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Day 238: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 6 Apr 2024 (same type asked 7 times) See all 7 of this type

    175
    From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable XX denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of XX is mn\frac{m}{n}, where gcd(m,n)=1gcd(m,n) = 1, then n−mn-m is equal to

  2. Question 2

    Quadratic Equations. Asked once: 25 Jan 2023 (same type asked 7 times) See all 7 of this type

    173
    Let a∈Ra \in R and let α,β\alpha,\beta be the roots of the equation x2+6014x+a=0x^{2}+60^{\frac{1}{4}}x + a = 0 If α4+β4=−30\alpha^{4}+\beta^{4}= - 30, then the product of all possible values of a is

  3. Question 3

    Binomial Theorem. Asked once: 24 Jan 2023 (same type asked 7 times) See all 7 of this type

    75
    The value of ∑r=022 22Cr 23Cr\sum_{r = 0}^{22} \ ^{22}C_{r}\ ^{23}C_{r} is

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  4. Question 4

    Application of Derivatives. Asked once: 28 Jun 2022 (same type asked 7 times) See all 7 of this type

    72
    The number of real solutions of x7+5x3+3x+1=x^{7}+ 5x^{3}+ 3x + 1 = 0 is equal to

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  5. Question 5

    Three Dimensional Geometry. Asked once: 11 Apr 2023 (same type asked 7 times) See all 7 of this type

    152
    Let the line passing through the points, P(2,−1,2)P(2, - 1,2) and Q(5,3,4)Q(5,3,4) meet the plane x−y+z=4x - y + z = 4 at the point RR. Then the distance of the point RR from the plane x+2y+3z+2=0x + 2y + 3z + 2 = 0 measured parallel to the line x−72=y+32=z−21\frac{x - 7}{2}=\frac{y + 3}{2}=\frac{z - 2}{1} is equal to

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