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.

Which of the following sets of planes are parallel to each other?

A. 2x+3y+4z=8 and 3x+9y+12z=7
B. 2x+3y+4z=2 and 4x+6y+8z=9
C. 3x+2y+4z=0 and 3x+4y+2z=0
D. 2x+4y+8z=9 and 4x+2y+7z=0
Answer» C. 3x+2y+4z=0 and 3x+4y+2z=0
Discussion
2.

Find the angle between the planes ( vec{r}.(4 hat{i}+ hat{j}-2 hat{k}) )=6 and ( vec{r}.(5 hat{i}-6 hat{j}+ hat{k}) )=7?

A. (cos^{-1} u2061 frac{12}{ sqrt{1302}} )
B. (cos^{-1} u2061 frac{1}{ sqrt{1392}} )
C. (cos^{-1} frac{ u206123}{ sqrt{102}} )
D. (cos^{-1} u2061 frac{15}{ sqrt{134}} )
Answer» B. (cos^{-1} u2061 frac{1}{ sqrt{1392}} )
Discussion
3.

Which of the given set of planes are perpendicular to each other?

A. ( vec{r}.(2 hat{i}+2 hat{j}+ hat{k}) )=5 and ( vec{r}.( hat{i}+2 hat{j}+2 hat{k}) )=5
B. ( vec{r}.( hat{i}-2 hat{j}+ hat{k}) )=7 and ( vec{r}.( hat{i}+ hat{j}+2 hat{k}) )=2
C. ( vec{r}.(2 hat{i}-2 hat{j}+ hat{k}) )=4 and ( vec{r}.( hat{i}+2 hat{j}+2 hat{k}) )=5
D. ( vec{r}.(3 hat{i}-2 hat{j}+ hat{k}) )=2 and ( vec{r}.( hat{i}+2 hat{j}+8 hat{k}) )=8
Answer» D. ( vec{r}.(3 hat{i}-2 hat{j}+ hat{k}) )=2 and ( vec{r}.( hat{i}+2 hat{j}+8 hat{k}) )=8
Discussion
4.

Find the angle between the two planes 2x+2y+z=2 and x-y+z=1?

A. (cos^{-1} frac{ u20611}{3} )
B. (cos^{-1} u2061 sqrt{3} )
C. (cos^{-1} u2061 frac{1}{3} )
D. (cos^{-1} u2061 frac{1}{3 sqrt{3}} )
Answer» E.
Discussion
5.

If two vectors ( vec{r}. vec{n_1}=d_1 ) and ( vec{r}. vec{n_2}=d_2 ) are such that ( vec{n_1}. vec{n_2} )=0, then which of the following is true?

A. The planes are perpendicular to each other
B. The planes are parallel to each other
C. Depends on the value of the vector
D. The planes are at an angle greater than 90
Answer» B. The planes are parallel to each other
Discussion
6.

Find the angle between the planes 6x-3y+7z=8 and 2x+3y-2z=5?

A. (cos^{-1} frac{ u206111}{ sqrt{98}} )
B. (cos^{-1} u2061 frac{ u206111}{ sqrt{1598}} )
C. (cos^{-1} frac{ u2061 u206113}{ sqrt{198}} )
D. (cos^{-1} frac{ u2061 u206111}{1598} )
Answer» C. (cos^{-1} frac{ u2061 u206113}{ sqrt{198}} )
Discussion
7.

If the planes (A_1 x+B_1 y+C_1 z+D_1 )=0 and (A_2 x+B_2 y+C_2 z+D_2 )=0 are at right angles to each other, then which of the following is true?

A. ( frac{A_1+B_1+C_1}{A_2+B_2+C_2} )=0
B. (A_1+A_2+B_1 +B_2+C_1+C_2 )=0
C. (A_1+B_1+C_1=A_2 B_2 C_2 )
D. (A_1 A_2+B_1 B_2+C_1 C_2 )=0
Answer» E.
Discussion
8.

Find the angle between two planes ( vec{r}.(2 hat{i}- hat{j}+ hat{k})=3 ) and ( vec{r}.(3 hat{i}+2 hat{j}-3 hat{k}) )=5.

A. (cos^{-1} u2061 frac{1}{ sqrt{22}} )
B. (cos^{-1} u2061 frac{1}{ sqrt{6}} )
C. (cos^{-1} u2061 frac{1}{ sqrt{132}} )
D. (cos^{-1} u2061 frac{1}{ sqrt{13}} )
Answer» D. (cos^{-1} u2061 frac{1}{ sqrt{13}} )
Discussion
9.

Which of the following is the correct formula for the angle between two planes (A_1 x+B_1 y+C_1 z+D_1 )=0 and (A_2 x+B_2 y+C_2 z+D_2 )=0?

A. cos u2061 = ( frac{A_1 B_1 C_1}{A_2 B_2 C_2} )
B. cos u2061 = ( 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. sin u2061 = ( 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. cos u2061 = (A_1 A_2+B_1 B_2+C_1 C_2 )
Answer» C. sin u2061 = ( 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 | )
Discussion
10.

Which of the following is the correct formula for the angle between two planes?

A. cos u2061 = ( left | frac{ vec{n_1}. vec{n_2}}{| vec{n_1}|| vec{n_2}|} right | )
B. sin u2061 = ( left | frac{ vec{n_1}. vec{n_2}}{| vec{n_1}|| vec{n_2}|} right | )
C. cos u2061 = ( left | frac{ vec{n_1}+ vec{n_2}}{| vec{n_1}|| vec{n_2}|} right | )
D. sin u2061 = ( left | frac{ vec{n_1}+ vec{n_2}}{(| vec{n_1}|+| vec{n_2}|} right | )
Answer» B. sin u2061 = ( left | frac{ vec{n_1}. vec{n_2}}{| vec{n_1}|| vec{n_2}|} right | )
Discussion