Question

[
19. Rays incident on ........... diverges from a focal plane of concave lens.
A) Focus
B) Parallel to principal axis
C) Parallel rays making some angle with principal axis
D) Through centre of curvature​

Answer 1

Answer:

We simplify the working as;

a² × a = a³;

a² × 3b = 3a²b;

b² × 3a = 3ab²;

b² × b = b³;

Examples on the method for finding the cube of a two-digit number:

1. Find the value of (29)³ by the short-cut method.

Solution:

Method for Finding the Cube of a Two-Digit Number

Here, a = 2 and b =9.

a² × a = a³;

a² × 3b = 3a² × b;

b² × 3a = 3a × b²;

b² × b = b³

Therefore, (29)³ = 24389

2. Find the value of (71)³ by the short-cut method.

Solution:

Method for Finding the Cube of a Two-Digit Number

Here, a = 7 and b = 1

a² × a = a³;

a² × 3b = 3a² × b;

b² × 3a = 3a × b²;

b² × b = b³

Therefore, (71)³ = 357911

By following the above examples on the method for finding the cube of a two-digit number; we can try to find the value of each of the following using the short-cut method;

1. (25)³

2. (47)³

3. (68)³

4. (84)³We will learn the short-cut method for finding the cube of a two-digit number.

Suppose, we have (a + b)³ = a³ + 3a²b + 3ab² + b³.

METHOD:

For finding the cube of a two-digit number with the tens digit = a

and the units digit = b, we make four columns, headed by

a³, (3a² × b), (3a × b²) and b³

The rest of the procedure is the same as followed in squaring a number by the column method.

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