IIT-JEE Exam

The point P is the intersection of the straight line joining the points Q(2,3,5) and R(1, –1, 4) with the plane
5x – 4y – z = 1. If S is the foot of the perpendicular drawn from the point T(2, 1,4) to QR, then the length of the
line segment PS is

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IIT-JEE Other Question
29.2% (w/w) HCl stock solution has a density of 1.25 g mL–1. The molecular weight of HCl is 36.5 g mol–1. The
volume (mL) of stock solution required to prepare a 200 mL solution of 0.4 M HCl is Let z be a complex number such that the imaginary part of z is non zero and a = z^2 + z + 1 is real. Then a cannot
take the value