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1
JEE Main 2021 (Online) 26th August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of all patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set :
A
{80, 83, 86, 89}
B
{84, 86, 88, 90}
C
{79, 81, 83, 85}
D
{84, 87, 90, 93}
2
JEE Main 2021 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
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)
3
JEE Main 2021 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Let N be the set of natural numbers and a relation R on N be defined by $$R = \{ (x,y) \in N \times N:{x^3} - 3{x^2}y - x{y^2} + 3{y^3} = 0\} $$. Then the relation R is :
A
symmetric but neither reflexive nor transitive
B
reflexive but neither symmetric nor transitive
C
reflexive and symmetric, but not transitive
D
an equivalence relation
4
JEE Main 2021 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
If [x] be the greatest integer less than or equal to x,

then $$\sum\limits_{n = 8}^{100} {\left[ {{{{{( - 1)}^n}n} \over 2}} \right]} $$ is equal to :
A
0
B
4
C
$$-$$2
D
2
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