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Day 591: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 2021 Paper 3

    80
    When a missile is fired from a ship, the probability that it is intercepted is 13\frac{1}{3} and the probability that the missile hits the target, given that it is not intercepted, is 34\frac{3}{4}. If three missiles are fired independently from the ship, then the probability that all three hit the target, is:

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  2. Question 2

    Quadratic Equations. Asked once: 2021 Paper 24

    85
    Let f(x)f(x) be a polynomial of degree 3 such that f(k)=−2kf(k) = -\frac{2}{k} for k=2,3,4,5k= 2,3,4,5. Then the value of 52−10f(10)52 - 10f(10) is equal to:

  3. Question 3

    Relations and Functions. Asked once: 2021 Paper 21

    74
    Let Z\mathbb{Z} be the set of all integers, A={(x,y)∈Z×Z:(x−2)2+y2≤4}A=\left\{ (x,y) \in\mathbb{Z}\times\mathbb{Z}:(x- 2)^{2}+y^{2}\leq 4 \right\}, B={(x,y)∈Z×Z:x2+y2≤4}B =\left\{ (x,y) \in\mathbb{Z}\times\mathbb{Z}:x^{2}+y^{2}\leq 4 \right\} and
    C={(x,y)∈Z×Z:(x−2)2+(y−2)2≤4}C =\left\{ (x,y) \in\mathbb{Z}\times\mathbb{Z}:(x - 2)^{2}+ (y - 2)^{2}\leq 4 \right\}
    If the total number of relation from A∩BA \cap B to A∩CA \cap C is 2p2^{p}, then the value of pp is:

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  4. Question 4

    Sequences and Series. Asked once: 13 Apr 2023

    175
    Let [α]\lbrack\alpha\rbrack denote the greatest integer ≤α\leq \alpha. Then [1]+[2]+[3]+……+[120]\lbrack\sqrt{1}\rbrack + \lbrack\sqrt{2}\rbrack + \lbrack\sqrt{3}\rbrack + \ldots\ldots + \lbrack\sqrt{120}\rbrack is equal to.

  5. Question 5

    Straight Lines. Asked once: 27 Jul 2022

    78
    Let A(1,1),B(−4,3)C(−2,−5)A(1,1),B( - 4,3)C( - 2, - 5) be vertices of a triangle ABC,PABC,P be a point on side BCBC, and Δ1\Delta_{1} and Δ2\Delta_{2} be the areas of triangle APBAPB and ABCABC respectively. If Δ1:Δ2=4:7\Delta_{1}:\Delta_{2}= 4:7, then the area enclosed by the lines AP,ACAP,AC and the xx-axis is

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