Explore topic-wise MCQs in Mathematics.

This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.

Find the shortest distance between the lines whose equations are given below.
( vec{r}=(1- ) hat{i}+(1+2 ) hat{j}+ hat{k} )

A. n ( vec{r}=( hat{i}-3 hat{j}- hat{k})+ (2 hat{i}+ hat{j}+2 hat{k}) )
B. ( frac{11}{50} )
C. ( frac{21}{ sqrt{50}} )
D. ( frac{11}{ sqrt{50}} )
E. ( frac{51}{ sqrt{30}} )
Answer» D. ( frac{11}{ sqrt{50}} )
Discussion
2.

Find the shortest distance between the lines given below.
( vec{r}=(1-p) hat{i}+(p-3) hat{j}+(1+p) hat{k} )

A. n ( vec{r}=(q-1) hat{i}-(2q+3) hat{j}+(1+q) hat{k} )
B. ( frac{32}{ sqrt{14}} )
C. ( frac{6}{ sqrt{24}} )
D. ( frac{12}{ sqrt{14}} )
E. ( frac{6}{ sqrt{14}} )
Answer» E. ( frac{6}{ sqrt{14}} )
Discussion
3.

Find the shortest distance between the set of parallel lines.
( vec{r}=( hat{i}+2 hat{j}- hat{k})+ ( hat{i}+ hat{j}+ hat{k}) )

A. n ( vec{r}=(3 hat{i}- hat{j}+3 hat{k})+ ( hat{i}+ hat{j}+ hat{k}) )
B. ( sqrt{34} )
C. ( sqrt{26} )
D. 5
E. ( sqrt{27} )
Answer» C. ( sqrt{26} )
Discussion
4.

Find the distance between the lines l1 and l2 with the following vector equations.
( vec{r}=2 hat{i}+2 hat{j}-2 hat{k}+ (3 hat{i}+2 hat{j}+5 hat{k}) )

A. n ( vec{r}=4 hat{i}- hat{j}+5 hat{k}+ (3 hat{i}-2 hat{j}+4 hat{k}) )
B. ( frac{57}{ sqrt{47}} )
C. ( frac{57}{ sqrt{77}} )
D. ( frac{7}{ sqrt{477}} )
E. ( frac{57}{ sqrt{477}} )
Answer» E. ( frac{57}{ sqrt{477}} )
Discussion
5.

Find the shortest distance between the following set of parallel lines.
( vec{r}=6 hat{i}+2 hat{j}- hat{k}+ ( hat{i}+2 hat{j}-4 hat{k}) )

A. n ( vec{r}= hat{i}+ hat{j}+ hat{k}+ ( hat{i}+2 hat{j}-4 hat{k}) )
B. d= ( sqrt{ frac{324}{45}} )
C. d= ( sqrt{ frac{405}{21}} )
D. d= ( sqrt{ frac{24}{21}} )
E. d= ( sqrt{ frac{21}{567}} )
Answer» C. d= ( sqrt{ frac{405}{21}} )
Discussion
6.

Which of the following is the correct formula for the distance between the parallel lines l1 and l2?

A. d= ( left| frac{ vec{a_2}+ vec{a_1}) ( vec{a_2}- vec{a_1})}{| vec{b}|} right | )
B. d<sup>2</sup>= ( left| frac{ vec{b} ( vec{a_2}- vec{a_1})}{| vec{b}|} right | )
C. 2d= ( left| frac{ vec{b} ( vec{a_2}- vec{a_1})}{| vec{b}|} right | )
D. d= ( left| frac{ vec{b} ( vec{a_2}- vec{a_1})}{| vec{b}|} right | )
Answer» E.
Discussion
7.

Find the shortest distance between the lines given.
l1: ( frac{x-5}{2}= frac{y-2}{5}= frac{z-1}{4} )

A. nl<sub>2</sub>: ( frac{x+4}{3}= frac{y-7}{6}= frac{z-3}{7} )
B. ( frac{115}{ sqrt{134}} )
C. ( frac{115}{ sqrt{184}} )
D. ( frac{115}{134} )
E. ( frac{ sqrt{115}}{134} )
Answer» B. ( frac{115}{ sqrt{134}} )
Discussion
8.

Find the equation between the two parallel lines l1 and l2 whose equations is given below.
( vec{r}=3 hat{i}+2 hat{j}- hat{k}+ (3 hat{i}-2 hat{j}+ hat{k}) )

A. n ( vec{r}=2 hat{i}- hat{j}+ hat{k}+ (3 hat{i}-2 hat{j}+ hat{k}) )
B. ( sqrt{ frac{172}{14}} )
C. ( sqrt{ frac{145}{14}} )
D. ( sqrt{ frac{171}{14}} )
E. ( sqrt{ frac{171}{134}} )
Answer» D. ( sqrt{ frac{171}{14}} )
Discussion
9.

Find the shortest distance between two lines l1 and l2 whose vector equations is given below.
( vec{r}=3 hat{i}-4 hat{j}+2 hat{k}+ (4 hat{i}+ hat{j}+ hat{k}) )

A. n ( vec{r}=5 hat{i}+ hat{j}- hat{k}+ (2 hat{i}- hat{j}-3 hat{k}) )
B. ( frac{11}{ sqrt{12}} )
C. ( frac{23}{ sqrt{10}} )
D. ( frac{18}{ sqrt{10}} )
E. ( frac{10}{ sqrt{11}} )
Answer» D. ( frac{18}{ sqrt{10}} )
Discussion
10.

Which of the below given is the correct formula for the distance between two skew lines l1 and l2?

A. d= ( left | frac{( vec{b_1} vec{b_2}).(a_2-a_1)}{| vec{b_1} vec{b_2}|} right | )
B. 2d= ( left | frac{( vec{b_1}- vec{b_2}).(a_2-a_1)}{| vec{b_1}- vec{b_2}|} right | )
C. d= ( left | frac{( vec{b_1} vec{b_2}).(a_2.a_1)}{3| vec{b_1} vec{b_2}|} right | )
D. d<sup>2</sup>= ( left | frac{( vec{b_1} vec{b_2}).(a_2-a_1)}{| vec{b_1}- vec{b_2}|} right | )
Answer» B. 2d= ( left | frac{( vec{b_1}- vec{b_2}).(a_2-a_1)}{| vec{b_1}- vec{b_2}|} right | )
Discussion