Explore topic-wise MCQs in Linear Algebra.

This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Linear Algebra knowledge and support exam preparation. Choose a topic below to get started.

1.

What is the area of a cardiod y = a(1+cos ).

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

Calculate the area enclosed by parabolas x2 = y and y2 = x.

A. ( frac{1}{2} )
B. ( frac{1}{3} )
C. ( frac{1}{4} )
D. ( frac{1}{6} )
Answer» C. ( frac{1}{4} )
Discussion
3.

Evaluate ( int_0^ int_x^ frac{e^{-y}}{y} dydx ) by changing the order of integration.

A. 0
B. 1
C. 2
D. 1/2
Answer» C. 2
Discussion
4.

Evaluate the following integral by transforming into polar coordinates. ( displaystyle int_0^a int_0^ sqrt{a^2-x^2} y sqrt{x^2-y^2} dxdy )

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

Evaluate ( int_0^ int_0^ e^{-(x^2+y^2 )} dxdy ) by changing into polar coordinates.

A. ( pi )
B. ( frac{ pi}{2} )
C. ( frac{ pi}{4} )
D. ( frac{ pi}{8} )
Answer» D. ( frac{ pi}{8} )
Discussion
6.

Evaluate rsin drd over the cardiod r = a(1+cos ) above the initial line.

A. (4 frac{a^2}{3} )
B. ( frac{a^2}{3} )
C. (8 frac{a^2}{3} )
D. (4 frac{a^2}{6} )
Answer» B. ( frac{a^2}{3} )
Discussion
7.

Evaluate ( int_0^ int_0^{ /2} e^{-r^{2}} rd dr ).

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

Evaluate x2+y2 dxdy in the positive quadrant for which x+y<=1.

A. ( frac{1}{2} )
B. ( frac{1}{3} )
C. ( frac{1}{6} )
D. ( frac{1}{12} )
Answer» D. ( frac{1}{12} )
Discussion
9.

Evaluate xy dxdy over the region bounded by x axis, ordinate x=2a and the curve x2=4ay.

A. ( frac{a^4}{3} )
B. ( frac{a^4}{6} )
C. ( frac{a^3}{3} )
D. ( frac{a^2}{6} )
Answer» B. ( frac{a^4}{6} )
Discussion
10.

Evaluate xy dxdy over the positive quadrant of the circle x2+y2=a2.

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