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Day 310: JEE Mains Maths

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

  1. Question 1

    Relations and Functions. Asked once: 6 Apr 2024 (same type asked 5 times) See all 5 of this type

    65
    The function f(x)=x2+2x−15x2−4x+9,x∈Rf(x) =\frac{x^{2}+ 2x- 15}{x^{2}- 4x+ 9},x\in R is

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  2. Question 2

    Three Dimensional Geometry. Asked once: 6 Apr 2024 (same type asked 5 times) See all 5 of this type

    164
    Let P(α,β,γ)P(\alpha,\beta,\gamma) be the image of the point Q(3,−3,1)Q(3, - 3,1) in the line x−01=y−31=z−1−1\frac{x - 0}{1}=\frac{y - 3}{1}=\frac{z - 1}{- 1} and RR be the point (2,5,−1)(2,5, - 1). If the area of the triangle PQRPQR is λ\lambda and λ2=14 K\lambda^{2}= 14\text{ }K, then KK is equal to:

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  3. Question 3

    Application of Integrals. Asked once: 24 Jan 2023 (same type asked 5 times) See all 5 of this type

    64
    The area enclosed by the curves y2+4x=4y^{2}+ 4x = 4 and y−2x=2y - 2x = 2 is:

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  4. Question 4

    Relations and Functions. Asked once: 2021 Paper 11 (same type asked 5 times) See all 5 of this type

    50
    Let [x]\lbrack x\rbrack denote the greatest integer ≤x\leq x, where x∈Rx\in R. If the domain of the real valued function f(x)=∣[x]∣−2∣[x]∣−3f\left( x \right)=\sqrt{\frac{\left| \left\lbrack x \right\rbrack \right|- 2}{\left| \left\lbrack x \right\rbrack \right|- 3}} is (−∞,a)∪[b,c)∪[4,∞),a<b<c( - \infty,a) \cup \lbrack b,c) \cup \lbrack 4,\infty),a<b<c, then the value of a+b+ca+b+c is:

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  5. Question 5

    Sequences and Series. Asked once: 6 Apr 2023 (same type asked 5 times) See all 5 of this type

    169
    If gcd(m,n)=1gcd(m,n) = 1 and 12−22+32−42+1^{2}-2^{2}+3^{2}-4^{2}+ +(2021)2−(2022)2+(2023)2=1012m2n+ (2021)^{2}- (2022)^{2}+ (2023)^{2}= 1012m^{2}n, then m2−n2m^{2}-n^{2} is equal to

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