1
JEE Main 2023 (Online) 8th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let the vectors $$\vec{u}_{1}=\hat{i}+\hat{j}+a \hat{k}, \vec{u}_{2}=\hat{i}+b \hat{j}+\hat{k}$$ and $$\vec{u}_{3}=c \hat{i}+\hat{j}+\hat{k}$$ be coplanar. If the vectors $$\vec{v}_{1}=(a+b) \hat{i}+c \hat{j}+c \hat{k}, \vec{v}_{2}=a \hat{i}+(b+c) \hat{j}+a \hat{k}$$ and $$\vec{v}_{3}=b \hat{i}+b \hat{j}+(c+a) \hat{k}$$ are also coplanar, then $$6(\mathrm{a}+\mathrm{b}+\mathrm{c})$$ is equal to :

A
12
B
6
C
0
D
4
2
JEE Main 2023 (Online) 8th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the probability that the random variable $$\mathrm{X}$$ takes values $$x$$ is given by $$\mathrm{P}(\mathrm{X}=x)=\mathrm{k}(x+1) 3^{-x}, x=0,1,2,3, \ldots$$, where $$\mathrm{k}$$ is a constant, then $$\mathrm{P}(\mathrm{X} \geq 2)$$ is equal to :

A
$$\frac{7}{18}$$
B
$$\frac{20}{27}$$
C
$$\frac{7}{27}$$
D
$$\frac{11}{18}$$
3
JEE Main 2023 (Online) 8th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\mathrm{A}=\{1,2,3,4,5,6,7\}$$. Then the relation $$\mathrm{R}=\{(x, y) \in \mathrm{A} \times \mathrm{A}: x+y=7\}$$ is :

A
reflexive but neither symmetric nor transitive
B
transitive but neither symmetric nor reflexive
C
symmetric but neither reflexive nor transitive
D
an equivalence relation
4
JEE Main 2023 (Online) 8th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the mean and variance of 12 observations be $$\frac{9}{2}$$ and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is $$\frac{m}{n}$$, where $$\mathrm{m}$$ and $$\mathrm{n}$$ are coprime, then $$\mathrm{m}+\mathrm{n}$$ is equal to :

A
317
B
316
C
314
D
315
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