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Day 89: JEE Mains Maths

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

  1. Question 1

    Relations and Functions. Asked 2 times: 25 Jul 2022*, 11 Apr 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    176
    Let A={1,2,3,4,5}\mathbf{A = \{ 1,2,3,4,5\}} and B={1,2,3,4,5,6}\mathbf{B = \{ 1,2,3,4,5,6\}}. Then the number of functions f:A→Bf:A \rightarrow B satisfying f(1)+f(2)=f(4)−1f(1) + f(2) = f(4) - 1 is equal to

  2. Question 2

    Vector Algebra. Asked 2 times: 26 Jul 2022*, 11 Apr 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    78
    Let a→\overrightarrow{a} be a non-zero vector parallel to the line of intersection of the two planes determined by the vectors i^+j^,i^+k^\widehat{i}+\widehat{j},\widehat{i}+\widehat{k} and i^−j^,j^−k^\widehat{i}-\widehat{j},\widehat{j}-\widehat{k}. If θ\theta is the angle between the vector a→\overrightarrow{a} and the vector b→=2i^−2j^+k^\overrightarrow{b}= 2\widehat{i}- 2\widehat{j}+\widehat{k} and a→⋅b→=6\overrightarrow{a}\cdot\overrightarrow{b}= 6 then the ordered pair (θ,∣a→×b→∣)(\theta,|\overrightarrow{a}\times\overrightarrow{b}|) is equal to

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  3. Question 3

    Indefinite Integration. Asked 2 times: 8 Apr 2023*, 10 Apr 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    153
    For, α,β,γ,δ∈N\alpha,\beta,\gamma,\delta \in N, if ∫((xe)2x+(ex)2x)log⁡exdx=1α(xe)βx−1γ(ex)δx+C\int\left( \left( \frac{x}{e} \right)^{2x}+\left( \frac{e}{x} \right)^{2x} \right)\log_{e}xdx =\frac{1}{\alpha}\left( \frac{x}{e} \right)^{\beta x}-\frac{1}{\gamma}\left( \frac{e}{x} \right)^{\delta x}+ C, Where e=∑n=0∞1n!e =\sum_{n = 0}^{\infty} \frac{1}{n!} and CC is constant of integration, then α+2β+3γ−4δ\alpha + 2\beta + 3\gamma - 4\delta is equal to:

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  4. Question 4

    Permutations and Combinations. Asked 2 times: 2021 Paper 9, 10 Apr 2023 See all 2 times it was asked

    178
    The sum of all the four-digit numbers that can be formed using all the digits 2,1,2,32,1,2,3 is equal to

  5. Question 5

    Conic Sections. Asked 2 times: 29 Jul 2022*, 8 Apr 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    87
    Consider a circle C1:x2+y2−4x−2y=α−5C_{1}:x^{2}+y^{2}- 4x - 2y = \alpha - 5. Let its mirror image in the line y=2x+1y = 2x + 1 be another circle C2:5x2+5y2−10fx−10gy+36=0C_{2}:5x^{2}+ 5y^{2}- 10fx - 10gy + 36 = 0. Let  r\ r be the radius of C2C_{2}. Then α+r\alpha + r is equal to