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Day 197: JEE Mains Maths

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

  1. Question 1

    Straight Lines. Asked once: 12 Apr 2023 (same type asked 2 times) See all 2 of this type

    78
    If the point (α,733)\left( \alpha,\frac{7\sqrt{3}}{3} \right) lies on the curve traced by the mid-points of the line segments of the lines xcos⁡θ+ysin⁡θ=7,θ∈(0,π2)x\cos\theta + y\sin\theta = 7,\theta \in\left( 0,\frac{\pi}{2} \right) between the coordinates axes, then α\alpha is equal to

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  2. Question 2

    Permutations and Combinations. Asked once: 28 Jan 2026 S2 (same type asked 2 times) See all 2 of this type

    72
    Three persons enter in a lift at the ground floor. The lift will go upto 10th 10^{\text{th~}} floor. The number of ways, in which the three persons can exit the lift at three different floors, if the lift does not stop at first, second and third floors, is equal to ____\_\_\_\_ .

  3. Question 3

    Complex Numbers. Asked once: 2021 Paper 1 (same type asked 2 times) See all 2 of this type

    89
    If the least and the largest real values of α\alpha, for which the equation z+α∣z−1∣+2i=0z+\alpha|z- 1| + 2i= 0 (z∈C(z\in C and i=−1)i=\sqrt{- 1}) has a solution, are pp and qq respectively; then 4(p2+q2)4\left( p^{2}+q^{2} \right) is equal to

  4. Question 4

    Inverse Trigonometric Functions. Asked once: 2021 Paper 26 (same type asked 2 times) See all 2 of this type

    68
    If 0<a,b<10 < a,b < 1, and tan⁡−1a+tan⁡−1b=π4\tan^{-1}a +\tan^{-1}b =\frac{\pi}{4}, then the value of (a+b)−(a2+b22)+(a3+b33)−(a4+b44)+…(a + b) -\left( \frac{a^{2}+b^{2}}{2} \right)+\left( \frac{a^{3}+b^{3}}{3} \right)-\left( \frac{a^{4}+b^{4}}{4} \right)+ \ldots is:

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  5. Question 5

    Probability. Asked once: 7 Apr 2025 (same type asked 2 times) See all 2 of this type

    130
    A bag contains 19 unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and head turns up. If the probability that the drawn coin was unbiased, is mn,gcd(m,n)=1\frac{m}{n},gcd(m,n) = 1, then n2−m2n^{2}-m^{2} is equal to:

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