions f:S→P(S)f:S \rightarrow P(S), where P(S)P(S) denote the power set of SS, such that f(n)⊂f(m)f(n) \subset f(m) where n<mn < m is

  4. Question 4

    Trigonometric Equations. Asked once: 27 Jan 2024 (same type asked 2 times) See all 2 of this type

    165
    If 2tan⁡2θ−5sec⁡θ=12\tan^{2}\theta - 5\sec\theta = 1 has exactly 7 solutions in the interval [0,nπ2]\left\lbrack 0,\frac{n\pi}{2} \right\rbrack, for the least value of n∈Nn \in N then ∑k=1nk2k\sum_{k = 1}^{n} \frac{k}{2^{k}} is equal to :

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  5. Question 5

    Complex Numbers. Asked once: 8 Apr 2023 (same type asked 2 times) See all 2 of this type

    80
    If for z=α+iβ,∣z+2∣=z+4(1+i)z = \alpha + i\beta,|z + 2| = z + 4(1 + i), then α+β\alpha + \beta and αβ\alpha\beta are the roots of the equation

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