Explore topic-wise MCQs in Mathematics Questions and Answers.

This section includes 4 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics Questions and Answers 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.

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
4.

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