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Day 401: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 27 Jan 2024 (same type asked 9 times) See all 9 of this type

    62
    The distance, of the point (7,−2,11)(7, - 2,11) from the line x−61=y−40=z−83\frac{x - 6}{1}=\frac{y - 4}{0}=\frac{z - 8}{3} along the line x−52=y−1−3=z−56\frac{x - 5}{2}=\frac{y - 1}{- 3}=\frac{z - 5}{6}, is :

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  2. Question 2

    Three Dimensional Geometry. Asked once: 27 Jun 2022 (same type asked 9 times) See all 9 of this type

    163
    Let the foot of the perpendicular from the point (1,2,4)(1,2,4) on the line x+24=y−12=z+13\frac{x + 2}{4}=\frac{y - 1}{2}=\frac{z + 1}{3} be PP. Then the distance of PP from the plane 3x+4y+12z+23=03x + 4y + 12z + 23 = 0

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  3. Question 3

    Relations and Functions. Asked once: 31 Jan 2024 (same type asked 9 times) See all 9 of this type

    180
    Let A={1,2,3,…….100}\mathbf{A = \{ 1,2,3,\ldots\ldots.100\}}. Let RR be a relation on A defined by (x,y)∈R(x,y) \in R if and only if 2x=3y2x= 3y. Let R1R_{1} be a symmetric relation on AA such that R⊂R1R \subset R_{1} and the number of elements in R1R_{1} is nn. Then, the minimum value of nn is

  4. Question 4

    Sequences and Series. Asked once: 2021 Paper 10 (same type asked 9 times) See all 9 of this type

    69
    Let S1S_{1} be the sum of first 2n2n terms of an arithmetic progression. Let S2S_{2} be the sum of first 4n4n terms of the same arithmetic progression. If (S2−S1)\left( S_{2}-S_{1} \right) is 1000, then the sum of the first 6n6n terms of the arithmetic progression is equal to:

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  5. Question 5

    Determinants. Asked once: 2021 Paper 26 (same type asked 9 times) See all 9 of this type

    70
    Consider the following system of equations:
    x+2y−3z=ax + 2y - 3z = a
    2x+6y−11z=b2x + 6y - 11z = b
    x−2y+7z=cx - 2y + 7z = c
    Where a,ba,b and cc are real constants. Then the system of equations:

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