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Day 592: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 26 Jun 2022

    79
    Let f(x)=2cos⁡−1x+4cot⁡−1x−3x2−2x+10,x∈[−f(x) = 2\cos^{- 1}x + 4\cot^{- 1}x - 3x^{2}- 2x + 10,x \in \lbrack - 1,1]1,1\rbrack. If [a,b]\lbrack a,b\rbrack is the range of the function then 4a−4a - bb is equal to:

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  2. Question 2

    Application of Integrals. Asked once: 27 Jun 2022

    177
    If the area of the region {(x,y):x23+y23≤1, x+y≥0,y≥0}\left\{ (x,y):x^{\frac{2}{3}}+y^{\frac{2}{3}}\leq 1,\ x+y\geq 0,y\geq 0 \right\} is A, then 256Aπ\frac{256A}{\pi} is

  3. Question 3

    Complex Numbers. Asked once: 25 Jul 2022

    63
    For n∈Nn \in N, let Sn={z∈C:∣z−3+2i∣=n4}S_{n}=\left\{ z \in C:|z - 3 + 2i| =\frac{n}{4} \right\} and Tn={z∈C:∣z−2+3i∣=1n}T_{n}=\left\{ z \in C:|z - 2 + 3i| =\frac{1}{n} \right\}. Then the number of elements in the set {n∈N:Sn∩Tn=ϕ}\left\{ n \in N:S_{n}\cap T_{n}= \phi \right\} is:

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  4. Question 4

    Conic Sections. Asked once: 28 Jan 2025

    67
    Let  nCr−1=28, nCr=56\ ^{n}C_{r - 1}= 28,\ ^{n}C_{r}= 56 and  nCr+1=70\ ^{n}C_{r + 1}= 70. Let A(4cos⁡t,4sin⁡t),B(2sin⁡t,−2cos⁡t)A(4\cos t,4\sin t),B(2\sin t, - 2\cos t) and C(3r−n,r2−n−1)C\left( 3r - n,r^{2}- n - 1 \right) be the vertices of a triangle ABCABC, where tt is a parameter. If (3x−1)2+(3y)2=α(3x - 1)^{2}+ (3y)^{2}= \alpha, is the locus of the centroid of triangle ABC , then α\alpha equals :

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  5. Question 5

    Definite Integration. Asked once: 13 Apr 2023

    179
    Let fn=∫0π2(∑k=1nsin⁡k−1x)(∑k=1n(2k−1)sin⁡k−1x)cos⁡xf_{n}=\int_{0}^{\frac{\pi}{2}} \left( \sum_{k = 1}^{n} \sin^{k - 1}x \right)\left( \sum_{k = 1}^{n} (2k - 1)\sin^{k - 1}x \right)\cos x dx,n∈Ndx,n \in N. Then f21−f20f_{21}-f_{20} is equal to