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.

If a line makes an angle of 60 , 150 , 45 with the positive x, y, z-axis respectively, find its direction cosines.

A. ( frac{1}{2},- frac{ sqrt{3}}{2}, frac{1}{ sqrt{2}} )
B. ( frac{1}{2},- frac{ sqrt{3}}{2},- frac{1}{ sqrt{2}} )
C. ( frac{1}{2},- frac{ sqrt{3}}{2}, frac{1}{ sqrt{2}} )
D. ( frac{1}{2}, frac{ sqrt{3}}{2},- frac{1}{ sqrt{2}} )
Answer» D. ( frac{1}{2}, frac{ sqrt{3}}{2},- frac{1}{ sqrt{2}} )
Discussion
2.

If the direction cosines of the line are ( frac{1}{2},- frac{ sqrt{3}}{2} ),x respectively, then find the value of x.

A. 1
B. 0
C. ( frac{ sqrt{3}}{2} )
D. ( frac{1}{2} )
Answer» C. ( frac{ sqrt{3}}{2} )
Discussion
3.

If a, b, c are the direction ratios of the line and l, m, n are the direction cosines of the line, then which of the following is incorrect?

A. ( frac{l}{a}= frac{m}{b}= frac{n}{c}=k )
B. l<sup>2</sup>+m<sup>2</sup>+n<sup>2</sup>=1
C. k=&amp;pm; ( frac{1}{ sqrt{(a^2+b^2+c^2)}} )
D. l<sup>2</sup>-m<sup>2</sup>=n<sup>2</sup>-1
Answer» E.
Discussion
4.

If the direction ratios of a line are 5, 4, -7 respectively, then find the direction cosines.

A. ( frac{75}{ sqrt{90}}, frac{4}{ sqrt{90}}, frac{5}{ sqrt{90}} )
B. ( frac{5}{ sqrt{90}}, frac{4}{ sqrt{90}},- frac{7}{ sqrt{90}} )
C. ( frac{5}{ sqrt{70}}, frac{4}{ sqrt{70}},- frac{7}{ sqrt{70}} )
D. ( frac{3}{ sqrt{90}}, frac{4}{ sqrt{90}},- frac{5}{ sqrt{90}} )
Answer» C. ( frac{5}{ sqrt{70}}, frac{4}{ sqrt{70}},- frac{7}{ sqrt{70}} )
Discussion
5.

Find the direction cosines of the line passing through two points P(-6,7,3) and Q(3,-2,5).

A. ( frac{2}{ sqrt{166}}, frac{-9}{ sqrt{166}}, frac{2}{ sqrt{166}} )
B. ( frac{9}{ sqrt{166}}, frac{-7}{ sqrt{166}}, frac{2}{ sqrt{166}} )
C. ( frac{9}{ sqrt{66}}, frac{-9}{ sqrt{66}}, frac{2}{ sqrt{66}} )
D. ( frac{9}{ sqrt{166}}, frac{-9}{ sqrt{166}}, frac{2}{ sqrt{166}} )
Answer» E.
Discussion
6.

The direction ratios of the line segment joining (P(x_1,y_1,z_1) ) and (Q(x_2,y_2,z_2) ) is given by _______, ____________ and __________

A. (x_2+x_1,y_2+y_1,z_2+z_1 )
B. (x_2-x_1,y_2+y_1,z_2-z_1 )
C. (x_2-x_1,y_2-y_1,z_2-z_1 )
D. (x_2+x_1,y_2-y_1,z_2+z_1 )
Answer» D. (x_2+x_1,y_2-y_1,z_2+z_1 )
Discussion
7.

Find the direction cosines of the line passing through two points (4, -5, -6) and (-1, 2, 8).

A. ( frac{5}{270}, frac{7}{ sqrt{270}}, frac{14}{ sqrt{270}} )
B. ( frac{7}{ sqrt{270}}, frac{7}{ sqrt{270}}, frac{7}{ sqrt{270}} )
C. ( frac{5}{ sqrt{270}}, frac{7}{ sqrt{270}}, frac{14}{ sqrt{270}} )
D. ( frac{5}{ sqrt{20}}, frac{7}{ sqrt{720}}, frac{14}{ sqrt{270}} )
Answer» D. ( frac{5}{ sqrt{20}}, frac{7}{ sqrt{720}}, frac{14}{ sqrt{270}} )
Discussion
8.

If a line has direction ratios 2, -3, 7 then find the direction cosines.

A. l= ( frac{2}{ sqrt{62}},m=- frac{7}{ sqrt{62}},n= frac{7}{ sqrt{62}} )
B. l= ( frac{2}{ sqrt{6}},m=- frac{3}{ sqrt{6}},n= frac{7}{ sqrt{6}} )
C. l=- ( frac{2}{ sqrt{62}},m=- frac{3}{ sqrt{62}},n=- frac{7}{ sqrt{62}} )
D. l= ( frac{2}{ sqrt{62}},m=- frac{3}{ sqrt{62}},n= frac{7}{ sqrt{62}} )
Answer» E.
Discussion
9.

If a line makes an angle of 120 , 45 , 30 with the positive x, y, z-axis respectively then find the direction cosines.

A. l= ( frac{1}{2}, ,m= frac{1}{ sqrt{2}}, ,n= frac{ sqrt{3}}{2} )
B. l=- ( frac{1}{2}, ,m=- frac{1}{ sqrt{2}}, ,n=- frac{ sqrt{3}}{2} )
C. l=- ( frac{1}{2}, ,m= frac{1}{ sqrt{2}}, ,n= frac{ sqrt{3}}{2} )
D. l= (0, ,m= frac{1}{ sqrt{2}}, ,n= frac{ sqrt{3}}{2} )
Answer» D. l= (0, ,m= frac{1}{ sqrt{2}}, ,n= frac{ sqrt{3}}{2} )
Discussion
10.

If a, b, c are the direction ratios of the line and l, m, n are the direction cosines of the line, then which of the following is true?

A. ( frac{l}{a}= frac{m}{b}= frac{n}{c}= )
B. ( frac{l}{a}= frac{m}{b}= frac{n}{c}= -1 )
C. ( frac{l}{a}= frac{m}{c}= frac{n}{b}= )
D. ( frac{l}{a}= frac{n+1}{b}= frac{n}{c}= )
Answer» B. ( frac{l}{a}= frac{m}{b}= frac{n}{c}= -1 )
Discussion