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Day 219: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 29 Jan 2023 (same type asked 2 times) See all 2 of this type

    179
    A circle with centre (2,3)(2,3) and radius 4 intersects the line x+y=3x + y = 3 at the points PP and QQ. If the tangents at PP and QQ intersect at the point S(α,β)S(\alpha,\beta), then 4α−7β4\alpha - 7\beta is equal to

  2. Question 2

    Sequences and Series. Asked once: 2021 Paper 19 (same type asked 2 times) See all 2 of this type

    84
    Let a1,a2,…,a10a_{1},a_{2},\ldots,a_{10} be an AP with common difference -3 and b1,b2,….,b10b_{1},b_{2},\ldots.,b_{10} be a GP with common ratio 2 . Let ck=ak+bk,k=1,2,…,10c_{k}=a_{k}+b_{k},k= 1,2,\ldots,10. If c2=12c_{2}= 12 and c3=13c_{3}= 13, then ∑k=110ck\sum_{k = 1}^{10} c_{k} is equal to

  3. Question 3

    Conic Sections. Asked once: 26 Jul 2022 (same type asked 2 times) See all 2 of this type

    162
    The equation of a common tangent to the parabolas y=x2y =x^{2} and y=−(x−2)2y = - (x - 2)^{2} is

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  4. Question 4

    Vector Algebra. Asked once: 25 Jun 2022 (same type asked 2 times) See all 2 of this type

    74
    Let a→=a1i^+a2j^+a3k^ ai>0,i=1,2,3\overrightarrow{a}=a_{1}\widehat{i}+a_{2}\widehat{j}+a_{3}\widehat{k}\ a_{i}> 0,i = 1,2,3 be a vector which makes equal angles with the coordinates axes OX, OY and OZ. Also, let the projection of a→\overrightarrow{a} on the vector 3i^+4j^3\widehat{i}+ 4\widehat{j} be 7 . Let b→\overrightarrow{b} be a vector obtained by rotating a→\overrightarrow{a} with 90∘90^{\circ}. If a→,b→\overrightarrow{a},\overrightarrow{b} and xx-axis are coplanar, then projection of a vector b→\overrightarrow{b} on 3i^+4j^3\widehat{i}+ 4\widehat{j} is equal to

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  5. Question 5

    Limits and Continuity. Asked once: 27 Jun 2022 (same type asked 2 times) See all 2 of this type

    65
    Let aa be an integer such that lim⁡x→718−[1−x][x−3a]\lim_{x\rightarrow 7} \frac{18 - \lbrack 1 -x\rbrack}{\lbrack x- 3a\rbrack} exists, where [t]\lbrack t\rbrack is greatest integer ≤t\leq t. Then a is equal to:

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