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Day 46: JEE Mains Maths

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

  1. Question 1

    Differentiation. This type asked 4 times: 2021 Paper 10, 26 Jun 2022, 29 Jan 2023, 22 Jan 2025. This one: 22 Jan 2025 See all 4 of this type

    66
    Let f(x)f(x) be a real differentiable function such that f(0)=1f(0) = 1 and f(x+y)=f(x)f′(y)+f′(x)f(y)f(x + y) = f(x)f^{'}(y) +f^{'}(x)f(y) for all x,y∈Rx,y \in R. Then ∑n=1100log⁡ef(n)\sum_{n = 1}^{100} \log_{e}f(n) is equal to :

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  2. Question 2

    Three Dimensional Geometry. This type asked 4 times: 29 Jan 2024, 1 Feb 2024, 5 Apr 2024, 22 Jan 2025. This one: 22 Jan 2025 See all 4 of this type

    58
    Let L1:x−12=y−23=z−34L_{1}:\frac{x- 1}{2}=\frac{y- 2}{3}=\frac{z- 3}{4} and L2:x−23=y−44=z−55L_{2}:\frac{x- 2}{3}=\frac{y- 4}{4}=\frac{z- 5}{5} be two lines. Then which of the following points lies on the line of the shortest distance between L1L_{1} and L2L_{2} ?

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  3. Question 3

    Straight Lines. This type asked 4 times: 2021 Paper 24, 28 Jun 2022, 8 Apr 2024, 9 Apr 2024. This one: 9 Apr 2024 See all 4 of this type

    64
    A ray of light coming from the point P(1,2)P(1,2) gets reflected from the point QQ on the xx-axis and then passes through the point R(4,3)R(4,3). If the point SS (h, kk ) is such that PQRSPQRS is a parallelogram, then hk2hk^{2} is equal to:

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  4. Question 4

    Quadratic Equations. This type asked 4 times: 2021 Paper 23, 14 Jun 2022, 27 Jun 2022, 8 Apr 2024. This one: 8 Apr 2024 See all 4 of this type

    62
    The sum of all the solutions of the equation (8)2x−16⋅(8)x+48=0(8)^{2x}- 16 \cdot (8)^{x}+ 48 = 0 is :

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  5. Question 5

    Definite Integration. This type asked 4 times: 2021 Paper 2, 28 Jun 2022, 8 Apr 2023, 6 Apr 2024. This one: 6 Apr 2024 See all 4 of this type

    174
    Let [t]\lbrack t\rbrack denote the largest integer less than or equal to tt. If ∫03([x2]+[x22])dx=a+b2−3−5+c6−7\int_{0}^{3} \left( \left\lbrack x^{2} \right\rbrack+\left\lbrack \frac{x^{2}}{2} \right\rbrack \right)dx=a+b\sqrt{2}-\sqrt{3}-\sqrt{5}+c\sqrt{6}-\sqrt{7}, where a,b,c∈za,b,c \in z, then a+b+ca + b + c is equal to