JEE Advanced 2020 Paper 1 Offline | JEE Advanced Year Wise Previous Years Questions

JEE Advanced 2020 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

Let the function f : R $$ \to $$ R be defined by f(x) = x³ $$-$$ x² + (x $$-$$ 1)sin x and let g : R $$ \to $$ R be an arbitrary function. Let fg : R $$ \to $$ R be the product function defined by (fg)(x) = f(x)g(x). Then which of the following statements is/are TRUE?

If g is continuous at x = 1, then fg is differentiable at x = 1

If f g is differentiable at x = 1, then g is continuous at x = 1

If g is differentiable at x = 1, then fg is differentiable at x = 1

If f g is differentiable at x = 1, then g is differentiable at x = 1

JEE Advanced 2020 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

Let M be a 3 $$ \times $$ 3 invertible matrix with real entries and let I denote the 3 $$ \times $$ 3 identity matrix. If M^$$-$$1 = adj(adj M), then which of the following statements is/are ALWAYS TRUE?

M = I

det M = 1

M² = I

(adj M)² = I

JEE Advanced 2020 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

Let S be the set of all complex numbers z
satisfying |z² + z + 1| = 1. Then which of the following statements is/are TRUE?

$$\left| {z + {1 \over 2}} \right|$$ $$ \le $$ $${{1 \over 2}}$$ for all z$$ \in $$S

|z| $$ \le $$ 2 for all z$$ \in $$S

$$\left| {z + {1 \over 2}} \right|\, \ge {1 \over 2}$$ for all z$$ \in $$S

The set S has exactly four elements

JEE Advanced 2020 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

Let x, y and z be positive real numbers. Suppose x, y and z are the lengths of the sides of a triangle opposite to its angles X, Y, and Z, respectively. If

$$\tan {X \over 2} + \tan {Z \over 2} = {{2y} \over {x + y + z}}$$, then which of the following statements is/are TRUE?

2Y = X + Z

Y = X + Z

$$\tan {X \over 2}$$ = $${x \over {y + z}}$$

x² + z² $$-$$ y² = xz

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