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Day 488: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 4 Apr 2025

    68
    Consider the equation x2+4x−n=0x^{2}+ 4x-n= 0, where n∈[20,100]n \in \lbrack 20,100\rbrack is a natural number. Then the number of all distinct values of nn, for which the given equation has integral roots, is equal to.

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  2. Question 2

    Relations and Functions. Asked once: 23 Jan 2025

    127
    Let A={(x,y)∈R×R:∣x+y∣≥3}\mathbf{A = \{(x,y) \in R \times R:|x + y| \geq 3\}} and
    B={(x,y)∈R×R:∣x∣+∣y∣≤3}.\mathbf{B = \{(x,y) \in R \times R:|x| + |y| \leq 3\}.}
    If C={(x,y)∈A∩B:x=0\mathbf{C = \{(x,y) \in A \cap B:x = 0} or y=0}y = 0\}, then ∑(x,y)∈C∣x+y∣\sum_{(x,y) \in C} |x + y| is :

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  3. Question 3

    Sequences and Series. Asked once: 24 Jan 2026 S1

    65
    Consider an A.P.: a1,a2,…,an;a1>0a_{1},a_{2},\ldots,a_{n};a_{1}> 0. If a2−a1=−34,an=14a1a_{2}-a_{1}=\frac{- 3}{4},a_{n}=\frac{1}{4}a_{1}, and ∑i=1nai=5252\sum_{i = 1}^{n} a_{i}=\frac{525}{2}, then ∑i=117ai\sum_{i = 1}^{17} a_{i} is equal to

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  4. Question 4

    Statistics. Asked once: 2021 Paper 9

    87
    The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is.

  5. Question 5

    Straight Lines. Asked once: 3 Apr 2025

    63
    A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines L1:2x+y+6=0L_{1}:2x + y + 6 = 0 and L2:4x+2y−p=0,p>0L_{2}:4x + 2y - p = 0,p > 0, at the points A and B , respectively. If AB=92AB =\frac{9}{\sqrt{2}} and the foot of the perpendicular from the point A on the line L2L_{2} is MM, then AMBM\frac{AM}{BM} is equal to.

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