1
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
2
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let P be a variable point on the parabola $$y = 4{x^2} + 1$$. Then, the locus of the mid-point of the point P and the foot of the perpendicular drawn from the point P to the line y = x is :
A
$${(3x - y)^2} + (x - 3y) + 2 = 0$$
B
$$2{(3x - y)^2} + (x - 3y) + 2 = 0$$
C
$${(3x - y)^2} + 2(x - 3y) + 2 = 0$$
D
$$2{(x - 3y)^2} + (3x - y) + 2 = 0$$
3
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The value of k $$\in$$R, for which the following system of linear equations

3x $$-$$ y + 4z = 3,

x + 2y $$-$$ 3z = $$-$$2

6x + 5y + kz = $$-$$3,

has infinitely many solutions, is :
A
3
B
$$-$$5
C
5
D
$$-$$3
4
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
If sum of the first 21 terms of the series $${\log _{{9^{1/2}}}}x + {\log _{{9^{1/3}}}}x + {\log _{{9^{1/4}}}}x + .......$$, where x > 0 is 504, then x is equal to
A
243
B
9
C
7
D
81
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