Avichal solutions for Computer Applications [English] Class 10 ICSE chapter 1.6 - Mathematical Library Methods [Latest edition]

What values will be stored in the variables p and q after executing the following code?

double a = −6.35; double b = 14.74; 
double p = Math.abs(Math.ceil(a)); 
double q = Math.rint(Math.max(a, b)); 

What values will be stored in the variables p and q after executing the following code?

double b = −15.6; 
double p = Math.rint(Math.abs(b)); 

What values will be stored in the variables p and q after executing the following code?

int p = Math.abs(Math.min(−61, −79)); 
double q = Math.cbrt(4.913);

What values will be stored in the variables p and q after executing the following code?

double a = −99.51, b = −56.25; 
double p = Math.abs(Math.floor(a)); 
double q = Math.sqrt(Math.abs(b)); 

What values will be stored in the variables p and q after executing the following code?

double x = 5.9, y = 6.5; 
double p = (Math.min(Math.floor(x), y)); 
double q = (Math.max(Math.ceil(x), y)); 

What will the following function return?

Math.round(Math.pow(2.4, 2)); 

What will the following function return?

Math.abs(Math.max(−8, −11));

What will the following function return?

Math.min(−23, −29); 

What will the following function return?

Math.ceil(14.8); 

What will the following function display?

System.out.println(Math.floor(−0.48));

What will the following function display? 

System.out.println(Math.ceil(−0.45));

What will the following function display?

System.out.println(Math.ceil(8)); 

What will the following function display?

System.out.println(Math.ceil(−8));

Given: double a = - 8.35;

double p = Math.abs(Math.floor(a));

What will be the final value stored in the variable p? 

Given: double m = Math.max(Math.cei1(14.55),15.5); 

What will be the final value stored in the variable m?

Given: d = Math.min(−15.5, −19.5) 

What data type will you refer for the variable d? 

Given: double k = Math.rint(−9.4) + Math.sqrt(9.0); 

Given: double b = Math.ceil(3.4) + Math.pow(2, 3);

The return data type of Math.log() is double. 

Java.Math class is used for different mathematical functions.

The output of Math.abs(−99.99) is 100.00.

Math.sqrt(−225) can't be defined.

The output of Math.cbrt(−3) will be −27.

Math.round() returns the value in float data type. 

Write down the syntax for the following function:

To find the natural log of q.

Write down the syntax for the following function:

To find the cube root of a number m.

Write down the syntax for the following function: 

To find the round-off of a number k. 

Write down the syntax for the following function:

To find the absolute value of a number y.

Write down the syntax for the following function:

To find the exponent of a number p. 

Explain the following function: 

Math.random()

Explain the following function:

Math.pow()

Explain the following function:

Math.cbrt()

Explain the following function:

Math.log()

Distinguish between Math.cell() and Math.floor().

Distinguish between Math.rint( ) and Math.round( ).

Write a program to calculate the value of the given expression: 

`1/a^2 + 2/b^2 + 3/c^2`

Take the values of a, b and c as input from the console. Finally, display the result of the expression to its nearest whole number.

For every natural number m>1; 2m, m² − 1 and m² + 1 form a Pythagorean triplet. Write a program to input the value of 'm' through console to display a 'Pythagorean Triplet'. 

Sample Input: 3

Then 2m = 6, m² - 1 = 8 and m² + 1 = 10 

Thus 6, 8, 10 form a 'Pythagorean Triplet'. 

Write a program to input a number. Calculate its square root and cube root. Finally, display the result by rounding it off. 

Sample Input: 5
Square root of 5 = 2.2360679
Rounded form = 2
Cube root of 5 = 1.7099759
Rounded form = 2 

The volume of a sphere is calculated by using formula: 

v = `4/3 ∗ 22/7 ∗ r^3`

Write a program to calculate the radius of a sphere by taking its volume as an input. 

Hint: radius = `root3 ("volume" ∗ 3/4 ∗ 7/22)`

A trigonometrical expression is given as: 

`(tan "A" − tan "B")/(1 +tan "A" ∗ tan "B")`

Write a program to calculate the value of the given expression by taking the values of angles A and B (in degrees) as input.

Hint: radian = `(22/(7 ∗ 180))` ∗ degree 

The standard form of quadratic equation is represented as:

ax² + bx + c = 0 

where d = b² − 4ac, known as 'Discriminant' of the equation.

Write a program to input the values of a, b and c. Calculate the value of discriminant and display the output to the nearest whole number. 

The sum of first n odd natural numbers can be calculated as n², where n is the number of odd natural.

For example,
Sum = 1 + 3 + 5 + 7; number of odd natural = 4
Therefore, Sum = 4² = 16

Write a program to input number of odd natural terms and display sum of the given series:

1. 1 + 3 + 5 + .......... + 29 + 31
2. 1 + 3 + 5 + 7 + .......... + 47 + 49

Write a program to input the sum. Calculate and display the compound interest in 3 years, when the rates for the successive years are r1%, r2% and r3% respectively.

Hint: `["A" = "P" "*" (1 + ("r"1)/100) "*" (1 + ("r"2)/100) "*" (1 + ("r"3)/100), "CI" = "A" − "P"]`