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Day 167: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. Asked once: 11 Apr 2023 (same type asked 4 times) See all 4 of this type

    153
    If the 1011th 1011^{\text{th~}} term from the end in the binomial expansion of (4x5−52x)2022\left( \frac{4x}{5}-\frac{5}{2x} \right)^{2022} is 1024 times 1011th 1011^{\text{th~}} term from the beginning, then ∣x∣|x| is equal to

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  2. Question 2

    Relations and Functions. Asked once: 9 Apr 2024 (same type asked 4 times) See all 4 of this type

    175
    Let A={(x,y):2x+3y=23,x,y∈N}\mathbf{A = \{(x,y):2x + 3y = 23,x,y \in N\}} and B={x:(x,y)∈A}\mathbf{B = \{ x:(x,y) \in A\}}. Then the number of one-one functions from AA to BB is equal to

  3. Question 3

    Three Dimensional Geometry. Asked once: 22 Jan 2025 (same type asked 4 times) See all 4 of this type

    131
    Let a line pass through two distinct points P(−2,−1,3)P( - 2, - 1,3) and Q , and be parallel to the vector 3i^+2j^+2k3\widehat{i}+ 2\widehat{j}+ 2k. If the distance of the point QQ from the point R(1,3,3)R(1,3,3) is 5 , then the square of the area of △PQR\bigtriangleup PQR is equal to:

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  4. Question 4

    Binomial Theorem. Asked once: 28 Jan 2025 (same type asked 4 times) See all 4 of this type

    143
    Let the coefficients of three consecutive terms TrT_{r}, Tr+1T_{r + 1} and Tr+2T_{r + 2} in the binomial expansion of (a+b)12(a + b)^{12} be in a G.P. and let p be the number of all possible values of rr. Let qq be the sum of all rational terms in the binomial expansion of (34+43)12(\sqrt[4]{3}+\sqrt[3]{4})^{12}. Then p+qp + q is equal to :

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  5. Question 5

    Conic Sections. Asked once: 23 Jan 2025 (same type asked 4 times) See all 4 of this type

    138
    Let the shortest distance from (a,0),a>0(a,0),a > 0, to the parabola y2=4xy^{2}= 4x be 4 . Then the equation of the circle passing through the point (a,0)(a,0) and the focus of the parabola, and having its centre on the axis of the parabola is:

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