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Day 184: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked once: 28 Jan 2025 (same type asked 3 times) See all 3 of this type

    128
    If the components of a→=αi^+βj^+γk^\overrightarrow{a}= \alpha\widehat{i}+ \beta\widehat{j}+ \gamma\widehat{k} along and perpendicular to b→=3i^+j^−k^\overrightarrow{b}= 3\widehat{i}+\widehat{j}-\widehat{k} respectively, are 1611(3i^+j^−k^)\frac{16}{11}(3\widehat{i}+\widehat{j}-\widehat{k}) and 111(−4i^−5j^−17k^)\frac{1}{11}( - 4\widehat{i}- 5\widehat{j}- 17\widehat{k}), then α2+β2+γ2\alpha^{2}+\beta^{2}+\gamma^{2} is equal to :

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  2. Question 2

    Binomial Theorem. Asked once: 2021 Paper 9 (same type asked 3 times) See all 3 of this type

    63
    Let (1+x+2x2)20=a0+a1x+a2x2+…+a40x40\left( 1 +x+ 2x^{2} \right)^{20}=a_{0}+a_{1}x+a_{2}x^{2}+ \ldots +a_{40}x^{40}. then a1+a3+a5+…+a37a_{1}+a_{3}+a_{5}+ \ldots +a_{37} is equal to

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  3. Question 3

    Definite Integration. Asked once: 27 Jan 2024 (same type asked 3 times) See all 3 of this type

    69
    If ∫0113+x+1+xdx=a+b2+c3\int_{0}^{1} \frac{1}{\sqrt{3 + x}+\sqrt{1 + x}}dx = a + b\sqrt{2}+ c\sqrt{3}, where a,b,ca,b,c are rational numbers, then 2a+3b−4c2a + 3b - 4c is equal to :

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  4. Question 4

    Sequences and Series. Asked once: 14 Jun 2022 (same type asked 3 times) See all 3 of this type

    73
    If {ai}i=1n\left\{ a_{i} \right\}_{i = 1}^{n} where nn is an even integer, is an arithmetic progression with common difference 1 , and ∑i=1nai=192,∑i=1n/2a2i=120\sum_{i = 1}^{n} a_{i}= 192,\sum_{i = 1}^{n/2} a_{2i}= 120, then nn is equal to:

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  5. Question 5

    Permutations and Combinations. Asked once: 5 Apr 2024 (same type asked 3 times) See all 3 of this type

    155
    60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then the 50th 50^{\text{th~}} word is:

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