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Day 60: JEE Mains Maths

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

  1. Question 1

    Determinants. This type asked 3 times: 2021 Paper 19, 24 Jan 2023, 22 Jan 2026 S2. This one: 22 Jan 2026 S2 See all 3 of this type

    51
    Let n be the number obtained on rolling a fair die. If the probability that the system x−ny+z=6x - ny + z = 6, x+(n−2)y+(n+1)z=8x + (n - 2)y + (n + 1)z = 8, (n−1)y+z=1(n - 1)y + z = 1 has a unique solution is k6\frac{k}{6}, then the sum of k and all possible values of nn is :

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  2. Question 2

    Relations and Functions. This type asked 3 times: 29 Jul 2022, 6 Apr 2023, 22 Jan 2026 S2. This one: 22 Jan 2026 S2 See all 3 of this type

    53
    The number of elements in the relation R={(x,y)\mathbf{R = \{(x,y)} :  4x2+y2<52,x,y∈Z}\left. \ 4x^{2}+y^{2}< 52,x,y \in Z \right\} is

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  3. Question 3

    Sequences and Series. This type asked 3 times: 25 Jun 2022, 24 Jan 2023, 22 Jan 2026 S2. This one: 22 Jan 2026 S2 See all 3 of this type

    69
    Let ff and gg be functions satisfying f(x+y)=f(x)f(y),f(1)=7f(x + y) = f(x)f(y),f(1) = 7 and g(x+y)=g(xy)g(x + y) = g(xy), g(1)=1g(1) = 1, for all x,y∈Nx,y \in N. If ∑x=1n(f(x)g(x))=19607\sum_{x = 1}^{n} \left( \frac{f(x)}{g(x)} \right)= 19607, then n is equal to :

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  4. Question 4

    Straight Lines. This type asked 3 times: 6 Apr 2024, 9 Apr 2024, 22 Jan 2026 S2. This one: 22 Jan 2026 S2 See all 3 of this type

    57
    Among the statements (S1) : If A(5,−1)A(5, - 1) and B(−2,3)B( - 2,3) are two vertices of a triangle, whose orthocentre is (0,0)(0,0), then its third vertex is (−4,−7)( - 4, - 7) and (S2) : If positive numbers 2a,b,c2a,b,c are three consecutive terms of an A.P., then the lines ax+by+c=0ax+by+c=0 are concurrent at (2,−2)(2,-2).

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  5. Question 5

    Application of Integrals. This type asked 3 times: 2021 Paper 23, 14 Jun 2022, 22 Jan 2026 S1. This one: 22 Jan 2026 S1 See all 3 of this type

    53
    Let the line x=−1x = - 1 divide the area of the region {(x,y):1+x2≤y≤3−x}\left\{ (x,y):1 +x^{2}\leq y \leq 3 - x \right\} in the ratio m:n,gcd(m,n)=1m:n,gcd(m,n) = 1. Then m+nm + n is equal to

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