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Day 248: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 7 Apr 2025 (same type asked 5 times) See all 5 of this type

    131
    Let a random variable X take values 0,1,2,30,1,2,3 with P(X=0)=P(X=1)=P\left( X= 0 \right)=P\left( X= 1 \right)= p,P(X=2)=P(X=3)p,P(X= 2) =P(X= 3) and E(X2)=2E(X)E\left( X^{2} \right)= 2E(X). Then the value of 8p−18p- 1 is :

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  2. Question 2

    Vector Algebra. Asked once: 28 Jan 2025 (same type asked 5 times) See all 5 of this type

    127
    Let A, B, C be three points in xy-plane, whose position vector are given by 3i^+j^,i^+3j^\sqrt{3}\widehat{i}+\widehat{j},\widehat{i}+\sqrt{3}\widehat{j} and a i^+(1−a)j^\widehat{i}+ (1 - a)\widehat{j} respectively with respect to the origin O. If the distance of the point C from the line bisecting the angle between the vectors OA→\overrightarrow{OA} and OB→\overrightarrow{OB} is 92\frac{9}{\sqrt{2}}, then the sum of all the possible values of aa is:

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  3. Question 3

    Statistics. Asked once: 4 Apr 2024 (same type asked 5 times) See all 5 of this type

    73
    Let a,b∈Ra,b \in R. Let the mean and the variance of 6 observations −3,4,7,−6- 3,4,7, - 6, a, b be 2 and 23, respectively. The mean deviation about the mean of these 6 observations is:

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  4. Question 4

    Vector Algebra. Asked once: 22 Jan 2025 (same type asked 5 times) See all 5 of this type

    140
    Let a→\overrightarrow{a} and b→\overrightarrow{b} be two - unit vectors such that the angle between them is π3\frac{\pi}{3}. If λa→+2b→\lambda\overrightarrow{a}+ 2\overrightarrow{b} and 3a→−λb→3\overrightarrow{a}- \lambda\overrightarrow{b} are perpendicular to each other, then the number of values of λ\lambda in [−1,3]\lbrack - 1,3\rbrack is :

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  5. Question 5

    Definite Integration. Asked once: 29 Jun 2022 (same type asked 5 times) See all 5 of this type

    157
    Let ff be a real valued continuous function on [0,1]\lbrack 0,1\rbrack and f(x)=x+∫01(x−t)f(t)dtf(x) = x +\int_{0}^{1} (x - t)f(t)dt. Then which of the following points (x,y)(x,y) lies on the curve y=f(x)y = f(x)?

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