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Day 507: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 5 Apr 2024

    85
    If S={a∈R:∣2a−1∣=3[a]+2{a}}S = \{ a \in R:|2a - 1| = 3\lbrack a\rbrack + 2\{ a\}\}, where [t]\lbrack t\rbrack denotes the greatest integer less than or equal to tt and {t}\{ t\} represents the fractional part of tt, then 72∑a∈Sa72\sum_{a \in S} a is equal to

  2. Question 2

    Relations and Functions. Asked once: 8 Apr 2024

    167
    Let f(x)={−a if −a≤x≤0x+a if 0<x≤af(x) =\left\{ \begin{matrix} - a & \text{~if~}- a \leq x \leq 0 \\ x + a & \text{~if~}0 < x \leq a \end{matrix} \right. where a>0a > 0 and g(x)=(f(∣x∣)−∣f(x)∣)/2g(x) = (f(|x|) - |f(x)|)/2. Then the function g:[−a,a]→[−a,a]g:\lbrack - a,a\rbrack \rightarrow \lbrack - a,a\rbrack is

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  3. Question 3

    Sequences and Series. Asked once: 4 Apr 2025

    60
    Let f:R→Rf:\mathbb{R}\rightarrow\mathbb{R} be a continuous function satisfying f(0)=1f(0) = 1 and f(2x)−f(x)=xf(2x) -f(x) = x for all x∈Rx \in\mathbb{R}. If lim⁡n→∞{f(x)−f(x2n)}=G(x)\underset{n\rightarrow \infty}{\lim} \left\{ f(x) -f\left( \frac{x}{2^{n}} \right) \right\}=G(x), then ∑r=110G(r2)\sum_{r= 1}^{10} G\left( r^{2} \right) is equal to

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  4. Question 4

    Straight Lines. Asked once: 23 Jan 2025

    63
    Let the area of a △PQR\bigtriangleup PQR with vertices P(5,4),Q(−2,4)P(5,4),Q( - 2,4) and R(a,b)R(a,b) be 35 square units. If its orthocenter and centroid are O(2,145)O\left( 2,\frac{14}{5} \right) and C(c,d)C(c,d) respectively, then c+2 dc + 2\text{ }d is equal to

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  5. Question 5

    Three Dimensional Geometry. Asked once: 31 Jan 2023

    165
    Let the plane P:8x+α1y+α2z+12=0P:8x +\alpha_{1}y +\alpha_{2}z + 12 = 0 be parallel to the line L:x+22=y−33=z+45L:\frac{x + 2}{2}=\frac{y - 3}{3}=\frac{z + 4}{5}. If the intercept of PP on the yy-axis is 1 , then the distance between PP and LL is :

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