1
WB JEE 2022
MCQ (More than One Correct Answer)
+2
-0
Change Language

Let $$f(x) = {x^2} + x\sin x - \cos x$$. Then

A
f(x) = 0 has at least one real root
B
f(x) = 0 has no real root
C
f(x) = 0 has at least one positive root
D
f(x) = 0 has at least one negative root
2
WB JEE 2022
MCQ (More than One Correct Answer)
+2
-0
Change Language

Let z1 and z2 be two non-zero complex numbers. Then

A
Principal value of arg(z1z2) may not be equal to Principal value of argz1 + Principal value of arg z2
B
Principal value of arg(z1z2) = Principal value of argz1 + Principal value of arg z2
C
Principal value of arg(z1/z2) = Principal value of argz1 $$-$$ Principal value of arg z2
D
Principal value of arg(z1/z2) may not be argz1 $$-$$ arg z2
3
WB JEE 2022
MCQ (More than One Correct Answer)
+2
-0
Change Language

Let $$\Delta = \left| {\matrix{ {\sin \theta \cos \phi } & {\sin \theta \sin \phi } & {\cos \theta } \cr {\cos \theta \cos \phi } & {\cos \theta \sin \phi } & { - \sin \theta } \cr { - \sin \theta \sin \phi } & {\sin \theta \cos \phi } & 0 \cr } } \right|$$. Then

A
$$\Delta$$ is independent of $$\theta$$
B
$$\Delta$$ is independent of $$\varphi $$
C
$$\Delta$$ is a constant
D
$${\left( {{{d\Delta } \over {d\theta }}} \right)_{\theta = {\pi \over 2}}} = 0$$
4
WB JEE 2022
MCQ (More than One Correct Answer)
+2
-0
Change Language

Let R and S be two equivalence relations on a non-void set A. Then

A
R $$\cup$$ S is equivalence relation
B
R $$\cap$$ S is equivalence relation
C
R $$\cap$$ S is not equivalence relation
D
R $$\cup$$ S is not equivalence relation
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