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Day 39: JEE Mains Maths

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

  1. Question 1

    Permutations and Combinations. This type asked 4 times: 8 Apr 2023, 2 Apr 2025, 21 Jan 2026 S2, 24 Jan 2026 S2. This one: 24 Jan 2026 S2 See all 4 of this type

    60
    The largest value of n , for which 40n40^{n} divides 60 !, is

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  2. Question 2

    Relations and Functions. This type asked 4 times: 2021 Paper 2, 1 Feb 2023, 3 Apr 2025, 24 Jan 2026 S2. This one: 24 Jan 2026 S2 See all 4 of this type

    67
    Let f be a function such that 3f(x)+2f(m19x)=5x3f(x) + 2f\left( \frac{m}{19x} \right)= 5x, x≠0x \neq 0, where m=∑i=19(i)2m =\sum_{i = 1}^{9} (i)^{2}. Then f(5)−f(2)f(5) - f(2) is equal to

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  3. Question 3

    Differentiation. This type asked 4 times: 2021 Paper 9, 8 Apr 2023, 30 Jan 2024, 24 Jan 2026 S1. This one: 24 Jan 2026 S1 See all 4 of this type

    66
    Let α,β∈R\alpha,\beta \in R be such that the function f(x)={2α(x2−2)+2βx,x<1(α+3)x+(α−β),x≥1f\left( x \right)=\left\{ \begin{matrix} 2\alpha\left( x^{2}- 2 \right)+ 2\beta x & ,x < 1 \\ \left( \alpha + 3 \right)x +\left( \alpha - \beta \right) & ,x \geq 1 \end{matrix} \right. be differentiable at all x∈Rx \in R. Then 34(α+β)34(\alpha + \beta) is equal to

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  4. Question 4

    Vector Algebra. This type asked 4 times: 2021 Paper 11, 6 Apr 2024, 28 Jan 2025, 24 Jan 2026 S1. This one: 24 Jan 2026 S1 See all 4 of this type

    55
    Let a→=2i^+j^−2k^,b→=i^+j^\overrightarrow{a}= 2\widehat{i}+\widehat{j}- 2\widehat{k},\overrightarrow{b}=\widehat{i}+\widehat{j} and c→=a→×b→\overrightarrow{c}=\overrightarrow{a}\times\overrightarrow{b}. Let d→\overrightarrow{d} be a vector such that ∣d→−a→∣=11,∣c→×d→∣=3|\overrightarrow{d}-\overrightarrow{a}| =\sqrt{11},|\overrightarrow{c}\times\overrightarrow{d}| = 3 and the angle between c→\overrightarrow{c} and d→\overrightarrow{d} is π4\frac{\pi}{4}. Then a→⋅d→\overrightarrow{a}\cdot\overrightarrow{d} is equal to

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  5. Question 5

    Permutations and Combinations. This type asked 4 times: 31 Jan 2024, 8 Apr 2024, 29 Jan 2025, 23 Jan 2026 S1. This one: 23 Jan 2026 S1 See all 4 of this type

    75
    The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is ____\_\_\_\_.