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. |
Find the angle between the pair of lines \(\frac{x-3}{5}=\frac{y+7}{3}=\frac{z-2}{2} \,and \,\frac{x+1}{3}=\frac{y-5}{4}=\frac{z+2}{8}\). |
| A. | \(cos^{-1}\frac{43}{\sqrt{3482}}\) |
| B. | \(cos^{-1}\frac{43}{\sqrt{3382}}\) |
| C. | \(cos^{-1}\frac{85}{\sqrt{3382}}\) |
| D. | \(cos^{-1}\frac{34}{\sqrt{3382}}\) |
| Answer» C. \(cos^{-1}\frac{85}{\sqrt{3382}}\) | |
| 2. |
If two lines L1 and L2 are having direction cosines \(l_1,m_1,n_1 \,and \,l_2,m_2,n_2\) respectively, then what is the angle between the two lines? |
| A. | cotθ=\(\left |l_1 \,l_2+m_1 \,m_2+n_1 \,n_2\right |\) |
| B. | sinθ=\(\left |l_1 \,l_2+m_1 \,n_2+n_1 \,m_2\right |\) |
| C. | tanθ=\(\left |l_1 \,l_2+m_1 \,m_2+n_1 \,n_2\right |\) |
| D. | cosθ=\(\left |l_1 \,l_2+m_1 \,m_2+n_1 \,n_2\right |\) |
| Answer» E. | |
| 3. |
Find the angle between the lines \(\vec{r}=2\hat{i}+6\hat{j}-\hat{k}+λ(\hat{i}-2\hat{j}+3\hat{k})\) and \(\vec{r}=4\hat{i}-7\hat{j}+3\hat{k}+μ(5\hat{i}-3\hat{j}+3\hat{k})\). |
| A. | θ=\(cos^{-1}\frac{20}{\sqrt{602}}\) |
| B. | θ=\(cos^{-1}\frac{20}{\sqrt{682}}\) |
| C. | θ=\(cos^{-1}\frac{8}{\sqrt{602}}\) |
| D. | θ=\(cos^{-1}\frac{14}{\sqrt{598}}\) |
| Answer» B. θ=\(cos^{-1}\frac{20}{\sqrt{682}}\) | |
| 4. |
If the equations of two lines L1 and L2 are \(\vec{r}=\vec{a_1}+λ\vec{b_1}\) and \(\vec{r}=\vec{a_2}+μ\vec{b_2}\), then which of the following is the correct formula for the angle between the two lines? |
| A. | cosθ=\(\left |\frac{\vec{a_1}.\vec{a_2}}{|\vec{b_1}||\vec{a_2}|}\right |\) |
| B. | cosθ=\(\left |\frac{\vec{a_1}.\vec{a_2}}{|\vec{a_1}||\vec{a_2}|}\right |\) |
| C. | cosθ=\(\left |\frac{\vec{b_1}.\vec{b_2}}{|\vec{b_1}||\vec{b_2}|}\right |\) |
| D. | cosθ=\(\left |\frac{\vec{a_1}.\vec{b_2}}{|\vec{a_1}||\vec{b_2}|}\right |\) |
| Answer» D. cosθ=\(\left |\frac{\vec{a_1}.\vec{b_2}}{|\vec{a_1}||\vec{b_2}|}\right |\) | |
| 5. |
If two lines L1 and L2 with direction ratios \(a_1,b_1,c_1 \,and \,a_2,b_2,c_2\) respectively are perpendicular to each other then\(a_1 a_2+b_1 b_2+c_1 c_2=0\) |
| A. | True |
| B. | False |
| Answer» B. False | |
| 6. |
Find the angle between the two lines if the equations of the lines are\(\vec{r}=\hat{i}+\hat{j}+\hat{k}+λ(3\hat{i}-\hat{j}+\hat{k}) \,and \,\vec{r}=4\hat{i}+\hat{j}-2\hat{k}+μ(2\hat{i}+3\hat{j}+\hat{k})\) |
| A. | \(cos^{-1}\frac{4}{\sqrt{14}}\) |
| B. | \(cos^{-1}\frac{7}{\sqrt{154}}\) |
| C. | \(cos^{-1}\frac{4}{154}\) |
| D. | \(cos^{-1}\frac{4}{\sqrt{154}}\) |
| Answer» E. | |
| 7. |
Find the value of p such that the lines\(\frac{x-1}{3}=\frac{y+4}{p}=\frac{z-9}{1}\) \(\frac{x+2}{1}=\frac{y-3}{1}=\frac{z-7}{-2}\) are at right angles to each other. |
| A. | p=2 |
| B. | p=1 |
| C. | p=-1 |
| D. | p=-2 |
| Answer» D. p=-2 | |
| 8. |
Find the angle between the lines.\(\frac{x+2}{1}=\frac{y+5}{6}=\frac{z-3}{2}\) \(\frac{x-4}{5}=\frac{y-3}{-2}=\frac{z+3}{1}\) |
| A. | \(cos^{-1}\frac{5}{\sqrt{1230}}\) |
| B. | \(cos^{-1}\frac{3}{\sqrt{3120}}\) |
| C. | \(cos^{-1}\frac{7}{\sqrt{2310}}\) |
| D. | \(cos^{-1}\frac{48}{\sqrt{1230}}\) |
| Answer» B. \(cos^{-1}\frac{3}{\sqrt{3120}}\) | |
| 9. |
If L1 and L2 have the direction ratios \(a_1,b_1,c_1 \,and \,a_2,b_2,c_2\) respectively then what is the angle between the lines? |
| A. | \(θ=tan^{-1}\left|\frac{a_1 a_2+b_1 b_2+c_1 c_2}{\sqrt{a_1^2+b_1^2+c_1^2} \sqrt{a_2^2+b_2^2+c_2^2}}\right |\) |
| B. | \(θ=2tan^{-1}\left|\frac{a_1 a_2+b_1 b_2+c_1 c_2}{\sqrt{a_1^2+b_1^2+c_1^2} \sqrt{a_2^2+b_2^2+c_2^2}}\right |\) |
| C. | \(θ=cos^{-1}\left|\frac{a_1 a_2+b_1 b_2+c_1 c_2}{\sqrt{a_1^2+b_1^2+c_1^2} \sqrt{a_2^2+b_2^2+c_2^2}}\right |\) |
| D. | \(θ=2 \,cos^{-1}\left|\frac{a_1 a_2+b_1 b_2+c_1 c_2}{\sqrt{a_1^2+b_1^2+c_1^2} \sqrt{a_2^2+b_2^2+c_2^2}}\right |\) |
| Answer» D. \(θ=2 \,cos^{-1}\left|\frac{a_1 a_2+b_1 b_2+c_1 c_2}{\sqrt{a_1^2+b_1^2+c_1^2} \sqrt{a_2^2+b_2^2+c_2^2}}\right |\) | |