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Day 149: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 4 Apr 2025 (same type asked 5 times) See all 5 of this type

    59
    Let A and B be two distinct points on the line L:x−63=y−72=z−7−2L:\frac{x - 6}{3}=\frac{y - 7}{2}=\frac{z - 7}{- 2}. Both A and B are at a distance 2172\sqrt{17} from the foot of perpendicular drawn from the point (1,2,3)(1,2,3) on the line L . If O is the origin, then OA→⋅OB→\overrightarrow{OA}\cdot\overrightarrow{OB} is equal to:

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  2. Question 2

    Binomial Theorem. Asked once: 9 Apr 2024 (same type asked 5 times) See all 5 of this type

    66
    The coefficient of x70x^{70} in x2(1+x)98+x3(1+x)97+x^{2}(1 + x)^{98}+x^{3}(1 + x)^{97}+ x4(1+x)96+x^{4}(1 + x)^{96}+ +x54(1+x)46+x^{54}(1 + x)^{46} is  99Cp− 46Cq\ ^{99}C_{p}-\ ^{46}C_{q}. Then a possible value to p+qp + q is:

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  3. Question 3

    Conic Sections. Asked once: 21 Jan 2026 S1 (same type asked 5 times) See all 5 of this type

    61
    Let the foci of hyperbola coincide with the foci of the ellipse x236+y216=1\frac{x^{2}}{36}+\frac{y^{2}}{16}= 1. If the eccentricity of the hyperbola is 5 , then the length of its latus rectum is:

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  4. Question 4

    Definite Integration. Asked once: 8 Apr 2023 (same type asked 5 times) See all 5 of this type

    81
    Let [t]\lbrack t\rbrack denotes the greatest integer ≤t\leq t. Then 2π∫π/65π/6(8[csc⁡x]−5[cot⁡x])dx\frac{2}{\pi}\int_{\pi/6}^{5\pi/6} (8\lbrack \csc x\rbrack - 5\lbrack \cot x\rbrack)dx is equal to

  5. Question 5

    Probability. Asked once: 21 Jan 2026 S2 (same type asked 5 times) See all 5 of this type

    60
    A random variable XX takes values 0,1,2,30,1,2,3 with probabilities 2a+130,8a−130,4a+130\frac{2a + 1}{30},\frac{8a - 1}{30},\frac{4a + 1}{30}, b respectively, where a,b∈Ra,b \in R. Let μ\mu and σ\sigma respectively be the mean and standard deviation of XX such that σ2+μ2=2\sigma^{2}+\mu^{2}= 2. Then ab\frac{a}{b} is equal to :

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