Explore topic-wise MCQs in Linear Algebra.

This section includes 6 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.

The temperature of a point in space is given by T = x2 + y2 z. An insect located at a point (1, 1, 2) desire to fly in such a direction such that it will get warm as soon as possible. In what direction it should move?

A. ( frac{-2 hat{i}}{3}+ frac{2 hat{j}}{3}+ frac{- hat{k}}{3} )
B. ( frac{2 hat{i}}{3}+ frac{-2 hat{j}}{3}+ frac{- hat{k}}{3} )
C. ( frac{2 hat{i}}{3}+ frac{2 hat{j}}{3}+ frac{ hat{k}}{3} )
D. ( frac{2 hat{i}}{3}+ frac{2 hat{j}}{3}+ frac{- hat{k}}{3} )
Answer» E.
Discussion
2.

For what value of a & b for which the two surfaces ax2 byz = (a+2)x & 4x2y + z3 = 4 will be orthogonal to each other at the point (1,-1,2).

A. (a = 1 , & , b = frac{3}{2} )
B. (a = frac{-3}{2} , & , b = 1 )
C. (a = frac{3}{2} , & , b = 1 )
D. (a = frac{-3}{2} , & , b = -1 )
Answer» D. (a = frac{-3}{2} , & , b = -1 )
Discussion
3.

The unit normal vector n of the cone of revolution z2 = 4(x2 + y2) at the Point P (1, 0, 2) is?

A. ([ frac{2}{ sqrt{5}}, 0, frac{1}{ sqrt{5}}] )
B. ([ frac{2}{ sqrt{5}}, 0, frac{1}{ sqrt{5}}] )
C. ([- frac{2}{ sqrt{5}}, 0, - frac{1}{ sqrt{5}}] )
D. ([ frac{2}{ sqrt{5}}, 0, frac{1}{ sqrt{5}}] )
Answer» B. ([ frac{2}{ sqrt{5}}, 0, frac{1}{ sqrt{5}}] )
Discussion
4.

For the function f = x2y + 2y2x, at the point P(1,3), what is the direction in which the directional derivative is zero?

A. (-13 hat{i} 24 hat{j} )
B. (13 hat{i} + 24 hat{j} )
C. ( 13 hat{i} 24 hat{j} )
D. ( 13 hat{i} 24 hat{j} )
Answer» D. ( 13 hat{i} 24 hat{j} )
Discussion
5.

The directional derivative of (x,y) at the point A(3,2) towards the point B(2,3). What is (3 sqrt{2} ) and toward the point (1,0) is ( sqrt{8} ). What is the directional derivative at the point A towards the point D.

A. ( frac{6}{5} )
B. ( frac{7}{ sqrt{5}} )
C. ( frac{6}{ sqrt{5}} )
D. ( frac{7}{5} )
Answer» C. ( frac{6}{ sqrt{5}} )
Discussion
6.

Find the directional derivative of = xy2 + yz3 at (1, -1, 1), towards the point (2, 1, -1).

A. ( frac{5}{3} )
B. ( frac{-5}{3} )
C. ( frac{7}{3} )
D. ( frac{1}{3} )
Answer» B. ( frac{-5}{3} )
Discussion