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Day 362: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 29 Jan 2025 (same type asked 10 times) See all 10 of this type

    131
    Let a straight line LL pass through the point P(2,−1,3)P(2, - 1,3) and be perpendicular to the lines x−12=y+11=z−3−2\frac{x - 1}{2}=\frac{y + 1}{1}=\frac{z - 3}{- 2} and x−31=y−23=z+24\frac{x - 3}{1}=\frac{y - 2}{3}=\frac{z + 2}{4}. If the line L intersects the yz -plane at the point Q , then the distance between the points P and Q is :

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  2. Question 2

    Quadratic Equations. Asked once: 5 Apr 2024 (same type asked 10 times) See all 10 of this type

    89
    The number of distinct real roots of the equation ∣x∣∣x+2∣−5∣x+1∣−1=0|x||x+ 2| - 5|x+ 1| - 1 = 0 is

  3. Question 3

    Vector Algebra. Asked once: 27 Jul 2022 (same type asked 10 times) See all 10 of this type

    73
    Let a→=2i^−j^+5k^\overrightarrow{a}= 2\widehat{i}-\widehat{j}+ 5\widehat{k} and b→=αi^+βj^+2k^\overrightarrow{b}= \alpha\widehat{i}+ \beta\widehat{j}+ 2\widehat{k}. If ((a→×b→)×i^)⋅k^=232((\overrightarrow{a}\times\overrightarrow{b}) \times\widehat{i}) \cdot\widehat{k}=\frac{23}{2}, then ∣b→×2j^∣|\overrightarrow{b}\times 2\widehat{j}| is equal to

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  4. Question 4

    Sequences and Series. Asked once: 13 Apr 2023 (same type asked 10 times) See all 10 of this type

    155
    Let a1,a2,a3,…a_{1},a_{2},a_{3},\ldots be a G.P. of increasing positive numbers. Let the sum of its 6th 6^{\text{th~}} and 8th 8^{\text{th~}} terms be 2 and the product of its 3rd 3^{\text{rd~}} and 5th 5^{\text{th~}} terms be 19\frac{1}{9}. Then 6(a2+6\left( a_{2}+ \right.  a4)(a4+a6)\left. \ a_{4} \right)\left( a_{4}+a_{6} \right) is equal to

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  5. Question 5

    Matrices. Asked once: 12 Apr 2023 (same type asked 9 times) See all 9 of this type

    74
    Let A=[115101]A =\begin{bmatrix} 1 & \frac{1}{51} \\ 0 & 1 \end{bmatrix}. If B=[12−1−1]A[−1−211]B =\begin{bmatrix} 1 & 2 \\ - 1 & - 1 \end{bmatrix}A\begin{bmatrix} - 1 & - 2 \\ 1 & 1 \end{bmatrix}, then the sum of all the elements of the matrix ∑n=150Bn\sum_{n= 1}^{50} B^{n} is equal to

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