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Day 230: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 3 Apr 2025 (same type asked 10 times) See all 10 of this type

    66
    Let a1,a2,a3,…a_{1},a_{2},a_{3},\ldots be a G. P. of increasing positive numbers. If a3a5=729a_{3}a_{5}= 729 and a2+a4=1114a_{2}+a_{4}=\frac{111}{4}, then 24(a1+a2+a3)24\left( a_{1}+a_{2}+a_{3} \right) is equal to.

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  2. Question 2

    Matrices. Asked once: 21 Jan 2026 S2 (same type asked 9 times) See all 9 of this type

    64
    For the matrices A=[3−41−1]A =\begin{bmatrix} 3 & - 4 \\ 1 & - 1 \end{bmatrix} and B=[−2949−1318]B =\begin{bmatrix} - 29 & 49 \\ - 13 & 18 \end{bmatrix}, if (A15+B)[xy]=[00]\left( A^{15}+ B \right)\begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} 0 \\ 0 \end{bmatrix}, then among the following which one is true?

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  3. Question 3

    Application of Integrals. Asked once: 5 Apr 2024 (same type asked 9 times) See all 9 of this type

    83
    The area of the region enclosed by the parabolas y=x2−5xy=x^{2}- 5x and y=7x−x2y= 7x-x^{2} is

  4. Question 4

    Three Dimensional Geometry. Asked once: 28 Jan 2026 S1 (same type asked 9 times) See all 9 of this type

    68
    If the distances of the point (1,2,a)(1,2,a) from the line x−11=y2=z−11\frac{x- 1}{1}=\frac{y}{2}=\frac{z- 1}{1} along the lines L1:x−13=y−24=z−abL_{1}:\frac{x - 1}{3}=\frac{y - 2}{4}=\frac{z - a}{b} and L2:x−11=y−24=z−acL_{2}:\frac{x - 1}{1}=\frac{y - 2}{4}=\frac{z - a}{c} are equal, then a+b+ca + b + c is equal to

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  5. Question 5

    Three Dimensional Geometry. Asked once: 29 Jan 2025 (same type asked 9 times) See all 9 of this type

    138
    Let PP be the foot of the perpendicular from the point (1,2,2)(1,2,2) on the line L:x−11=y+1−1=z−22L:\frac{x - 1}{1}=\frac{y + 1}{- 1}=\frac{z - 2}{2}. Let the line r→=(−i^+j^−2k^)+λ(i^−j^+k^),λ∈R\overrightarrow{r}= ( -\widehat{i}+\widehat{j}- 2\widehat{k}) + \lambda(\widehat{i}-\widehat{j}+\widehat{k}),\lambda \in R, intersect the line L at Q . Then 2(PQ)22(PQ)^{2} is equal to:

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