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Day 16: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. This type asked 6 times: 27 Jan 2024, 29 Jan 2024, 4 Apr 2024, 5 Apr 2024, 24 Jan 2025, 5 Apr 2026 S1. This one: 5 Apr 2026 S1 See all 6 of this type

    65
    The square of the distance of the point of intersection of the line r→=(i^+j^−k^)+λ(a^−j^)\overrightarrow{r}= (\widehat{i}+\widehat{j}-\widehat{k}) +\lambda(\widehat{a}-\widehat{j}), a≠0a \neq 0 and r→=(4i^−k^)+μ(2i^+ak^)\overrightarrow{r}= (4\widehat{i}-\widehat{k}) +\mu(2\widehat{i}+ a\widehat{k}) from the origin is :

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  2. Question 2

    Binomial Theorem. This type asked 6 times: 2021 Paper 22, 1 Feb 2023, 8 Apr 2023, 5 Apr 2024, 8 Apr 2024, 4 Apr 2026 S2. This one: 4 Apr 2026 S2 See all 6 of this type

    59
    In the expansion of (9x−13x)18,x>0\left( 9x-\frac{1}{3\sqrt{x}} \right)^{18},x> 0, if the term independent of x is (221)k(221)k. then k is equal to:

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  3. Question 3

    Differentiation. This type asked 6 times: 2021 Paper 3, 2021 Paper 22, 29 Jul 2022, 31 Jan 2024, 1 Feb 2024, 4 Apr 2026 S2. This one: 4 Apr 2026 S2 See all 6 of this type

    72
    Let f(x)={ex−1,x<0x2−5x+6,x≥0f(x) = \left\{ \begin{matrix} e^{x - 1} & ,x < 0 \\ x^{2} - 5x + 6 & ,x \geq 0 \end{matrix} \right. and g(x)=f(∣x∣)+∣f(x)∣g(x) = f(|x|) + |f(x)|. If the number of points where g is not continuous and is not differentiable are α\alpha and β\beta respectively, then α+β\alpha + \beta is equal to ____\_\_\_\_

  4. Question 4

    Differentiation. This type asked 6 times: 2021 Paper 4, 26 Jun 2022, 15 Apr 2023, 28 Jan 2025, 4 Apr 2025, 4 Apr 2026 S1. This one: 4 Apr 2026 S1 See all 6 of this type

    75
    The number of points, at which the function f(x)=max{6x,2+3x2}+∣x−1∣cos⁡∣x2−14∣,x∈(−π,π)f(x) = max\left\{ 6x,2 + 3x^{2} \right\} + |x - 1|\cos\left| x^{2} - \frac{1}{4} \right|,x \in ( - \pi,\pi), is not differentiable, is ____\_\_\_\_ .

  5. Question 5

    Application of Derivatives. This type asked 6 times: 2021 Paper 3, 2021 Paper 10, 2021 Paper 23, 25 Jul 2022, 7 Apr 2025, 2 Apr 2026 S2. This one: 2 Apr 2026 S2 See all 6 of this type

    68
    Let f(x)f(x) be a polynomial of degree 5 and have extrema at x=1x= 1 and x=−1x= - 1. If lim⁡x→0(f(x)x3)=−5\lim_{x\rightarrow 0} \left( \frac{f(x)}{x^{3}} \right)= - 5, then f(2)−f(−2)f(2) - f( - 2) is equal to :

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