1
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$f:R \to R$$ is given by $$f(x) = x + 1$$, then the value of $$\mathop {\lim }\limits_{n \to \infty } {1 \over n}\left[ {f(0) + f\left( {{5 \over n}} \right) + f\left( {{{10} \over n}} \right) + ...... + f\left( {{{5(n - 1)} \over n}} \right)} \right]$$ is :
A
$${3 \over 2}$$
B
$${5 \over 2}$$
C
$${1 \over 2}$$
D
$${7 \over 2}$$
2
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let A, B and C be three events such that the probability that exactly one of A and B occurs is (1 $$-$$ k), the probability that exactly one of B and C occurs is (1 $$-$$ 2k), the probability that exactly one of C and A occurs is (1 $$-$$ k) and the probability of all A, B and C occur simultaneously is k2, where 0 < k < 1. Then the probability that at least one of A, B and C occur is :
A
greater than $${1 \over 8}$$ but less than $${1 \over 4}$$
B
greater than $${1 \over 2}$$
C
greater than $${1 \over 4}$$ but less than $${1 \over 2}$$
D
exactly equal to $${1 \over 2}$$
3
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The sum of all the local minimum values of the twice differentiable function f : R $$\to$$ R defined by $$f(x) = {x^3} - 3{x^2} - {{3f''(2)} \over 2}x + f''(1)$$ is :
A
$$-$$22
B
5
C
$$-$$27
D
0
4
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let y = y(x) satisfies the equation $${{dy} \over {dx}} - |A| = 0$$, for all x > 0, where $$A = \left[ {\matrix{ y & {\sin x} & 1 \cr 0 & { - 1} & 1 \cr 2 & 0 & {{1 \over x}} \cr } } \right]$$. If $$y(\pi ) = \pi + 2$$, then the value of $$y\left( {{\pi \over 2}} \right)$$ is :
A
$${\pi \over 2} + {4 \over \pi }$$
B
$${\pi \over 2} - {1 \over \pi }$$
C
$${{3\pi } \over 2} - {1 \over \pi }$$
D
$${\pi \over 2} - {4 \over \pi }$$
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