MCQOPTIONS
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MCQOPTIONS
This section includes 6 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. |
Find the Cartesian equation of the plane passing through the point (3,2,-3) and the normal to the plane is \(4\hat{i}-2\hat{j}+5\hat{k}\)? |
| A. | 4x-2y+5z+7=0 |
| B. | 3x-2y-3z+1=0 |
| C. | 4x-y+5z+7=0 |
| D. | 4x-2y-z+7=0 |
| Answer» B. 3x-2y-3z+1=0 | |
| 2. |
Find the Cartesian equation of the plane \(\vec{r}.[(λ+2μ) \hat{i}+(2λ-μ) \hat{j}+(3λ-2μ)\hat{k}]\)=12. |
| A. | (λ-μ)x+y+(3λ-2μ)z=12 |
| B. | (λ+3μ)x+(2+μ)y+(3λ-2μ)z=12 |
| C. | (λ+2μ)x-2λy+(3λ-2μ)z=12 |
| D. | (λ+2μ)x+(2λ-μ)y+(3λ-2μ)z=12 |
| Answer» E. | |
| 3. |
Find the vector equation of the plane passing through the point (2,1,-1) and normal to the plane is \(2\hat{i}+\hat{j}-3\hat{k}\)? |
| A. | \((\vec{r}-(2\hat{i}-7\hat{k})).(2\hat{i}+\hat{j}-3\hat{k})\)=0 |
| B. | \((\vec{r}-(2\hat{i}+3\hat{j}-\hat{k})).(2\hat{i}-3\hat{k})\)=0 |
| C. | \((\vec{r}-(\hat{i}+\hat{j}-3\hat{k})).(2\hat{i}+6\hat{j}-3\hat{k})\)=0 |
| D. | \((\vec{r}-(2\hat{i}+\hat{j}-\hat{k})).(2\hat{i}+\hat{j}-3\hat{k})\)=0 |
| Answer» E. | |
| 4. |
Find the Cartesian equation of the plane \(\vec{r}.(2\hat{i}+\hat{j}-\hat{k})\)=4. |
| A. | x+y-z=-4 |
| B. | 2x+y-z=4 |
| C. | x+y+z=4 |
| D. | -2x-y+z=4 |
| Answer» C. x+y+z=4 | |
| 5. |
Find the vector equation of the plane which is at a distance of \(\frac{7}{\sqrt{38}}\) from the origin and the normal vector from origin is \(2\hat{i}+3\hat{j}-5\hat{k}\)? |
| A. | \(\vec{r}.(\frac{2\hat{i}}{38}+\frac{3\hat{j}}{\sqrt{38}}-\frac{5\hat{k}}{\sqrt{38}})=\frac{7}{\sqrt{56}}\) |
| B. | \(\vec{r}.(\frac{2\hat{i}}{\sqrt{38}}+\frac{3\hat{j}}{\sqrt{38}}-\frac{5\hat{k}}{\sqrt{38}})=\frac{7}{\sqrt{38}}\) |
| C. | \(\vec{r}.(\frac{2\hat{i}}{\sqrt{38}}+\frac{5\hat{j}}{\sqrt{38}}+\frac{3\hat{k}}{\sqrt{38}})=\frac{7}{\sqrt{38}}\) |
| D. | \(\vec{r}.(\frac{2\hat{i}}{\sqrt{58}}-\frac{3\hat{j}}{\sqrt{37}}-\frac{5\hat{k}}{\sqrt{38}})=\frac{7}{\sqrt{38}}\) |
| Answer» C. \(\vec{r}.(\frac{2\hat{i}}{\sqrt{38}}+\frac{5\hat{j}}{\sqrt{38}}+\frac{3\hat{k}}{\sqrt{38}})=\frac{7}{\sqrt{38}}\) | |
| 6. |
If the plane passes through three collinear points \((x_1,y_1,z_1),(x_2,y_2,z_2),(x_3,y_3,z_3)\) then which of the following is true? |
| A. | \(x_1 y_1 z_1+x_2 y_2 z_2+x_3 y_3 z_3\)=0 |
| B. | \(\begin{vmatrix}x_1&y_1&z_1\\x_2&y_2&z_2\\x_3&y_3&z_3\end{vmatrix}\)=0 |
| C. | \(\begin{vmatrix}x_1\\y_2\\z_3\end{vmatrix}\)=0 |
| D. | \(x_1 x_2 x_3+y_1 y_2 y_3+z_1 z_2 z_3=0\) |
| Answer» C. \(\begin{vmatrix}x_1\\y_2\\z_3\end{vmatrix}\)=0 | |