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Day 265: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked once: 10 Apr 2023 (same type asked 4 times) See all 4 of this type

    61
    Let OO be the origin and the position vector of the point PP be −i^−2j^+3k^-\widehat{i}- 2\widehat{j}+ 3\widehat{k}. If the position vectors of the points A,BA,B and CC are −2i^+j^−3k^,2i^+4j^−2k^- 2\widehat{i}+\widehat{j}- 3\widehat{k},2\widehat{i}+ 4\widehat{j}- 2\widehat{k} and −4i^+2j^−k^- 4\widehat{i}+ 2\widehat{j}-\widehat{k} respectively then the projection of the vector OP→\overrightarrow{OP} on a vector perpendicular to the vectors AB→\overrightarrow{AB} and AC→\overrightarrow{AC} is

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  2. Question 2

    Definite Integration. Asked once: 27 Jun 2022 (same type asked 4 times) See all 4 of this type

    158
    Let ff be a differentiable function in (0,π2)\left( 0,\frac{\pi}{2} \right). If ∫cos⁡x1t2f(t)dt=sin⁡3x+cos⁡x\int_{\cos x}^{1} t^{2}f(t)dt =\sin^{3}x + \cos x then 13f′(13)\frac{1}{\sqrt{3}}f^{'}\left( \frac{1}{\sqrt{3}} \right) is equal to:

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  3. Question 3

    Application of Integrals. Asked once: 29 Jan 2023 (same type asked 4 times) See all 4 of this type

    75
    Let A={(x,y)∈R2:y≥0,2x≤y≤4−(x−1)2}A =\left\{ (x,y) \in R^{2}:y \geq 0,2x \leq y \leq\sqrt{4 - (x - 1)^{2}} \right\} and
    B={(x,y)∈R×R:0≤y≤min{2x,4−(x−1)2}}B =\left\{ (x,y) \in R \times R:0 \leq y \leq min\left\{ 2x,\sqrt{4 - (x - 1)^{2}} \right\} \right\}
    Then the ratio of the area of AA to the area of BB is

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  4. Question 4

    Application of Integrals. Asked once: 26 Jul 2022 (same type asked 4 times) See all 4 of this type

    65
    The odd natural number a, such that the area of the region bounded by y=1,y=3,x=0,x=yay = 1,y = 3,x = 0,x =y^{a} is 3643\frac{364}{3}, is equal to:

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  5. Question 5

    Probability. Asked once: 2021 Paper 20 (same type asked 4 times) See all 4 of this type

    77
    When a certain biased die is rolled, a particular face occurs with probability 16−x\frac{1}{6}- x and its opposite face occurs with probability 16+x\frac{1}{6}+x. All other faces occur with probability 16\frac{1}{6}. Note that opposite faces sum to 7 in any die. If 0<x<160 <x<\frac{1}{6}, and the probability of obtaining total sum =7= 7, when such a die is rolled twice, is 1396\frac{13}{96}, then the value of xx is:

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