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 angle between the vectors if (| vec{a}|=| vec{b}|=3 sqrt{2} ) and ( vec{a}. vec{b}=9 sqrt{3} ).

A. ( frac{ }{6} )
B. ( frac{ }{5} )
C. ( frac{ }{3} )
D. ( frac{ }{2} )
Answer» B. ( frac{ }{5} )
Discussion
2.

If ( vec{a}=2 hat{i}+3 hat{j}+4 hat{k} ) and ( vec{b}=4 hat{i}-2 hat{j}+3 hat{k} ). Find (| vec{a} vec{b}| ).

A. ( sqrt{685} )
B. ( sqrt{645} )
C. ( sqrt{679} )
D. ( sqrt{689} )
Answer» C. ( sqrt{679} )
Discussion
3.

Find the vector product of the vectors ( vec{a}=- hat{j}+ hat{k} ) and ( vec{b}=- hat{i}- hat{j}- hat{k} ).

A. (2 hat{i}- hat{j}+ hat{k} )
B. (2 hat{i}- hat{j}-4 hat{k} )
C. ( hat{i}+ hat{j}- hat{k} )
D. (2 hat{i}- hat{j}- hat{k} )
Answer» E.
Discussion
4.

Find the product (( vec{a}+ vec{b}).(7 vec{a}-6 vec{b}) ).

A. (2| vec{a}|^2+6 vec{a}. vec{b}-3| vec{b}|^2 )
B. (8| vec{a}|^2+5 vec{a}. vec{b}-5| vec{b}|^2 )
C. (2| vec{a}|^2+6 vec{a}. vec{b}-8| vec{b}|^2 )
D. (7| vec{a}|^2+ vec{a}. vec{b}-6| vec{b}|^2 )
Answer» E.
Discussion
5.

If ( vec{a} ,and , vec{b} ) are two non-zero vectors then (( vec{a}- vec{b}) ( vec{a}+ vec{b}) )=_________

A. (2( vec{a} vec{b}) )
B. (( vec{a} vec{b}) )
C. (4( vec{a} vec{b}) )
D. (3( vec{a} vec{b}) )
Answer» B. (( vec{a} vec{b}) )
Discussion
6.

Find the vector product of the vectors ( vec{a}=2 hat{i}+4 hat{j} ) and ( vec{b}=3 hat{i}- hat{j}+2 hat{k} ).

A. ( hat{i}-19 hat{j}-4 hat{k} )
B. (3 hat{i}+19 hat{j}-14 hat{k} )
C. (3 hat{i}-19 hat{j}-14 hat{k} )
D. (3 hat{i}+5 hat{j}+4 hat{k} )
Answer» D. (3 hat{i}+5 hat{j}+4 hat{k} )
Discussion
7.

Find the angle between ( vec{a} ,and , vec{b} ) if (| vec{a}|=2,| vec{b}|= frac{1}{2 3} ) and ( vec{a} vec{b}= frac{1}{2} ).

A. ( frac{2 }{3} )
B. ( frac{4 }{5} )
C. ( frac{ }{3} )
D. ( frac{ }{2} )
Answer» D. ( frac{ }{2} )
Discussion
8.

If ( vec{a}= hat{i}- hat{j}+3 hat{k}, , vec{b}=5 hat{i}-2 hat{j}+ hat{k} ,and , vec{c}= hat{i}- hat{j} ) are such that ( vec{a}+ vec{b} ) is perpendicular to ( vec{c} ), then the value of .

A. ( frac{7}{2} )
B. ( frac{7}{2} )
C. ( frac{3}{2} )
D. ( frac{7}{9} )
Answer» C. ( frac{3}{2} )
Discussion
9.

Find the magnitude of ( vec{a} ) and ( vec{b} ) which are having the same magnitude and such that the angle between them is 60 and their scalar product is ( frac{1}{4} ).

A. (| vec{a}|=| vec{b}|= frac{1}{2 2} )
B. (| vec{a}|=| vec{b}|= frac{1}{ 2} )
C. (| vec{a}|=| vec{b}|= frac{1}{2 3} )
D. (| vec{a}|=| vec{b}|= frac{2}{ 3} )
Answer» B. (| vec{a}|=| vec{b}|= frac{1}{ 2} )
Discussion
10.

Evaluate the product ((2 vec{a}+5 vec{b}).(4 vec{a}-5 vec{b}) ).

A. (| vec{a}|^2+2 vec{a}. vec{b}-15| vec{b}|^2 )
B. (8| vec{a}|^2+2 vec{a}. vec{b}-15| vec{b}|^2 )
C. (8| vec{a}|^2-4 vec{a}. vec{b}-15| vec{b}|^2 )
D. (| vec{a}|^2+ vec{a}. vec{b}-5| vec{b}|^2 )
Answer» C. (8| vec{a}|^2-4 vec{a}. vec{b}-15| vec{b}|^2 )
Discussion