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Day 132: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 28 Jan 2026 S2 (same type asked 9 times) See all 9 of this type

    74
    If the distance of the point P(43,α,β),β<0P(43,\alpha,\beta),\beta < 0, from the line r→=4i^−k^+μ(2i^+3k^),μ∈R\overrightarrow{r} = 4\widehat{i} - \widehat{k} + \mu\left( 2\widehat{i} + 3\widehat{k} \right),\mu \in R along aa line with direction ratios 3,−1,03, - 1,0 is 131013\sqrt{10}, then α2+β2\alpha^{2} + \beta^{2} is equal to ............ .

  2. Question 2

    Three Dimensional Geometry. Asked once: 21 Jan 2026 S1 (same type asked 9 times) See all 9 of this type

    64
    Let (α,β,γ)(\alpha,\beta,\gamma) be the co-ordinates of the foot of the perpendicular drawn from the point (5,4,2)(5,4,2) on the line r→=(−i^+3j^+k^)+λ(2i^+3j^−k^)\overrightarrow{r}= ( -\widehat{i}+ 3\widehat{j}+\widehat{k}) + \lambda(2\widehat{i}+ 3\widehat{j}-\widehat{k}). Then the length of the projection of the vector αi^+βj^+γk^\alpha\widehat{i}+ \beta\widehat{j}+ \gamma\widehat{k} on the vector 6i^+2j^+3k^6\widehat{i}+ 2\widehat{j}+ 3\widehat{k} is :

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  3. Question 3

    Relations and Functions. Asked once: 22 Jan 2026 S1 (same type asked 9 times) See all 9 of this type

    52
    Let the relation R on the set M={1,2,3,…….16}\mathbf{M = \{ 1,2,3,\ldots\ldots.16\}} be given by R={(x,y):4y=5x−3,x,y∈M}\mathbf{R = \{(x,y):4y = 5x - 3,x,y \in M\}}. Then the minimum number of elements required to be added in R , in order to make the relation symmetric, is equal to

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  4. Question 4

    Sequences and Series. Asked once: 24 Jan 2025 (same type asked 9 times) See all 9 of this type

    134
    In an arithmetic progression, if S40=1030S_{40}= 1030 and S12=57S_{12}= 57, then S30−S10S_{30}-S_{10} is equal to:

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  5. Question 5

    Sequences and Series. Asked once: 11 Apr 2023 (same type asked 9 times) See all 9 of this type

    82
    Let S=109+1085+10752+……..+25107+15108S = 109 +\frac{108}{5}+\frac{107}{5^{2}}+ \ldots\ldots.. +\frac{2}{5^{107}}+\frac{1}{5^{108}}. Then the value of (16 S−(25)−54)\left( 16\text{ }S - (25)^{- 54} \right) is equal to