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Day 122: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. This type asked 2 times: 29 Jun 2022, 27 Jul 2022. This one: 27 Jul 2022 See all 2 of this type

    72
    Let a→=αi^+j^+βk^\overrightarrow{a}= \alpha\widehat{i}+\widehat{j}+ \beta\widehat{k} and b→=3i^−5j^+4k^\overrightarrow{b}= 3\widehat{i}- 5\widehat{j}+ 4\widehat{k} be two vectors, such that a→×b→=−i^+9j^+12k^\overrightarrow{a}\times\overrightarrow{b}= -\widehat{i}+ 9\widehat{j}+ 12\widehat{k}. Then the projection of b→−2a→\overrightarrow{b}- 2\overrightarrow{a} on b→+a→\overrightarrow{b}+\overrightarrow{a} is equal to

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  2. Question 2

    Conic Sections. This type asked 2 times: 2021 Paper 18, 26 Jul 2022. This one: 26 Jul 2022 See all 2 of this type

    72
    A point PP moves so that the sum of squares of its distances from the points (1,2)(1,2) and (−2,1)( - 2,1) is 14. Let f(x,y)=0f(x,y) = 0 be the locus of PP, which intersects the xx-axis at the points A,BA,B and the yy-axis at the point C, D. Then the area of the quadrilateral ACBD is equal to

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  3. Question 3

    Conic Sections. This type asked 2 times: 25 Jun 2022, 26 Jul 2022. This one: 26 Jul 2022 See all 2 of this type

    163
    Let the abscissae of the two points PP and QQ on a circle be the roots of x2−4x−6=0x^{2}- 4x - 6 = 0 and the ordinates of PP and QQ be the roots of y2+2y−7=y^{2}+ 2y - 7 = 0. If PQPQ is a diameter of the circle x2+y2+2ax+x^{2}+y^{2}+ 2ax + 2by+c=02by + c = 0, then the value of (a+b−c)(a + b - c) is

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  4. Question 4

    Relations and Functions. This type asked 2 times: 25 Jul 2022, 26 Jul 2022. This one: 26 Jul 2022 See all 2 of this type

    171
    Let A={1,2,3,4,5,6,7}\mathbf{A = \{ 1,2,3,4,5,6,7\}} and B={3,6,7,9}\mathbf{B = \{ 3,6,7,9\}}. Then the number of elements in the set {C⊆A:C∩B≠ϕ}\mathbf{\{ C \subseteq A:C \cap B \neq \phi\}} is

  5. Question 5

    Conic Sections. This type asked 2 times: 14 Jun 2022, 25 Jul 2022. This one: 25 Jul 2022 See all 2 of this type

    89
    The sum of diameters of the circles that touch (i) the parabola 75x2=64(5y−3)75x^{2}= 64(5y - 3) at the point (85,65)\left( \frac{8}{5},\frac{6}{5} \right) and (ii) the yy-axis, is equal to