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Day 341: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 10 Apr 2023 (same type asked 7 times) See all 7 of this type

    167
    Let the line x1=6−y2=z+85\frac{x}{1}=\frac{6 - y}{2}=\frac{z + 8}{5} intersect the lines x−54=y−73=z+21\frac{x - 5}{4}=\frac{y - 7}{3}=\frac{z + 2}{1} and x+36=3−y3=z−61\frac{x + 3}{6}=\frac{3 - y}{3}=\frac{z - 6}{1} at the points A and B respectively. Then the distance of the mid-point of the line segment ABAB from the plane 2x−2y+z=142x - 2y + z = 14 is

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  2. Question 2

    Limits and Continuity. Asked once: 5 Apr 2024 (same type asked 7 times) See all 7 of this type

    151
    Let f:[−1,2]→Rf:\lbrack - 1,2\rbrack \rightarrow R be given by f(x)=2x2+x+[x2]−[x]f(x) = 2x^{2}+ x +\left\lbrack x^{2} \right\rbrack- \lbrack x\rbrack, where [t]\lbrack t\rbrack denotes the greatest integer less than or equal to t. The number of points, where ff is not continuous, is:

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  3. Question 3

    Sequences and Series. Asked once: 1 Feb 2023 (same type asked 7 times) See all 7 of this type

    179
    The sum of the common terms of the following three arithmetic progressions.
    3,7,11,15,……,3993,7,11,15,\ldots\ldots,399
    2,5,8,11,……,3592,5,8,11,\ldots\ldots,359 and
    2,7,12,17,……,1972,7,12,17,\ldots\ldots,197
    is equal to

  4. Question 4

    Trigonometric Identities. Asked once: 25 Jul 2022 (same type asked 7 times) See all 7 of this type

    169
    2sin⁡(π22)sin⁡(3π22)sin⁡(5π22)sin⁡(7π22)sin⁡(9π22)2\sin\left( \frac{\pi}{22} \right)\sin\left( \frac{3\pi}{22} \right)\sin\left( \frac{5\pi}{22} \right)\sin\left( \frac{7\pi}{22} \right)\sin\left( \frac{9\pi}{22} \right) is equal to

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  5. Question 5

    Differential Equations. Asked once: 6 Apr 2023 (same type asked 7 times) See all 7 of this type

    156
    If the solution curve f(x,y)=0f(x,y) = 0 of the differential equation (1+log⁡ex)dxdy−xlog⁡ex=ey,x>0\left( 1 +\log_{e}x \right)\frac{dx}{dy}- x\log_{e}x =e^{y},x > 0, passes through the points (1,0)(1,0) and (α,2)(\alpha,2) then αα\alpha^{\alpha} is equal to

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