1
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let P1 : 2x + y $$-$$ z = 3 and P2 : x + 2y + z = 2 be two planes. Then, which of the following statement(s) is(are) TRUE?
A
The line of intersection of P1 and P2 has direction ratios 1, 2, $$-$$1
B
The line $${{3x - 4} \over 9} = {{1 - 3y} \over 9} = {z \over 3}$$ is perpendicular to the line of intersection of P1 and P2
C
The acute angle between P1 and P2 is 60$$^\circ$$
D
If P3 is the plane passing through the point (4, 2, $$-$$2) and perpendicular to the line of intersection of P1 and P2, then the distance of the point (2, 1, 1) from the plane P3 is $${2 \over {\sqrt 3 }}$$
2
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
For every twice differentiable function $$f:R \to [ - 2,2]$$ with $${(f(0))^2} + {(f'(0))^2} = 85$$, which of the following statement(s) is(are) TRUE?
A
There exist r, s $$\in$$ R, where r < s, such that f is one-one on the open interval (r, s)
B
There exists x0 $$\in$$ ($$-$$4, 0) such that |f'(x0)| $$\le$$ 1
C
$$\mathop {\lim }\limits_{x \to \infty } f(x) = 1$$
D
There exists $$\alpha$$$$\in$$($$-$$4, 4) such that f($$\alpha$$) + f"($$\alpha$$) = 0 and f'($$\alpha$$) $$\ne$$ 0
3
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let f : R $$\to$$ R and g : R $$\to$$ R be two non-constant differentiable functions. If f'(x) = (e(f(x) $$-$$ g(x))) g'(x) for all x $$\in$$ R and f(1) = g(2) = 1, then which of the following statement(s) is (are) TRUE?
A
f(2) < 1 $$-$$ loge 2
B
f(2) > 1 $$-$$ loge 2
C
g(1) > 1 $$-$$ loge 2
D
g(1) < 1 $$-$$ loge 2
4
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let f : [0, $$\infty$$) $$\to$$ R be a continuous function such that

$$f(x) = 1 - 2x + \int_0^x {{e^{x - t}}f(t)dt}$$ for all x $$\in$$ [0, $$\infty$$). Then, which of the following statement(s) is (are) TRUE?
A
The curve y = f(x) passes through the point (1, 2)
B
The curve y = f(x) passes through the point (2, $$-$$1)
C
The area of the region $$\{ (x,y) \in [0,1] \times R:f(x) \le y \le \sqrt {1 - {x^2}} \}$$ is $${{\pi - 2} \over 4}$$
D
The area of the region $$\{ (x,y) \in [0,1] \times R:f(x) \le y \le \sqrt {1 - {x^2}} \}$$ is $${{\pi - 1} \over 4}$$
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