1
JEE Advanced 2020 Paper 2 Offline
Numerical
+3
-1
Change Language
The value of the limit

$$\mathop {\lim }\limits_{x \to {\pi \over 2}} {{4\sqrt 2 (\sin 3x + \sin x)} \over {\left( {2\sin 2x\sin {{3x} \over 2} + \cos {{5x} \over 2}} \right) - \left( {\sqrt 2 + \sqrt 2 \cos 2x + \cos {{3x} \over 2}} \right)}}$$

is ...........
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2
JEE Advanced 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
Let b be a nonzero real number. Suppose f : R $$ \to $$ R is a differentiable function such that f(0) = 1. If the derivative f' of f satisfies the equation $$f'(x) = {{f(x)} \over {{b^2} + {x^2}}}$$

for all x$$ \in $$R, then which of the following statements is/are TRUE?
A
If b > 0, then f is an increasing function
B
If b < 0, then f is a decreasing function
C
f(x) f($$-$$x) = 1 for all x$$ \in $$R
D
f(x) $$-$$f($$-$$x) = 0 for all x$$ \in $$R
3
JEE Advanced 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
Let a and b be positive real numbers such that a > 1 and b < a. Let P be a point in the first quadrant that lies on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. Suppose the tangent to the hyperbola at P passes through the point (1, 0), and suppose the normal to the hyperbola at P cuts off equal intercepts on the coordinate axes. Let $$\Delta $$ denote the area of the triangle formed by the tangent at P, the normal at P and the X-axis. If e denotes the eccentricity of the hyperbola, then which of the following statements is/are TRUE?
A
$$1 < e < \sqrt 2 $$
B
$$\sqrt 2 < e < 2$$
C
$$\Delta = {a^4}$$
D
$$\Delta = {b^4}$$
4
JEE Advanced 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
Let f : R $$ \to $$ R and g : R $$ \to $$ R be functions
satisfying f(x + y) = f(x) + f(y) + f(x)f(y)
and f(x) = xg(x) for all x, y$$ \in $$R.
If $$\mathop {\lim }\limits_{x \to 0} g(x) = 1$$, then which of the following statements is/are TRUE?
A
f is differentiable at every x$$ \in $$R
B
If g(0) = 1, then g is differentiable at every x$$ \in $$R
C
The derivative f'(1) is equal to 1
D
The derivative f'(0) is equal to 1
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