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Day 212: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 31 Jan 2024 (same type asked 2 times) See all 2 of this type

    159
    Let 2nd ,8th 2^{\text{nd~}},8^{\text{th~}} and 44th 44^{\text{th~}}, terms of a non-constant A.P. be respectively the 1st ,2nd 1^{\text{st~}},2^{\text{nd~}} and 3rd 3^{\text{rd~}} terms of G.P. If the first term of A.P. is 1 then the sum of first 20 terms is equal to-

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  2. Question 2

    Vector Algebra. Asked once: 29 Jan 2024 (same type asked 2 times) See all 2 of this type

    170
    Let a unit vector u^=xi^+yj^+zk^\widehat{u}=x\widehat{i}+y\widehat{j}+z\widehat{k} make angles π2,π3\frac{\pi}{2},\frac{\pi}{3} and 2π3\frac{2\pi}{3} with the vectors 12i^+12k^,12j^+12k^\frac{1}{\sqrt{2}}\widehat{i}+\frac{1}{\sqrt{2}}\widehat{k},\frac{1}{\sqrt{2}}\widehat{j}+\frac{1}{\sqrt{2}}\widehat{k} and 12i^+12j^\frac{1}{\sqrt{2}}\widehat{i}+\frac{1}{\sqrt{2}}\widehat{j} respectively. v→=12i^+12j^+12k^\overrightarrow{v}=\frac{1}{\sqrt{2}}\widehat{i}+\frac{1}{\sqrt{2}}\widehat{j}+\frac{1}{\sqrt{2}}\widehat{k}, then ∣u^−v→∣2|\widehat{u}-\overrightarrow{v}|^{2} is equal to

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  3. Question 3

    Conic Sections. Asked once: 24 Jan 2023 (same type asked 2 times) See all 2 of this type

    156
    The locus of the mid points of the chords of the circle C1:(x−4)2+(y−5)2=4C_{1}:(x - 4)^{2}+ (y - 5)^{2}= 4 which subtend an angle θ1\theta_{1} at the centre of the circle C1C_{1}, is a circle of radius rir_{i}. If θ1=π3,θ3=2π3\theta_{1}=\frac{\pi}{3},\theta_{3}=\frac{2\pi}{3} and r12=r22+r32r_{1}^{2}=r_{2}^{2}+r_{3}^{2}, then θ2\theta_{2} is equal to

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  4. Question 4

    Conic Sections. Asked once: 31 Jan 2024 (same type asked 2 times) See all 2 of this type

    87
    Let the foci and length of the latus rectum of an ellipse x2a2+y2 b2=1,a>b\frac{x^{2}}{a^{2}}+\frac{y^{2}}{{\text{ }b}^{2}}= 1,a > b be (±5,0)( \pm 5,0) and 50\sqrt{50}, respectively. Then, the square of the eccentricity of the hyperbola x2b2−y2a2b2=1\frac{x^{2}}{b^{2}}-\frac{y^{2}}{a^{2}b^{2}}= 1 equals

  5. Question 5

    Relations and Functions. Asked once: 28 Jun 2022 (same type asked 2 times) See all 2 of this type

    81
    Let R1R_{1} and R2R_{2} be relations on the set {1,2,…,50}\mathbf{\{ 1,2,\ldots,50\}} such that R1={(p,pn):pR_{1}=\left\{ \left( p,p^{n} \right):p \right. is a prime and n≥0n \geq 0 is an integer }\} and R2={(p,pn):pR_{2}=\left\{ \left( p,p^{n} \right):p \right. is a prime and n=0n= 0 or 1}\}. Then, the number of elements in R1−R2R_{1}-R_{2} is