1
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
Which of the following inequalities is/are TRUE?
A
$$\int_0^1 {x\cos xdx\, \ge \,{3 \over 8}} $$
B
$$\int_0^1 {x\sin xdx\, \ge \,{3 \over {10}}} $$
C
$$\int_0^1 {{x^2}\cos xdx\, \ge \,{1 \over 2}} $$
D
$$\int_0^1 {{x^2}\sin xdx\, \ge \,{2 \over 9}} $$
2
JEE Advanced 2020 Paper 1 Offline
Numerical
+4
-0
Change Language
Let m be the minimum possible value of $${\log _3}({3^{{y_1}}} + {3^{{y_2}}} + {3^{{y_3}}})$$, where $${y_1},{y_2},{y_3}$$ are real numbers for which $${{y_1} + {y_2} + {y_3}}$$ = 9. Let M be the maximum possible value of $$({\log _3}{x_1} + {\log _3}{x_2} + {\log _3}{x_3})$$, where $${x_1},{x_2},{x_3}$$ are positive real numbers for which $${{x_1} + {x_2} + {x_3}}$$ = 9. Then the value of $${\log _2}({m^3}) + {\log _3}({M^2})$$ is ...........
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3
JEE Advanced 2020 Paper 1 Offline
Numerical
+4
-0
Change Language
Let a1, a2, a3, .... be a sequence of positive integers in arithmetic progression with common difference 2. Also, let b1, b2, b3, .... be a sequence of positive integers in geometric progression with common ratio 2. If a1 = b1 = c, then the number of all possible values of c, for which the equality 2(a1 + a2 + ... + an) = b1 + b2 + ... + bn holds for some positive integer n, is ...........
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4
JEE Advanced 2020 Paper 1 Offline
Numerical
+4
-0
Change Language
Let f : [0, 2] $$ \to $$ R be the function defined by

$$f(x) = (3 - \sin (2\pi x))\sin \left( {\pi x - {\pi \over 4}} \right) - \sin \left( {3\pi x + {\pi \over 4}} \right)$$

If $$\alpha ,\,\beta \in [0,2]$$ are such that $$\{ x \in [0,2]:f(x) \ge 0\} = [\alpha ,\beta ]$$, then the value of $$\beta - \alpha $$ is ..........
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