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.

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
Discussion
2.

Find the equation of the plane passing through the three points (2,2,0), (1,2,1), (-1,2,-2).

A. (( vec{r}-(2 hat{i}+2 hat{j})).[(- hat{i}+ hat{k}) (-3 hat{i}-2 hat{k})] )=0
B. (( vec{r}-(3 hat{i}-2 hat{k})).[(- hat{i}+ hat{k}) (2 hat{i}-2 hat{j})] )=0
C. (( vec{r}+(2 hat{i}+2 hat{j})).[(- hat{i}- hat{k}) (-3 hat{i}-2 hat{k})] )=0
D. (( vec{r}-(2 hat{i}+2 hat{j})).[(- hat{i}- hat{k}) (3 hat{i}+2 hat{k})] )=0
Answer» B. (( vec{r}-(3 hat{i}-2 hat{k})).[(- hat{i}+ hat{k}) (2 hat{i}-2 hat{j})] )=0
Discussion
3.

Find the Cartesian equation of the plane ( vec{r}.[( +2 ) hat{i}+(2 - ) hat{j}+(3 -2 ) hat{k}] )=12.

A. ( - )x+y+(3 -2 )z=12
B. ( +3 )x+(2+ )y+(3 -2 )z=12
C. ( +2 )x-2 y+(3 -2 )z=12
D. ( +2 )x+(2 - )y+(3 -2 )z=12
Answer» E.
Discussion
4.

Find the distance of the plane 3x+4y-5z-7=0.

A. ( frac{7}{ sqrt{40}} )
B. ( frac{6}{ sqrt{34}} )
C. ( frac{8}{ sqrt{50}} )
D. ( frac{7}{ sqrt{50}} )
Answer» E.
Discussion
5.

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.
Discussion
6.

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
Discussion
7.

Find the equation of the plane passing through three points (1,2,-1), (0,-1,2) and (3,1,1).

A. (( vec{r}-( hat{i}+2 hat{j}- hat{k})).[(- hat{j}+2 hat{k}) (2 hat{i}- hat{j}+2 hat{k})] )=0
B. (( vec{r}-( hat{i}+2 hat{j}- hat{k})).[( hat{i}-3 hat{j}+3 hat{k}) (2 hat{i}- hat{j}+2 hat{k})] )=0
C. (( vec{r}-( hat{i}+2 hat{j}- hat{k})).[(3 hat{i}+ hat{j}+ hat{k}) (2 hat{i}- hat{j}+2 hat{k})] )=0
D. (( vec{r}-( hat{i}+2 hat{j})).[(- hat{i}-3 hat{j}+3 hat{k}) (2 hat{i}- hat{j}+2 hat{k})] )=0
Answer» C. (( vec{r}-( hat{i}+2 hat{j}- hat{k})).[(3 hat{i}+ hat{j}+ hat{k}) (2 hat{i}- hat{j}+2 hat{k})] )=0
Discussion
8.

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}} )
Discussion
9.

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
Discussion
10.

Which of the following is not the correct formula for representing a plane?

A. ( vec{r}. hat{n}=d )
B. ax+by+cz=d
C. lx+my+nz=d
D. al+mb+cn=d<sup>2</sup>
Answer» E.
Discussion