1
JEE Main 2023 (Online) 11th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

For $$a \in \mathbb{C}$$, let $$\mathrm{A}=\{z \in \mathbb{C}: \operatorname{Re}(a+\bar{z}) > \operatorname{Im}(\bar{a}+z)\}$$ and $$\mathrm{B}=\{z \in \mathbb{C}: \operatorname{Re}(a+\bar{z})<\operatorname{Im}(\bar{a}+z)\}$$. Then among the two statements :

(S1): If $$\operatorname{Re}(a), \operatorname{Im}(a) > 0$$, then the set A contains all the real numbers

(S2) : If $$\operatorname{Re}(a), \operatorname{Im}(a) < 0$$, then the set B contains all the real numbers,

A
both are false
B
only (S1) is true
C
only (S2) is true
D
both are true
2
JEE Main 2023 (Online) 11th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the letters of the word MATHS are permuted and all possible words so formed are arranged as in a dictionary with serial numbers, then the serial number of the word THAMS is :

A
103
B
104
C
102
D
101
3
JEE Main 2023 (Online) 11th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

The converse of $$((\sim p) \wedge q) \Rightarrow r$$ is

A
$$((\sim p) \vee q) \Rightarrow r$$
B
$$(\sim \mathrm{r}) \Rightarrow \mathrm{p} \wedge \mathrm{q}$$
C
$$(\mathrm{p} \vee(\sim \mathrm{q})) \Rightarrow(\sim \mathrm{r})$$
D
$$(\sim \mathrm{r}) \Rightarrow((\sim \mathrm{p}) \wedge \mathrm{q})$$
4
JEE Main 2023 (Online) 11th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

If four distinct points with position vectors $$\vec{a}, \vec{b}, \vec{c}$$ and $$\vec{d}$$ are coplanar, then $$[\vec{a} \,\,\vec{b} \,\,\vec{c}]$$ is equal to :

A
$$[\vec{d} \,\,\,\,\,\vec{b} \,\,\,\,\,\vec{a}]+[\vec{a} \,\,\,\,\,\vec{c} \,\,\,\,\,\vec{d}]+[\vec{d} \,\,\,\,\,\vec{b} \,\,\,\,\,\vec{c}]$$
B
$$[\vec{b} \,\,\,\,\,\vec{c} \,\,\,\,\,\vec{d}]+[\vec{d} \,\,\,\,\,\vec{a} \,\,\,\,\,\vec{c}]+[\vec{d} \,\,\,\,\,\vec{b} \,\,\,\,\,\vec{a}]$$
C
$$[\vec{a} \,\,\,\,\,\vec{d} \,\,\,\,\,\vec{b}]+[\vec{d} \,\,\,\,\,\vec{c} \,\,\,\,\,\vec{a}]+[\vec{d} \,\,\,\,\,\vec{b} \,\,\,\,\,\vec{c}]$$
D
$$[\vec{d} \,\,\,\,\,\vec{c} \,\,\,\,\,\vec{a}]+[\vec{b} \,\,\,\,\,\vec{d} \,\,\,\,\,\vec{a}]+[\vec{c} \,\,\,\,\,\vec{d} \,\,\,\,\,\vec{b}]$$
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