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Day 128: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 8 Apr 2023 (same type asked 15 times) See all 15 of this type

    62
    If the equation of the plane containing the line x+2y+3z−4=0=2x+y−z+5x + 2y + 3z - 4 = 0 = 2x + y - z + 5 and perpendicular to the plane r→=(i^−j^)+λ(i^+j^+k^)+μ(i^−2j^+3k)\overrightarrow{r}= (\widehat{i}-\widehat{j}) + \lambda(\widehat{i}+\widehat{j}+\widehat{k}) + \mu(\widehat{i}- 2\widehat{j}+ 3k) is ax+by+cz=4ax + by + cz = 4, then (a−b+c)(a - b + c) is equal to

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  2. Question 2

    Determinants. Asked once: 21 Jan 2026 S2 (same type asked 14 times) See all 14 of this type

    68
    If the system of equations 3x+y+4z=33x + y + 4z = 3, 2x+αy−z=−32x + \alpha y - z = - 3, x+2y+z=4x + 2y + z = 4 has no solution, then the value of α\alpha is equal to:

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  3. Question 3

    Statistics. Asked once: 23 Jan 2026 S1 (same type asked 13 times) See all 13 of this type

    63
    Let the mean and variance of 8 numbers −10,−7,−1,x,y,9,2,16- 10, - 7, - 1,x,y,9,2,16 be 72\frac{7}{2} and 2934\frac{293}{4}, respectively. Then the mean of 4 numbers x,y,x+y+1,∣x−y∣x,y,x + y + 1,|x - y| is:

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  4. Question 4

    Vector Algebra. Asked once: 21 Jan 2026 S1 (same type asked 13 times) See all 13 of this type

    55
    Let a→=−i^+2j^+2k^,b→=8i^+7j^−3k^\overrightarrow{a}= -\widehat{i}+ 2\widehat{j}+ 2\widehat{k},\overrightarrow{b}= 8\widehat{i}+ 7\widehat{j}- 3\widehat{k} and c→\overrightarrow{c} be a vector such that a→×c→=b→\overrightarrow{a}\times\overrightarrow{c}=\overrightarrow{b}. If c→⋅(i^+j^+k^)=4\overrightarrow{c}\cdot (\widehat{i}+\widehat{j}+\widehat{k}) = 4, then ∣a→+c→∣2|\overrightarrow{a}+\overrightarrow{c}|^{2} is equal to :

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  5. Question 5

    Differential Equations. Asked once: 2 Apr 2026 S1 (same type asked 13 times) See all 13 of this type

    67
    If the curve y=f(x)y=f(x) passes through the point ( 1,e)1,e) and satisfies the differential equation dy=y(2+log⁡ex)dx,x>0dy=y\left( 2 +\log_{e}x \right)dx,x> 0, then f(e)f(e) is equal to :

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