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Day 294: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 10 Apr 2023 (same type asked 11 times) See all 11 of this type

    154
    Let the image of the point P(1,2,6)P(1,2,6) in the plane passing through the points A(1,2,0),B(1,4,1)A(1,2,0),B(1,4,1) and C(0,5,1)C(0,5,1) be Q(α,β,γ)Q(\alpha,\beta,\gamma). Then (α2+β2+γ2)\left( \alpha^{2}+\beta^{2}+\gamma^{2} \right) is equal to:

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  2. Question 2

    Three Dimensional Geometry. Asked once: 24 Jan 2026 S1 (same type asked 10 times) See all 10 of this type

    72
    Let a line L passing through the point P(1,1,1)P(1,1,1) be perpendicular to the lines x−44=y−11=z−11\frac{x - 4}{4} = \frac{y - 1}{1} = \frac{z - 1}{1} and x−171=y−711=z0\frac{x - 17}{1} = \frac{y - 71}{1} = \frac{z}{0}. Let the line L intersect the yz -plane at the point Q . Another line parallel to L and passing through the point S(1,0,−1)S(1,0, - 1) intersects the yz -plane at the point R . Then the square of the area of the parallelogram PQRS is equal to ____\_\_\_\_ .

  3. Question 3

    Quadratic Equations. Asked once: 24 Jan 2025 (same type asked 10 times) See all 10 of this type

    143
    The number of real solution(s) of the equation x2+3x+2=min⁡{∣x−3∣,∣x+2∣}x^{2}+ 3x+ 2 = \min\{|x- 3|,|x+ 2|\} is :

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  4. Question 4

    Vector Algebra. Asked once: 25 Jan 2023 (same type asked 10 times) See all 10 of this type

    63
    Let a→,b→\overrightarrow{a},\overrightarrow{b} and c→\overrightarrow{c} be three non zero vectors such that b→⋅c→=0\overrightarrow{b}\cdot\overrightarrow{c}= 0 and a→×(b→×c→)=b→−c→2\overrightarrow{a}\times (\overrightarrow{b}\times\overrightarrow{c}) =\frac{\overrightarrow{b}-\overrightarrow{c}}{2}. If d→\overrightarrow{d} be a vector such that b→⋅d→=a→⋅b→\overrightarrow{b}\cdot\overrightarrow{d}=\overrightarrow{a}\cdot\overrightarrow{b}, then (a→×b→)⋅(c→×d→)(\overrightarrow{a}\times\overrightarrow{b}) \cdot (\overrightarrow{c}\times\overrightarrow{d}) is equal to

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  5. Question 5

    Sequences and Series. Asked once: 22 Jan 2025 (same type asked 10 times) See all 10 of this type

    57
    Let a1,a2,a3…a_{1},a_{2},a_{3}\ldots. be a G.P. of increasing positive terms. If a1a5=28a_{1}a_{5}= 28 and a2+a4=29a_{2}+a_{4}= 29, the a6a_{6} is equal to

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