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Day 454: JEE Mains Maths

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

  1. Question 1

    Permutations and Combinations. Asked once: 21 Jan 2026 S1

    73
    Let S={(m,n):m,n∈{1,2,3,…..,50}}S = \{(m,n):m,n \in \{ 1,2,3,\ldots..,50\}\}. If the number of elements (m,nm,n) in S such that 6m+9n6^{m} + 9^{n} is a multiple of 5 is p and the number of elements (m,n)(m,n) in S such that m+nm + n is a square of a prime number is q , then p+qp + q is equal to ____\_\_\_\_

  2. Question 2

    Probability. Asked once: 2 Apr 2026 S2

    58
    A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5 points for each tail he throws. If the probability that he gets exactly 30 points is mn,gcd(m,n)=1\frac{m}{n},gcd(m,n) = 1, then m+nm + n is equal to :

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  3. Question 3

    Quadratic Equations. Asked once: 2 Apr 2026 S2

    51
    Let α,β\alpha,\beta be the roots of the equation x2−3x+r=0x^{2}- 3x+r= 0, and α2,2β\frac{\alpha}{2},2\beta be the roots of the equation x2+3x+r=0x^{2}+ 3x + r = 0. If the roots of the equation x2+6x=mx^{2}+ 6x=m are 2α+β+2r2\alpha+\beta+ 2r and α−2β−r2\alpha- 2\beta-\frac{r}{2}, then m is equal to :-

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  4. Question 4

    Relations and Functions. Asked once: 22 Jan 2026 S2

    68
    Let f(x)=[x]2−[x+3]−3,x∈Rf(x) = \lbrack x\rbrack^{2}- \lbrack x + 3\rbrack - 3,x \in R where [∙]\lbrack \bullet \rbrack is the greatest integer function. Then

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  5. Question 5

    Sequences and Series. Asked once: 6 Apr 2026 S1

    56
    The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8 . If the first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to common difference of the A.P., then the sum of all possible values of the first term of the G.P. is:

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