JEE Advanced 2017 · Paper 2

The equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x + y − 2z = 5 and 3x − 6y − 2z = 7, is

1. A14x + 2y − 15z = 1
2. B14x − 2y + 15z = 27
3. C14x + 2y + 15z = 31
4. D−14x + 2y + 15z = 3

Let O be the origin and let PQR be an arbitrary triangle. The point S is such that OP⃗ · OQ⃗ + OR⃗ · OS⃗ = OR⃗ · OP⃗ + OQ⃗ · OS⃗ = OQ⃗ · OR⃗ + OP⃗ · OS⃗. Then the triangle PQR has S as its

1. Acentroid
2. Bcircumcentre
3. Cincentre
4. Dorthocenter

If y = y(x) satisfies the differential equation 8√x(√(9 + √x)) dy = (√(4 + √(9 + √x)))⁻¹ dx, x > 0 and y(0) = √7, then y(256) =

1. A3
2. B9
3. C16
4. D80

If f(x) = | cos(2x) cos(2x) sin(2x); −cos x cos x −sin x; sin x sin x cos x |, then

1. Af′(x) = 0 at exactly three points in (−π, π)
2. Bf′(x) = 0 at more than three points in (−π, π)
3. Cf(x) attains its maximum at x = 0
4. Df(x) attains its minimum at x = 0

|OX⃗ × OY⃗| =

1. Asin(P + Q)
2. Bsin 2R
3. Csin(P + R)
4. Dsin(Q + R)

If the triangle PQR varies, then the minimum value of cos(P + Q) + cos(Q + R) + cos(R + P) is

1. A−5/3
2. B−3/2
3. C3/2
4. D5/3