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Day 144: JEE Mains Maths

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

  1. Question 1

    Straight Lines. Asked once: 29 Jan 2025 (same type asked 6 times) See all 6 of this type

    54
    Let ABCABC be a triangle formed by the lines 7x−6y+3=0,x+2y−31=07x- 6y+ 3 = 0,x+ 2y- 31 = 0 and 9x−2y−19=09x- 2y- 19 = 0, Let the point (h,k)(h,k) be the image of the centroid of ΔABC\Delta ABC in the line 3x+6y−53=03x + 6y - 53 = 0. Then h2+k2+hkh^{2}+k^{2}+ hk is equal to

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  2. Question 2

    Determinants. Asked once: 2021 Paper 18 (same type asked 6 times) See all 6 of this type

    66
    Let θ∈(0,π2)\theta\in\left( 0,\frac{\pi}{2} \right). If the system of linear equations
    (1+cos⁡2θ)x+sin⁡2θy+4sin⁡3θz=0\left( 1 +\cos^{2}\theta \right)x +\sin^{2}\theta y + 4\sin3\theta z = 0
    cos⁡2θx+(1+sin⁡2θ)y+4sin⁡3θz=0\cos^{2}\theta x +\left( 1 +\sin^{2}\theta \right)y + 4\sin3\theta z = 0
    cos⁡2θx+sin⁡2θy+(1+4sin⁡3θ)z=0\cos^{2}\theta x +\sin^{2}\theta y + (1 + 4\sin3\theta)z = 0
    has a non-trivial solution, then the value of θ\theta is:

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  3. Question 3

    Permutations and Combinations. Asked once: 28 Jan 2025 (same type asked 6 times) See all 6 of this type

    146
    The number of natural numbers, between 212 and 999 , such that the sum of their digits is 15 , is____\_\_\_\_ .

  4. Question 4

    Inverse Trigonometric Functions. Asked once: 10 Apr 2023 (same type asked 6 times) See all 6 of this type

    177
    If the domain of the function f(x)=sec⁡−1(2x5x+3)f(x) =\sec^{- 1}\left( \frac{2x}{5x + 3} \right) is [α,β)∪(γ,δ]\lbrack\alpha,\beta) \cup (\gamma,\delta\rbrack, then ∣3α+10(β+γ)+21δ∣|3\alpha + 10(\beta + \gamma) + 21\delta| is equal to

  5. Question 5

    Relations and Functions. Asked once: 8 Apr 2024 (same type asked 6 times) See all 6 of this type

    168
    Let A={2,3,6,8,9,11}\mathbf{A = \{ 2,3,6,8,9,11\}} and B={1,4,5,10,15}\mathbf{B = \{ 1,4,5,10,15\}} Let RR be a relation on A×BA \times B define by (a,b)R(c,d)(a,b)R(c,d) if and only if 3ad−7bc3ad - 7bc is an even integer. Then the relation RR is

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