1
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If the distance between the plane $$\alpha x - 2y + z = k$$ and the plane containing the lines $${{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over 4}$$ and $${{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}$$ is $$\sqrt 6 $$, then $$|k|$$ is

A
36
B
12
C
6
D
$$2\sqrt 3 $$
2
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The angle between a normal to the plane $$2x - y + 2z - 1 = 0$$ and the X-axis is

A
$${\cos ^{ - 1}}{2 \over 3}$$
B
$${\cos ^{ - 1}}{1 \over 5}$$
C
$${\cos ^{ - 1}}{3 \over 4}$$
D
$${\cos ^{ - 1}}{1 \over 3}$$
3
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $$f(x) = [{x^2}]\sin \pi x,x > 0$$. Then

A
f is discontinuous everywhere.
B
f is continuous everywhere.
C
f is continuous at only those points which are perfect squares.
D
f is continuous at only those points which are not perfect squares.
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$y = {\log ^n}x$$, where $${\log ^n}$$ means $${\log _e}{\log _e}{\log _e}\,...$$ (repeated n times), then $$x\log x{\log ^2}x{\log ^3}x\,.....\,{\log ^{n - 1}}x{\log ^n}x{{dy} \over {dx}}$$ is equal to

A
$$\log x$$
B
$$x$$
C
1
D
$${\log ^n}x$$
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