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Day 288: JEE Mains Maths

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

  1. Question 1

    Straight Lines. Asked once: 26 Jul 2022 (same type asked 3 times) See all 3 of this type

    88
    The equations of the sides AB,BCAB,BC and CACA of a triangle ABCABC are 2x+y=0,x+py=15a2x+y= 0,x+py= 15a and x−y=3x-y= 3 respectively. If its ortho centre is (2,a)(2,a), −12<a<2-\frac{1}{2}< a < 2, then pp is equal to

  2. Question 2

    Application of Derivatives. Asked once: 2021 Paper 1 (same type asked 3 times) See all 3 of this type

    83
    The minimum value of α\alpha for which the equation 4sin⁡x+11−sin⁡x=α\frac{4}{\sin x}+\frac{1}{1 - \sin x}=\alpha has at least one solution in (0,π2)\left( 0,\frac{\pi}{2} \right) is

  3. Question 3

    Application of Derivatives. Asked once: 2021 Paper 2 (same type asked 3 times) See all 3 of this type

    66
    If PP is a point on the parabola y=x2+4y=x^{2}+ 4 which is closest to the straight line y=4x−1y= 4x- 1, then the co-ordinates of PP are :

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  4. Question 4

    Inverse Trigonometric Functions. Asked once: 2021 Paper 20 (same type asked 3 times) See all 3 of this type

    64
    If (sin⁡−1x)2−(cos⁡−1x)2=a;0<x<1,a≠0\left( \sin^{- 1}x \right)^{2}-\left( \cos^{- 1}x \right)^{2}=a;0 <x< 1,a\neq 0, then the value of 2x2−12x^{2}- 1 is :

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  5. Question 5

    Three Dimensional Geometry. Asked once: 2021 Paper 19 (same type asked 3 times) See all 3 of this type

    85
    Let QQ be the foot of the perpendicular from the point P(7,−2,13)P(7, - 2,13) on the plane containing the lines x+16=y−17=z−38\frac{x+ 1}{6}=\frac{y- 1}{7}=\frac{z- 3}{8} and x−13=y−25=z−37\frac{x- 1}{3}=\frac{y- 2}{5}=\frac{z- 3}{7} . Then (PQ)2(PQ)^{2}, is equal to