1
VITEEE 2021
MCQ (Single Correct Answer)
+1
-0

Five persons entered the lift cabin on the ground floor of an eight floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floors is

A
$$\frac{{ }^7 P_5}{7^5}$$
B
$$\frac{7^5}{{ }^7 P_5}$$
C
$$\frac{6}{{ }^6 P_5}$$
D
$$\frac{{ }^5 P_5}{5^5}$$
2
VITEEE 2021
MCQ (Single Correct Answer)
+1
-0

If $$(3,4,-1)$$ and $$(-1,2,3)$$ be end points of the diameter of a sphere, then the radius of the sphere is

A
2
B
3
C
6
D
7
3
VITEEE 2021
MCQ (Single Correct Answer)
+1
-0

The following lines are

$$\begin{aligned} \mathbf{r} & =(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\lambda^{\prime}(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}), \\ \text { and } \quad \mathbf{r} & =(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\mu(-\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}) \end{aligned}$$

A
collinear
B
skew-lines
C
coplanar lines
D
parallel lines
4
VITEEE 2021
MCQ (Single Correct Answer)
+1
-0

The position vector of a point $$R$$ which divides the line joining $$P(6,3,-2)$$ and $$Q(3,1,-4)$$ in the ratio $$2 : 1$$ externally is

A
$$\hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$$
B
$$3 \hat{\mathbf{i}}=\hat{\mathbf{k}}$$
C
$$-\hat{\mathbf{j}}-6 \hat{\mathbf{k}}$$
D
$$2 \hat{\mathbf{i}}-\hat{\mathbf{j}}$$
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