MCQOPTIONS
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MCQOPTIONS
This section includes 9 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. \(\frac{1}{2},\frac{\sqrt{3}}{2},-\frac{1}{\sqrt{2}}\) | |
| 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. \(\frac{\sqrt{3}}{2}\) | |
| 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. | l2+m2+n2=1 |
| C. | k=±\(\frac{1}{\sqrt{(a^2+b^2+c^2)}}\) |
| D. | l2-m2=n2-1 |
| Answer» E. | |
| 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. \(\frac{5}{\sqrt{70}},\frac{4}{\sqrt{70}},-\frac{7}{\sqrt{70}}\) | |
| 5. |
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. \(x_2+x_1,y_2-y_1,z_2+z_1\) | |
| 6. |
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. –\(\frac{5}{\sqrt{20}}, \frac{7}{\sqrt{720}},\frac{14}{\sqrt{270}}\) | |
| 7. |
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. | |
| 8. |
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=\(0, \,m=\frac{1}{\sqrt{2}}, \,n=\frac{\sqrt{3}}{2}\) | |
| 9. |
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. | \(\frac{l}{a}=\frac{m}{b}=\frac{n}{c}=μ\) |
| B. | \(\frac{l}{a}=\frac{m}{b}=\frac{n}{c}=μ-1\) |
| C. | \(\frac{l}{a}=\frac{m}{c}=\frac{n}{b}=μ\) |
| D. | \(\frac{l}{a}=\frac{n+1}{b}=\frac{n}{c}=μ\) |
| Answer» B. \(\frac{l}{a}=\frac{m}{b}=\frac{n}{c}=μ-1\) | |