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Day 253: JEE Mains Maths

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

  1. Question 1

    Permutations and Combinations. Asked once: 2021 Paper 23 (same type asked 5 times) See all 5 of this type

    83
    The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is

  2. Question 2

    Probability. Asked once: 27 Jan 2024 (same type asked 5 times) See all 5 of this type

    86
    A fair die is tossed repeatedly until a six is obtained. Let XX denote the number of tosses required and let a=P(X=3),b=P(X≥3)a = P(X = 3),b = P(X \geq 3) and c=P(X≥6∣X>3)c = P(X \geq 6 \mid X > 3). Then b+ca\frac{b + c}{a} is equal to

  3. Question 3

    Relations and Functions. Asked once: 29 Jan 2024 (same type asked 5 times) See all 5 of this type

    168
    If RR is the smallest equivalence relation on the set {1,2,3,4}\mathbf{\{ 1,2,3,4\}} such that {(1,2),(1,3)}⊂R\mathbf{\{(1,2),(1,3)\} \subset R}, then the number of elements in RR is

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  4. Question 4

    Application of Derivatives. Asked once: 14 Jun 2022 (same type asked 5 times) See all 5 of this type

    170
    Let λ∗\lambda^{*} be the largest value of λ\lambda for which the function fλ(x)=4λx3−36λx2+36x+48f_{\lambda}(x) = 4\lambda x^{3}- 36\lambda x^{2}+ 36x + 48 is increasing for all x∈Rx \in R. Then fλ∗(1)+fλ∗(−1)f_{\lambda}*(1) +f_{\lambda}*( - 1) is equal to:

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  5. Question 5

    Complex Numbers. Asked once: 2021 Paper 17 (same type asked 5 times) See all 5 of this type

    83
    If the real part of the complex number z=3+2icosθ1−3icosθ,θ∈(0,π2)z =\frac{3 + 2icos\theta}{1 - 3icos\theta},\theta \in\left( 0,\frac{\pi}{2} \right) is zero, then the value of sin⁡23θ+cos⁡2θ\sin^{2}3\theta +\cos^{2}\theta is equal to