PYQ Vault

Day 174: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked once: 6 Apr 2023 (same type asked 4 times) See all 4 of this type

    79
    Let the position vectors of the points A,B,CA,B,C and DD be 5i^+5j^+2λk^,i^+2j^+3k^,−2i^+λj^+4k^5\widehat{i}+ 5\widehat{j}+ 2\lambda\widehat{k},\widehat{i}+ 2\widehat{j}+ 3\widehat{k}, - 2\widehat{i}+ \lambda\widehat{j}+ 4\widehat{k} and −i^+5j^+6k^-\widehat{i}+ 5\widehat{j}+ 6\widehat{k}. Let S={λ∈R:S=\{\lambda\in R: the points A,B,CA,B,C and DD are coplanar}\}. Then ∑λ∈S(λ+2)2\sum_{\lambda \in S} (\lambda + 2)^{2} is equal to

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  2. Question 2

    Application of Derivatives. Asked once: 29 Jun 2022 (same type asked 4 times) See all 4 of this type

    74
    A wire of length 22 m22\text{ }m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is :

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  3. Question 3

    Application of Integrals. Asked once: 2021 Paper 26 (same type asked 4 times) See all 4 of this type

    67
    Let A1A_{1} be the area of the region bounded by the curves y=sin⁡xy = \sin x, y=cos⁡xy = \cos x and yy-axis in the first quadrant. Also, let A2A_{2} be the area of the region bounded by the curves y=sin⁡x,y=cos⁡x,xy = \sin x,y = \cos x,x-axis and x=x = π2\frac{\pi}{2} in the first quadrant. Then,

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  4. Question 4

    Permutations and Combinations. Asked once: 26 Jun 2022 (same type asked 4 times) See all 4 of this type

    174
    The total number of 3-digit numbers, whose greatest common divisor with 36 is 2 , is
  5. Question 5

    Conic Sections. Asked once: 27 Jul 2022 (same type asked 4 times) See all 4 of this type

    179
    A common tangent TT to the curves C1:x24+y29=1C_{1}:\frac{x^{2}}{4}+\frac{y^{2}}{9}= 1 and C2:x242−y2143=1C_{2}:\frac{x^{2}}{42}-\frac{y^{2}}{143}= 1 does not pass through the fourth quadrant. If TT touches C1C_{1} at (x1,y1)\left( x_{1},y_{1} \right) and C2C_{2} at (x2,y2)\left( x_{2},y_{2} \right), then ∣2x1+x2∣\left| 2x_{1}+x_{2} \right| is equal to