1
JEE Advanced 2018 Paper 1 Offline
Numerical
+3
-0
Let a and b be two unit vectors such that a . b = 0. For some x, y$$ \in $$R, let $$\overrightarrow c = x\overrightarrow a + y\overrightarrow b + \overrightarrow a \times \overrightarrow b $$. If | $$\overrightarrow c $$| = 2 and the vector c is inclined at the same angle $$\alpha $$ to both a and b, then the value of $$8{\cos ^2}\alpha $$ is ..............
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2
JEE Advanced 2018 Paper 1 Offline
Numerical
+3
-0
Let a, b, c three non-zero real numbers such that the equation $$\sqrt 3 a\cos x + 2b\sin x = c,x \in \left[ { - {\pi \over 2},{\pi \over 2}} \right]$$, has two distinct real roots $$\alpha $$ and $$\beta $$ with $$\alpha + \beta = {\pi \over 3}$$. Then, the value of $${b \over a}$$ is ............
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3
JEE Advanced 2018 Paper 1 Offline
Numerical
+3
-0
A farmer F1 has a land in the shape of a triangle with vertices at P(0, 0), Q(1, 1) and R(2, 0). From this land, a neighbouring farmer F2 takes away the region which lies between the sides PQ and a curve of the form y = xn (n > 1). If the area of the region taken away by the farmer F2 is exactly 30% of the area of $$\Delta $$PQR, then the value of n is .................
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4
JEE Advanced 2018 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Let S be the circle in the XY-plane defined the equation x2 + y2 = 4.

Let E1E2 and F1F2 be the chords of S passing through the point P0 (1, 1) and parallel to the X-axis and the Y-axis, respectively. Let G1G2 be the chord of S passing through P0 and having slope$$-$$1. Let the tangents to S at E1 and E2 meet at E3, then tangents to S at F1 and F2 meet at F3, and the tangents to S at G1 and G2 meet at G3. Then, the points E3, F3 and G3 lie on the curve
A
x + y = 4
B
(x $$-$$ 4)2 + (y $$-$$ 4)2 = 16
C
(x $$-$$ 4)(y $$-$$ 4) = 4
D
xy = 4
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