JEE Advanced 2018 Paper 1 Offline | JEE Advanced Year Wise Previous Years Questions

JEE Advanced 2018 Paper 1 Offline

MCQ (More than One Correct Answer)

-1

In a $$\Delta $$PQR = 30$$^\circ $$ and the sides PQ and QR have lengths 10$$\sqrt 3 $$ and 10, respectively. Then, which of the following statement(s) is(are) TRUE?

$$\angle QPR = 45^\circ $$

The area of the $$\Delta PQR$$ is $$25\sqrt 3 $$ and $$\angle QRP = 120^\circ $$

The radius of the incircle of the $$\Delta PQR$$ is $$10\sqrt 3 $$ $$-$$ 15

The area of the circumcircle of the $$\Delta PQR$$ is 100$$\pi $$

JEE Advanced 2018 Paper 1 Offline

MCQ (More than One Correct Answer)

-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?

The line of intersection of P₁ and P₂ has direction ratios 1, 2, $$-$$1

The line $${{3x - 4} \over 9} = {{1 - 3y} \over 9} = {z \over 3}$$ is perpendicular to the line of intersection of P₁ and P₂

The acute angle between P₁ and P₂ is 60$$^\circ $$

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 $${2 \over {\sqrt 3 }}$$

JEE Advanced 2018 Paper 1 Offline

MCQ (More than One Correct Answer)

-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?

There exist r, s $$ \in $$ R, where r < s, such that f is one-one on the open interval (r, s)

There exists x₀ $$ \in $$ ($$-$$4, 0) such that |f'(x₀)| $$ \le $$ 1

$$\mathop {\lim }\limits_{x \to \infty } f(x) = 1$$

There exists $$\alpha $$$$ \in $$($$-$$4, 4) such that f($$\alpha $$) + f"($$\alpha $$) = 0 and f'($$\alpha $$) $$ \ne $$ 0

JEE Advanced 2018 Paper 1 Offline

MCQ (More than One Correct Answer)

-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?

f(2) < 1 $$-$$ log_e 2

f(2) > 1 $$-$$ log_e 2

g(1) > 1 $$-$$ log_e 2

g(1) < 1 $$-$$ log_e 2

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