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Day 561: JEE Mains Maths

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

  1. Question 1

    Relations and Functions. Asked once: 29 Jul 2022

    180
    Let S={(x,y)∈N×N:9(x−3)2+16(y−4)2≤144}S =\left\{ (x,y) \in N \times N:9(x - 3)^{2}+ 16(y - 4)^{2}\leq 144 \right\} and  T={(x,y)∈R×R:(x−7)2+(y−4)2≤36}\ T =\left\{ (x,y) \in R \times R:(x - 7)^{2}+ (y - 4)^{2}\leq 36 \right\}. Then n(S∩T)n(S \cap T) is equal to

  2. Question 2

    Sequences and Series. Asked once: 5 Apr 2024

    175
    If 1+3−223+5−2618+93−112363+49−206180+…1 +\frac{\sqrt{3}-\sqrt{2}}{2\sqrt{3}}+\frac{5 - 2\sqrt{6}}{18}+\frac{9\sqrt{3}- 11\sqrt{2}}{36\sqrt{3}}+\frac{49 - 20\sqrt{6}}{180}+ \ldots upto ∞=2(ba+1)log⁡e(ab)\infty = 2\left( \sqrt{\frac{b}{a}}+ 1 \right)\log_{e}\left( \frac{a}{b} \right), where aa and bb are integers with gcd(a,b)=1gcd(a,b) = 1, then 11a+18 b11a + 18\text{ }b is equal to -.

  3. Question 3

    Straight Lines. Asked once: 1 Feb 2023

    67
    The combined equation of the two lines ax+by+c=0ax + by + c = 0 and a′x+b′y+c′=0a^{'}x +b^{'}y +c^{'}= 0 can be written as (ax+by+c)(a′x+b′y+c′)=0(ax + by + c)\left( a^{'}x +b^{'}y +c^{'} \right)= 0. The equation of the angle bisectors of the lines represented by the equation
    2x2+xy−3y2=0 is 2x^{2}+ xy - 3y^{2}= 0\text{~is~}

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  4. Question 4

    Three Dimensional Geometry. Asked once: 2021 Paper 24

    64
    Let the acute angle bisector of the two planes x−2y−2z+1=0x - 2y - 2z + 1 = 0 and 2x−3y−6z+1=02x - 3y - 6z + 1 = 0 be the plane PP. Then which of the following points lies on PP?

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  5. Question 5

    Vector Algebra. Asked once: 28 Jul 2022

    66
    Let a vector a→\overrightarrow{a} has a magnitude 9. Let a vector b→\overrightarrow{b} be such that for every (x,y)∈R×R−{(0,0)}\mathbf{(x,y) \in R \times R - \{(0,0)\}}, the vector (xa→+yb→)(x\overrightarrow{a}+ y\overrightarrow{b}) is perpendicular to the vector (6ya→−18xb→)(6y\overrightarrow{a}- 18x\overrightarrow{b}). Then the value of ∣a→×b→∣|\overrightarrow{a}\times\overrightarrow{b}| is equal to:

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