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Day 275: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 31 Jan 2023 (same type asked 3 times) See all 3 of this type

    177
    Let AA be the event that the absolute difference between two randomly chosen real numbers in the sample space [0,60]\lbrack 0,60\rbrack is less than or equal to a . If P(A)=1136P(A) =\frac{11}{36}, then a is equal to

  2. Question 2

    Relations and Functions. Asked once: 29 Jul 2022 (same type asked 3 times) See all 3 of this type

    61
    Let RR be a relation from the set {1,2,3,…,60}\{1,2,3,\ldots,60\} to itself such that R={(a,b):b=pq\mathbf{R = \{(a,b):b = pq}, where p,q≥3p,q \geq 3 are prime numbers }\}. Then, the number of elements in RR is:

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  3. Question 3

    Sequences and Series. Asked once: 25 Jun 2022 (same type asked 3 times) See all 3 of this type

    64
    Let f:N→Rf:N \rightarrow R be a function such that f(x+y)=2f(x)f(y)f(x+y) = 2f(x)f(y) for natural numbers xx and yy. If f(1)=2f(1) = 2, then the value of α\alpha for which ∑k=110f(α+k)=5123(220−1)\sum_{k = 1}^{10} f(\alpha+ k) =\frac{512}{3}\left( 2^{20}- 1 \right) holds, is

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  4. Question 4

    Straight Lines. Asked once: 6 Apr 2024 (same type asked 3 times) See all 3 of this type

    165
    If P(6,1)P(6,1) be the orthocentre of the triangle whose vertices are A(5,−2),B(8,3)A(5, - 2),B(8,3) and C(h,k)C(h,k), then the point CC lies on the circle.

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  5. Question 5

    Application of Integrals. Asked once: 2021 Paper 23 (same type asked 3 times) See all 3 of this type

    88
    If the line y=mxy=mx bisects the area enclosed by the lines x=0,y=0,x=32x = 0,y = 0,x =\frac{3}{2} and the curve y=1+4x−x2y= 1 + 4x-x^{2}, then 12 m12\text{ }m is equal to