1
JEE Main 2021 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let f : R $$\to$$ R be defined as $$f(x + y) + f(x - y) = 2f(x)f(y),f\left( {{1 \over 2}} \right) = - 1$$. Then, the value of $$\sum\limits_{k = 1}^{20} {{1 \over {\sin (k)\sin (k + f(k))}}} $$ is equal to :
A
cosec2(21) cos(20) cos(2)
B
sec2(1) sec(21) cos(20)
C
cosec2(1) cosec(21) sin(20)
D
sec2(21) sin(20) sin(2)
2
JEE Main 2021 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let C be the set of all complex numbers. Let

S1 = {z$$\in$$C : |z $$-$$ 2| $$\le$$ 1} and

S2 = {z$$\in$$C : z(1 + i) + $$\overline z $$(1 $$-$$ i) $$\ge$$ 4}.

Then, the maximum value of $${\left| {z - {5 \over 2}} \right|^2}$$ for z$$\in$$S1 $$\cap$$ S2 is equal to :
A
$${{3 + 2\sqrt 2 } \over 4}$$
B
$${{5 + 2\sqrt 2 } \over 2}$$
C
$${{3 + 2\sqrt 2 } \over 2}$$
D
$${{5 + 2\sqrt 2 } \over 4}$$
3
JEE Main 2021 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$\tan \left( {{\pi \over 9}} \right),x,\tan \left( {{{7\pi } \over {18}}} \right)$$ are in arithmetic progression and $$\tan \left( {{\pi \over 9}} \right),y,\tan \left( {{{5\pi } \over {18}}} \right)$$ are also in arithmetic progression, then $$|x - 2y|$$ is equal to :
A
4
B
3
C
0
D
1
4
JEE Main 2021 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let the mean and variance of the frequency distribution

$$\matrix{ {x:} & {{x_1} = 2} & {{x_2} = 6} & {{x_3} = 8} & {{x_4} = 9} \cr {f:} & 4 & 4 & \alpha & \beta \cr } $$

be 6 and 6.8 respectively. If x3 is changed from 8 to 7, then the mean for the new data will be :
A
4
B
5
C
$${{17} \over 3}$$
D
$${{16} \over 3}$$
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