Explore topic-wise MCQs in Mathematics.

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} u2061 frac{43}{ sqrt{3482}} )
B. (cos^{-1} u2061 u2061 frac{43}{ sqrt{3382}} )
C. (cos^{-1} u2061 u2061 frac{85}{ sqrt{3382}} )
D. (cos^{-1} u2061 u2061 frac{34}{ sqrt{3382}} )
Answer» C. (cos^{-1} u2061 u2061 frac{85}{ sqrt{3382}} )
Discussion
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. cot u2061 = ( left |l_1 ,l_2+m_1 ,m_2+n_1 ,n_2 right | )
B. sin u2061 = ( left |l_1 ,l_2+m_1 ,n_2+n_1 ,m_2 right | )
C. tan u2061 = ( left |l_1 ,l_2+m_1 ,m_2+n_1 ,n_2 right | )
D. cos u2061 = ( left |l_1 ,l_2+m_1 ,m_2+n_1 ,n_2 right | )
Answer» E.
Discussion
3.

Find the angle between the lines ( vec{r}=2 hat{i}+6 hat{j}- hat{k}+ ( hat{i}-2 hat{j}+3 hat{k}) ) and ( vec{r}=4 hat{i}-7 hat{j}+3 hat{k}+ (5 hat{i}-3 hat{j}+3 hat{k}) ).

A. = (cos^{-1} frac{ u206120}{ sqrt{602}} )
B. = (cos^{-1} frac{ u206120}{ sqrt{682}} )
C. = (cos^{-1} frac{ u20618}{ sqrt{602}} )
D. = (cos^{-1} u2061 frac{14}{ sqrt{598}} )
Answer» B. = (cos^{-1} frac{ u206120}{ sqrt{682}} )
Discussion
4.

If the equations of two lines L1 and L2 are ( vec{r}= vec{a_1}+ vec{b_1} ) and ( vec{r}= vec{a_2}+ vec{b_2} ), then which of the following is the correct formula for the angle between the two lines?

A. cos u2061 = ( left | frac{ vec{a_1}. vec{a_2}}{| vec{b_1}|| vec{a_2}|} right | )
B. cos u2061 = ( left | frac{ vec{a_1}. vec{a_2}}{| vec{a_1}|| vec{a_2}|} right | )
C. cos u2061 = ( left | frac{ vec{b_1}. vec{b_2}}{| vec{b_1}|| vec{b_2}|} right | )
D. cos u2061 = ( left | frac{ vec{a_1}. vec{b_2}}{| vec{a_1}|| vec{b_2}|} right | )
Answer» D. cos u2061 = ( left | frac{ vec{a_1}. vec{b_2}}{| vec{a_1}|| vec{b_2}|} right | )
Discussion
5.

Find the value of p such that the lines ( frac{x+11}{4}= frac{y+3}{-2}= frac{z-3}{4} ,and , frac{x-3}{p}= frac{y+12}{2}= frac{z-3}{-12} ) are at right angles to each other.

A. p=11
B. p=12
C. p=13
D. p=4
Answer» D. p=4
Discussion
6.

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
Discussion
7.

Find the angle between the two lines if the equations of the lines are
( vec{r}= hat{i}+ hat{j}+ hat{k}+ (3 hat{i}- hat{j}+ hat{k}) ,and , vec{r}=4 hat{i}+ hat{j}-2 hat{k}+ (2 hat{i}+3 hat{j}+ hat{k}) )

A. (cos^{-1} frac{ u20614}{ sqrt{14}} )
B. (cos^{-1} u2061 frac{7}{ sqrt{154}} )
C. (cos^{-1} u2061 frac{4}{154} )
D. (cos^{-1} u2061 frac{4}{ sqrt{154}} )
Answer» E.
Discussion
8.

Find the angle between the lines.
( frac{x+2}{1}= frac{y+5}{6}= frac{z-3}{2} )

A. n ( frac{x-4}{5}= frac{y-3}{-2}= frac{z+3}{1} )
B. (cos^{-1} frac{ u20615}{ sqrt{1230}} )
C. (cos^{-1} u2061 frac{ u20613}{ sqrt{3120}} )
D. (cos^{-1} u2061 frac{ u20617}{ sqrt{2310}} )
E. (cos^{-1} frac{ u2061 u206148}{ sqrt{1230}} )
Answer» B. (cos^{-1} frac{ u20615}{ sqrt{1230}} )
Discussion
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. ( =tan^{-1} 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 | )
B. ( =2tan^{-1} 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. ( =cos^{-1} 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. ( =2 ,cos^{-1} 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 | )
Answer» D. ( =2 ,cos^{-1} 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