AZ : CX : : ? : JQ Option 1) IV Option 2) FU Option 3) KP Option 4) None of these

If $ A=(a, b, c) $ and $ B=(x, y, z) $, find $ B \times A $.

$ {(a, x), (a, y), (a, z), (b, x), (b, y), (b, z), (c, x), (c, y), (c, z)} $

$ {(x, a), (x, b), (x, c), (y, a), (y, b), (y, c), (z, a), (z, b), (z, c)} $

$ {(a, a), (b, b), (c, c), (x, x), (y, y), (z, z)} $

None of these

Show that $\mathbf{a} \cdot(\mathbf{b} \times \mathbf{c})$ is equal in magnitude to the volume of the parallelepiped formed on the three vectors, $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$.

The value of $\frac{52xyz(x y+y z+x z+y^{2})(z+x)}{104xy(x y+x z+y z+y^{2})}$ is:

A $\frac{z(z+x)}{2}$
B $\frac{z(z-x)}{2}$
C $\frac{x(z-x)}{2}$
D $\frac{x(z+x)}{2}$

Directions

Study the following information carefully to answer the question given below.

A, B, C, D, E, F and G are seven friends studying seven different branches of engineering, namely Mechanical, Chemical, Electrical, Electronics, Civil, Computers and Aeronautical Engineering not necessarily in this order. Each of them studies in three different colleges, X, Y and Z. Not less than two study in any college.

• D studies Electrical Engineering in college X.
• The one who studies Chemical Engineering does not study in college Z.
• F studies Aeronautical Engineering in college Y with only B.
• A does not study in college X and does not study Civil Engineering.
• E studies Computer Engineering and does not study in college X.
• G studies Electronics Engineering but not in college X.
• None in college X studies Mechanical or Civil Engineering.

Which of the following combinations is correct?

• Option 1) A-Civil-Z
• Option 2) B-Chemical-Y
• Option 3) C-Chemical-Z
• Option 4) G-Electronics-Y
• Option 5) None of these

AZ, FU, KP, ?, UF

Option 1) KF
Option 2) OL
Option 3) PK
Option 4) QK