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Day 564: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 27 Jun 2022

    167
    If a point A(x,y)A(x,y) lies in the region bounded by the yy-axis, straight lines 2y+x=62y + x = 6 and 5x−6y=305x - 6y = 30, then the probability that y<1y < 1 is:

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  2. Question 2

    Quadratic Equations. Asked once: 28 Jul 2022

    151
    Let S={x∈[−6,3]−{−2,2}:∣x+3∣−1∣x∣−2≥0}S =\left\{ x \in \lbrack - 6,3\rbrack - \{ - 2,2\}:\frac{|x + 3| - 1}{|x| - 2}\geq 0 \right\} and T={x∈Z:x2−7∣x∣+9≤0}T =\left\{ x \in Z:x^{2}- 7|x| + 9 \leq 0 \right\}. Then the number of elements in S∩TS \cap T is

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  3. Question 3

    Relations and Functions. Asked once: 28 Jul 2022

    154
    Let f(x)=ax2+bx+cf(x) = ax^{2} + bx + c be such that f(1)=3,f(−2)f(1) = 3,f( - 2) =λ= \lambda and f(3)=4f(3) = 4. If f(0)+f(1)+f(−2)+f(3)=14f(0) + f(1) + f( - 2) + f(3) = 14, then λ\lambda is equal to

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  4. Question 4

    Sequences and Series. Asked once: 5 Apr 2024

    87
    Let a1,a2,a3,…a_{1},a_{2},a_{3},\ldots be in an arithmetic progression of positive terms. Let Ak=a1 2−a22+a3 2−a42+…+a2k−1 2−a2k 2A_{k}=a_{1}\ ^{2}-a_{2}^{2}+a_{3}\ ^{2}-a_{4}^{2}+ \ldots +a_{2k - 1}\ ^{2}-a_{2k}\ ^{2}. If A3=−153, A5=−435A_{3}= - 153,{\text{ }A}_{5}= - 435 and a12+a22+a32=66a_{1}^{2}+a_{2}^{2}+a_{3}^{2}= 66, then a17−A7a_{17}-A_{7} is equal to

  5. Question 5

    Straight Lines. Asked once: 29 Jan 2023

    63
    Let BB and CC be the two points on the line y+x=0y + x = 0 such that BB and CC are symmetric with respect to the origin. Suppose AA is a point on y−2x=2y - 2x = 2 such that △ABC\bigtriangleup ABC is an equilateral triangle. Then, the area of the △ABC\bigtriangleup ABC is

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