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Day 278: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked once: 24 Jan 2023 (same type asked 3 times) See all 3 of this type

    154
    Let α→=4i^+3j^+5k^\overrightarrow{\alpha}= 4\widehat{i}+ 3\widehat{j}+ 5\widehat{k} and β→=i^+2j^−4k^\overrightarrow{\beta}=\widehat{i}+ 2\widehat{j}- 4\widehat{k}. Let β→1{\overrightarrow{\beta}}_{1} be parallel to α→\overrightarrow{\alpha} and β→2{\overrightarrow{\beta}}_{2} be perpendicular to α→\overrightarrow{\alpha}. If β→=\overrightarrow{\beta}= β→1+β→2{\overrightarrow{\beta}}_{1}+{\overrightarrow{\beta}}_{2}, then the value of 5β→2⋅(i^+j^+k^)5{\overrightarrow{\beta}}_{2}\cdot (\widehat{i}+\widehat{j}+\widehat{k}) is

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  2. Question 2

    Binomial Theorem. Asked once: 2021 Paper 5 (same type asked 3 times) See all 3 of this type

    76
    Let [x]\lbrack x\rbrack denote greatest integer less than or equal to xx. If for n∈N,(1−x+x3)n=∑j=03najxjn\in\mathbb{N},\left( 1 -x+x^{3} \right)^{n}=\sum_{j= 0}^{3n} a_{j}x^{j}, then ∑j=0[3n2]a2j+4∑j=0[3n−12]a2j+1\sum_{j = 0}^{\left\lbrack \frac{3n}{2} \right\rbrack} a_{2j}+ 4\sum_{j = 0}^{\left\lbrack \frac{3n - 1}{2} \right\rbrack} a_{2j}+ 1 is equal to:

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  3. Question 3

    Definite Integration. Asked once: 31 Jan 2023 (same type asked 3 times) See all 3 of this type

    153
    Let α>0\alpha > 0. If ∫0αxx+α−xdx=16+20215\int_{0}^{\alpha} \frac{x}{\sqrt{x + \alpha}-\sqrt{x}}dx =\frac{16 + 20\sqrt{2}}{15}, then α\alpha is equal to:

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  4. Question 4

    Sequences and Series. Asked once: 29 Jun 2022 (same type asked 3 times) See all 3 of this type

    72
    Let {an}n=0∞\left\{ a_{n} \right\}_{n = 0}^{\infty} be a sequence such that a0=a1=0a_{0}=a_{1}= 0 and an+2=2an+1−an+1a_{n + 2}= 2a_{n + 1}-a_{n}+ 1 for all n≥0n \geq 0. Then, ∑n=2∞an7n\sum_{n = 2}^{\infty} \frac{a_{n}}{7^{n}} is equal to

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  5. Question 5

    Application of Derivatives. Asked once: 30 Jan 2024 (same type asked 3 times) See all 3 of this type

    65
    The maximum area of a triangle whose one vertex is at (0,0)(0,0) and the other two vertices lie on the curve y=−2x2+54y = - 2x^{2}+ 54 at points (x,y(x,y ) and (−x,y)( - x,y) where y>0y> 0 is:

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