1
JEE Main 2021 (Online) 24th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let f(x) be a differentiable function defined on [0, 2] such that f'(x) = f'(2 $$-$$ x) for all x$$ \in $$ (0, 2), f(0) = 1 and f(2) = e2. Then the value of $$\int\limits_0^2 {f(x)} dx$$ is :
A
1 + e2
B
2(1 + e2)
C
1 $$-$$ e2
D
2(1 $$-$$ e2)
2
JEE Main 2021 (Online) 24th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
The negation of the statement

$$ \sim p \wedge (p \vee q)$$ is :
A
$$p \vee \sim q$$
B
$$ \sim p \vee q$$
C
$$ \sim p \wedge q$$
D
$$p \wedge \sim q$$
3
JEE Main 2021 (Online) 24th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
For the statements p and q, consider the following compound statements :

(a) $$( \sim q \wedge (p \to q)) \to \sim p$$

(b) $$((p \vee q) \wedge \sim p) \to q$$

Then which of the following statements is correct?
A
(b) is a tautology but not (a).
B
(a) and (b) both are not tautologies.
C
(a) and (b) both are tautologies.
D
(a) is a tautology but not (b).
4
JEE Main 2021 (Online) 24th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
If $$n \ge 2$$ is a positive integer, then the sum of the series $${}^{n + 1}{C_2} + 2\left( {{}^2{C_2} + {}^3{C_2} + {}^4{C_2} + ... + {}^n{C_2}} \right)$$ is :
A
$${{n(2n + 1)(3n + 1)} \over 6}$$
B
$${{n(n + 1)(2n + 1)} \over 6}$$
C
$${{n{{(n + 1)}^2}(n + 2)} \over {12}}$$
D
$${{n(n - 1)(2n + 1)} \over 6}$$
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