1
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let s, t, r be non-zero complex numbers and L be the set of solutions $$z = x + iy(x,y \in R,\,i = \sqrt { - 1} )$$ of the equation $$sz + t\overline z + r = 0$$ where $$\overline z $$ = x $$-$$ iy. Then, which of the following statement(s) is(are) TRUE?
A
If L has exactly one element, then |s|$$ \ne $$|t|
B
If |s| = |t|, then L has infinitely many elements
C
The number of elements in $$L \cap \{ z:|z - 1 + i| = 5\} $$ is at most 2
D
If L has more than one element, then L has infinitely many elements
2
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let f : (0, $$\pi $$) $$ \to $$ R be a twice differentiable function such that $$\mathop {\lim }\limits_{t \to x} {{f(x)\sin t - f(t)\sin x} \over {t - x}} = {\sin ^2}x$$ for all x$$ \in $$ (0, $$\pi $$).

If $$f\left( {{\pi \over 6}} \right) = - {\pi \over {12}}$$, then which of the following statement(s) is (are) TRUE?
A
$$f\left( {{\pi \over 4}} \right) = {\pi \over {4\sqrt 2 }}$$
B
$$f(x) < {{{x^4}} \over 6} - {x^2}$$ for all x$$ \in $$(0, $$\pi $$)
C
There exists $$\alpha $$$$ \in $$(0, $$\pi $$) such that f'($$\alpha $$) = 0
D
$$f''\left( {{\pi \over 2}} \right) + f\left( {{\pi \over 2}} \right) = 0$$
3
JEE Advanced 2018 Paper 2 Offline
Numerical
+3
-0
The value of the integral

$$\int_0^{1/2} {{{1 + \sqrt 3 } \over {{{({{(x + 1)}^2}{{(1 - x)}^6})}^{1/4}}}}dx} $$ is ........
Your input ____
4
JEE Advanced 2018 Paper 2 Offline
Numerical
+3
-0
Let P be a matrix of order 3 $$ \times $$ 3 such that all the entries in P are from the set {$$-$$1, 0, 1}. Then, the maximum possible value of the determinant of P is ............ .
Your input ____
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