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Day 120: JEE Mains Maths

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

  1. Question 1

    Permutations and Combinations. This type asked 2 times: 25 Jan 2023, 30 Jan 2023. This one: 30 Jan 2023 See all 2 of this type

    162
    The number of ways of selecting two numbers aa and b,a∈{2,4,6,…,100}\mathbf{b,a \in \{ 2,4,6,\ldots,100\}} and b∈{1,3,5,…,99}\mathbf{b \in \{ 1,3,5,\ldots,99\}} such that 2 is the remainder when a+ba + b is divided by 23 is

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  2. Question 2

    Permutations and Combinations. This type asked 2 times: 24 Jan 2023, 30 Jan 2023. This one: 30 Jan 2023 See all 2 of this type

    180
    The number of seven digits odd numbers, that can be formed using all the seven digits 1,2,2,2,3,3,51,2,2,2,3,3,5 is

  3. Question 3

    Conic Sections. This type asked 2 times: 29 Jul 2022, 29 Jan 2023. This one: 29 Jan 2023 See all 2 of this type

    77
    Let the tangents at the points A(4,−11)A(4, - 11) and B(8,−5)B(8, - 5) on the circle x2+y2−3x+10y−15=0x^{2}+y^{2}- 3x + 10y - 15 = 0, intersect at the point CC. Then the radius of the circle, whose centre is CC and the line joining AA and BB is its tangent, is equal to

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  4. Question 4

    Sequences and Series. This type asked 2 times: 2021 Paper 19, 29 Jan 2023. This one: 29 Jan 2023 See all 2 of this type

    180
    Let {ak}\left\{ a_{k} \right\} and {bk},k∈N\left\{ b_{k} \right\},k \in N, be two G.P.s with common ratios r1r_{1} and r2r_{2} respectively such that a1= b1=4a_{1}= \ b_{1}= 4 and r1<r2r_{1}<r_{2}. Let ck=ak+bk,k∈Nc_{k}=a_{k}+b_{k},k \in N. If c2=5c_{2}= 5 and c3=134c_{3}=\frac{13}{4} then ∑k=1∞ck−(12a6+8 b4)\sum_{k = 1}^{\infty} c_{k}-\left( 12a_{6}+ 8{\text{ }b}_{4} \right) is equal to

  5. Question 5

    Conic Sections. This type asked 2 times: 26 Jul 2022, 25 Jan 2023. This one: 25 Jan 2023 See all 2 of this type

    62
    The distance of the point (6,−22)(6, - 2\sqrt{2}) from the common tangent y=mx+c,m>0y = mx + c,m > 0, of the curves x=2y2x = 2y^{2} and x=1+y2x = 1 +y^{2} is:

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