1
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
$${\pi \over 2} - {4 \over \pi }$$
2
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Consider the line L given by the equation

$${{x - 3} \over 2} = {{y - 1} \over 1} = {{z - 2} \over 1}$$.

Let Q be the mirror image of the point (2, 3, $$-$$1) with respect to L. Let a plane P be such that it passes through Q, and the line L is perpendicular to P. Then which of the following points is on the plane P?
A
($$-$$1, 1, 2)
B
(1, 1, 1)
C
(1, 1, 2)
D
(1, 2, 2)
3
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If the mean and variance of six observations 7, 10, 11, 15, a, b are 10 and $${{20} \over 3}$$, respectively, then the value of | a $$-$$ b | is equal to :
A
9
B
11
C
7
D
1
4
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$g(t) = \int_{ - \pi /2}^{\pi /2} {\cos \left( {{\pi \over 4}t + f(x)} \right)} dx$$, where $$f(x) = {\log _e}\left( {x + \sqrt {{x^2} + 1} } \right),x \in R$$. Then which one of the following is correct?
A
g(1) = g(0)
B
$$\sqrt 2 g(1) = g(0)$$
C
$$g(1) = \sqrt 2 g(0)$$
D
g(1) + g(0) = 0
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