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 cartesian equation of the line which is passing through the point (-1, -8, 5) and parallel to the vector (7 hat{i}-3 hat{j}-3 hat{k} ).

A. ( frac{x+1}{-1}= frac{y+8}{-8}= frac{z-5}{5} )
B. ( frac{x+1}{7}= frac{y+8}{-3}= frac{z-5}{-3} )
C. ( frac{x-7}{7}= frac{y+8}{-3}= frac{z-3}{-3} )
D. ( frac{x+1}{7}= frac{y+8}{-8}= frac{z+5}{3} )
Answer» C. ( frac{x-7}{7}= frac{y+8}{-3}= frac{z-3}{-3} )
Discussion
2.

Find the vector equation of the line which is passing through the point (1, -4, 4) and parallel to the vector (2 hat{i}-5 hat{j}+2 hat{k} ).

A. ((1+2 ) hat{i}-(4+5 ) hat{j}+(4+2 ) hat{j} )
B. ((1+2 ) hat{i}-(4+5 ) hat{j}+2 hat{j} )
C. ((1-2 ) hat{i}+(4+5 ) hat{j}+(4+2 ) hat{j} )
D. ((8+ ) hat{i}-(4-5 ) hat{j}+(7- ) hat{j} )
Answer» B. ((1+2 ) hat{i}-(4+5 ) hat{j}+2 hat{j} )
Discussion
3.

Find the vector equation of a line passing through two points (1,0,4) and (6,-3,1).

A. ((1+5 ) hat{i}- hat{j}+(4-3 ) hat{k} )
B. ((1+5 ) hat{i}-3 hat{j}+(7-3 ) hat{k} )
C. ((1+ ) hat{i}+ hat{j}+(8-3 ) hat{k} )
D. ((1+5 ) hat{i}-3 hat{j}+(4-3 ) hat{k} )
Answer» E.
Discussion
4.

Find the cartesian equation of a line passing through two points (8,-5,7) and (7,1,4).

A. ( frac{x-8}{1}= frac{y+5}{-6}= frac{z-7}{3} )
B. ( frac{2x-8}{-1}= frac{3y+5}{6}= frac{4z-7}{-3} )
C. ( frac{x-8}{-1}= frac{y+5}{6}= frac{z-7}{-3} )
D. ( frac{x-8}{-2}= frac{y+5}{5}= frac{z-7}{-7} )
Answer» D. ( frac{x-8}{-2}= frac{y+5}{5}= frac{z-7}{-7} )
Discussion
5.

Find the cartesian equation of the line which is passing through the point (5,-6,1) and parallel to the vector (5 hat{i}+2 hat{j}-3 hat{k} ).

A. ( frac{x-5}{5}= frac{y-4}{6}= frac{z+1}{-3} )
B. ( frac{x-5}{5}= frac{z+6}{2}= frac{y-1}{3} )
C. ( frac{x+5}{4}= frac{y-8}{2}= frac{z-1}{-3} )
D. ( frac{x-5}{5}= frac{y+6}{2}= frac{z-1}{-3} )
Answer» E.
Discussion
6.

Find the cartesian equation of a line passing through two points (1,-9,8) and (4,-1,6).

A. ( frac{x+1}{3}= frac{y-9}{8}= frac{-z-8}{2} )
B. ( frac{x-1}{3}= frac{y+9}{8}= frac{z-8}{-2} )
C. ( frac{x-1}{7}= frac{y+9}{-2}= frac{z-8}{5} )
D. ( frac{2x-1}{3}= frac{6y+9}{8}= frac{4z-8}{-2} )
Answer» C. ( frac{x-1}{7}= frac{y+9}{-2}= frac{z-8}{5} )
Discussion
7.

Find the vector equation of a line passing through two points (-5,3,1) and (4,-3,2).

A. ((-5+ ) hat{i}+(3+ ) hat{j}+(1- ) hat{k} )
B. ((-5+ ) hat{i}+(3+6 ) hat{j}+(1+ ) hat{k} )
C. ((5+7 ) hat{i}+(8+6 ) hat{j}+(3-5 ) hat{k} )
D. ((-5+9 ) hat{i}+(3-6 ) hat{j}+(1+ ) hat{k} )
Answer» E.
Discussion
8.

If a line is passing through two points (A(x_1,y_1,z_1) ) and (B(x_2,y_2,z_2) ) then which of the following is the vector equation of the line?

A. ( vec{r}= vec{a}+ ( vec{b}+ vec{a}) )
B. ( vec{r}= vec{a}+ ( vec{a}- vec{b}) )
C. ( vec{r}= vec{a}+( vec{b}- vec{a}) )
D. ( vec{r}= vec{a}+ ( vec{b}- vec{a}) )
Answer» E.
Discussion
9.

If the line is passing through the points ((x_1, y_1, z_1) ) and has direction cosines l, m, n of the line, then which of the following is the cartesian equation of the line?

A. ( frac{x-x_1}{l}= frac{y-y_1}{m}= frac{z-z_1}{n} )
B. ( frac{x-x_1}{n}= frac{y-y_1}{m}= frac{z-z_1}{l} )
C. ( frac{x+x_1}{n}= frac{y+y_1}{m}= frac{z-z_1}{l} )
D. ( frac{x+x_1}{l}= frac{y+y_1}{m}= frac{z+z_1}{n} )
Answer» B. ( frac{x-x_1}{n}= frac{y-y_1}{m}= frac{z-z_1}{l} )
Discussion
10.

Find the vector equation of the line which is passing through the point (2,-3,5) and parallel to the vector (3 hat{i}+4 hat{j}-2 hat{k} ).

A. ((2+3 ) hat{i}+(4 +3) hat{j}+(5- ) hat{k} )
B. ((9+3 ) hat{i}+( -3) hat{j}+(5-2 ) hat{k} )
C. ((2+3 ) hat{i}+(4 -3) hat{j}+(5-2 ) hat{k} )
D. ((7+ ) hat{i}+(4 +3) hat{j}+(5-2 ) hat{k} )
Answer» D. ((7+ ) hat{i}+(4 +3) hat{j}+(5-2 ) hat{k} )
Discussion