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Day 85: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked 2 times: 1 Feb 2024*, 6 Apr 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    167
    Let a→=2i^+j^−k^,b→=((a→×(i^+j^))×i^)×i^\overrightarrow{a}= 2\widehat{i}+\widehat{j}-\widehat{k},\overrightarrow{b}= ((\overrightarrow{a}\times (\widehat{i}+\widehat{j})) \times\widehat{i}) \times\widehat{i}. Then the square of the projection of a→\overrightarrow{a} on b→\overrightarrow{b} is:

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  2. Question 2

    Binomial Theorem. Asked 2 times: 28 Jun 2022*, 5 Apr 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    82
    If the constant term in the expansion of (1+2x−3x3)(32x2−13x)9\left( 1 + 2x- 3x^{3} \right)\left( \frac{3}{2}x^{2}-\frac{1}{3x} \right)^{9} is pp, then 108p108p is equal to

  3. Question 3

    Permutations and Combinations. Asked 2 times: 2021 Paper 8*, 4 Apr 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    68
    There are 5 points P1,P2,P3,P4,P5P_{1},P_{2},P_{3},P_{4},P_{5} on the side ABAB, excluding AA and BB, of a triangle ABCABC. Similarly, there are 6 points P6,P7,…,P11P_{6},P_{7},\ldots,P_{11} on the side BCBC and 7 points P12,P13,…,P18P_{12},P_{13},\ldots,P_{18} on the side CACA of the triangle. The number of triangles, that can be formed using the points P1,P2,…,P18P_{1},P_{2},\ldots,P_{18} as vertices, is:

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  4. Question 4

    Sequences and Series. Asked 2 times: 1 Feb 2024*, 4 Apr 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    155
    Let three real numbers a,b,ca,b,c be in arithmetic progression and a+1, b,c+3a + 1,\text{ }b,c + 3 be in geometric progression. If a>10a > 10 and the arithmetic mean of a,ba,b and cc is 8 , then the cube of the geometric mean of a,ba,b and cc is

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  5. Question 5

    Three Dimensional Geometry. Asked 2 times: 31 Jan 2024*, 4 Apr 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    76
    Let the point, on the line passing through the points P(1,−2,3)P(1, - 2,3) and Q(5,−4,7)Q(5, - 4,7), farther from the origin and at a distance of 9 units from the point PP, be (α,β,γ)(\alpha,\beta,\gamma). Then α2+β2+γ2\alpha^{2}+\beta^{2}+\gamma^{2} is equal to:

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