Solve for x: 5x + 3 = 27 + 2x

solve for x : (9x -7)/(3x + 5) = (3x – 4)/(x + 6)

2/3 of a number is 20 less than the original number. Find the number.

Two numbers are such that the ratio between them is 3:5. If each is increased by 10, the ratio between the new numbers so formed is 5:7. Find the original numbers.

The sum of the digits of a two digit number is 15. If the number formed by reversing the digit is less than the original number by 27, find the original number.

Divide 4500 into two parts such that 5% of the first part is equal to 10% of the second part.

Rakhi’s mother is 4 times as old as rakhi. After 5 years her mother will be 3 times as old as she will be then, Find their present ages.

Sum of three consecutive integers is 51. Find the middle one.

The width of a rectangle is 2/3th its length.If the perimeter is 180m. Find the dimensions of the rectangle.

Half of a herd of dear are grazing in the field and 3/4th of the remaining are playing nearby, the rest 9 are drinking water from the pond, Find the number of the dear in the herd.

In the given figure, DE||BC, AD=2cm, BD=2.5cm, AE=3.2cm and DE=4cm. Find AC and BC.

If the areas of the two similar triangles are in the ratio 25:64, find the ratio of their corresponding sides.

Area of two similar traingles are and respestively. If the median of the first triangle is 12.1cm, find the corresponding median of the other.

In the Δ ABC, it is given that ∠C = 90° and tan A = 1/√3 , find the value of (sin A cos B+ cos A sin B)

If tan ( A+B) = √3 and tan (A-B) = 1/√3 , 0º < A+B<90º and A>B, find the values of A and B.

Evaluate

Without using trigonometric tables , evaluate the following

A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60° . When he moves 30 m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and the width of the river. [Take √3 = 1.732]

The angle of elevation of a jet fighter from a point A on the ground is 60°. After a flight of 15 seconds , the angle of elevation changes to 30°. If the jet is flying at a speed of 720 km/hr, find the constant height at which the jet is flying. [Take √3= 1.732]

The angle of elevation of a cloud from a point 60 m above a lake is 30° and angle of depression of the reflection of the cloud in the lake is 60°. Find the height of the cloud.

Evalute.

( 2 +√2 )²

Which of the statement is true for the two irrational numbers ?

√2 +  √3  and  √3 –  √2

Which irrational number is greater ?

2( 6)¼ , 3(2)¼

Solve for a and b.

3 / ( √3 – √2 )   = a√3 – b √2

If x = 5 – 2 √6 , find the value for

[math] x^2 + 1 / x^2 [/math ]

A man invests Rs 5000 for 2 years at compound interest . After one year his money amounts to Rs 5150. Find the interest for the 2nd year.

Shashank borrowed RS 20000 from bank at 10% p.a simple interest . He lent it to his friend Ashish at the same rate but compounded annually . Find his gain after 2 and 1/2 years.

The population of a city increases by 5% every year. What was the population in 2003, if in 2006 it was 1,85,220 ?

Given a – b = 0.9  and ab = 0.36. Find the value of  a + b .

If  (a + 1/a )² = 3  ,  find the value of  a³ + 1 / a³.

Evaluate :

( 1.2*1.2 + 1.2 * 0.3  + 0.3*0.3  )/ ( 1.2*1.2*1.2 – 0.3*0.3*0.3)

If  a + b = 11 and  a² + b²  = 65

Find the value of a³ + b³

Factorize  1 – 2(a + b ) – 3(a + b)²

Factorize .

4x² + 1 / 4x² + 1

Solve  for x and y

2x + 3y = 8

2x = 2 + 3y

If 2 is added to the numerator and denominator it becomes 9/10 and if 3 is subtracted from the numerator and denominator it become 4/5. Find the fractions.

Two pens and one eraser cost Rs. 35 and 3 pens and four erasers cost Rs. 65. Find the cost of pen and eraser separately.

A worker in a factory is paid Rs.20 per hour for normal work and Rs 30 per hour for overtime work. During a weak, he worked for 40 hours, out of which x hours was overtime.If he receives Rs 880 in all, find the number of hours of his normal work during the week.

Find the value of

log 5 + log 8 – 2 log 2

Simplify

2 log 15/18 – log 25/162 + log 4/9

Solve for x

log (x – 2) + log ( x + 2) = log 5

S.I unit of temperature is _______.

1 metric tonne is ________.

Which instrument is used for measuring mass of a object?

Thermometer is graduated in _________.

Name four basic measurement in our daily life.

Name the device which you will use to measure the perimeter of our playground.

Convert the following quantities.
2500 kg = ____ metric tonne.

Express in second:
5 hour 2 minute 5 second

What are derived physical quantities? Give any two examples of derived physical quantities.

Which of the following weighing devices has a very high accuracy and sensitivity?

Which of the following is not a common unit for measuring time?

A train departs from Delhi railway station at 21:50 hours everyday. The time shown in your analogue watch at the departure will be

The maximum and minimum thermometer is commonly used by a

Name the unit which is commonly in both the MKS and CGS systems

Name the instrument generally used to find the time interval between the two events accurately.

What is the function of the bulb in a thermometer?

A piece of wire is wound around a pencil 60 times, If the total width of all the turns is 4 cm, find the diameter of the wire.

What do you understand by the terms volume and capacity? which is most suitable unit for measuring the volume of glass filled with water.

What do you mean by mean solar day?

What is parallax error?

What is inheritance?

Name the operators listed down.
a) ?:
b) &&

State the number of bytes occupied by char and int datatypes.

String x[] = {“APPLE”, “ORANGE” , “BANANA” , “PINEAPPLE” , “GUAVA”} :
give the output of the following statement.

a) System.out.print(x[1]);
b) system.out.print(x[3].length());[2]

What are the two ways of invoking function?

Give the output of the following program segment and also mention the number of times the loop is executed:
int a,b;
for(a=6,b=4;a<=24;a=a+6) { if(a%b==0) break; } System.out.println(a);

Write the Output:
char ch= ‘G’;
int m=ch;
m=m+5;
System.out.println(m+ ” ” +ch);

What is the value of x1 if x=5 ?
x1=++x – x++ + ––x

What are the values stored in variables r1 and r2

i) double r1 = Math.abs(Math.min(-2.83,-5.83));
ii) double r2 = Math.sqrt(Math.floor(16.3));

Give the output of the following code
String A= “26”, B= “100” ;
String D=A+B+ “200”;
int x= Integer.parseInt(A);
int y=Integer.parseInt(B);
int d=x+y;
System.out.println(“Result 1=” +D);
System.out.println(“Result 2=”+d);

for(int i=3;i<=4;i++) { for(int j=2;j

Identify the correct keyword?

If int x[] = { 4, 3, 7, 8, 9, 10 }; what are the values of p and q?

(i) p = x.length
(ii) q = x[2] + x[5] * x[1]

Give the output of the following Math functions:

(i) Math.ceil(4.2)
(ii) Math.abs(-4)

Write down java expression for :
T = √a² +b² + c²

 How many times does the body of the loop gets executed?

for(int m=5; m<=20; m+=5) { if(m%3 == 0) break; else if(m%5 == 0) System.out.println(m); continue; }

Give the output of the following expression :

a+=a++ + ++a + -–a + a-– ; when a = 7

Name the wrapper class of char type and boolean type.

Evaluate the value of n if the value of p=5, q=19 [2]

int n = (q-p) > (p-q) ? (q-p) : (p-q);

What is the value stored in variable res given below:

double res = Math.pow(“345”.indexOf(‘5’), 3);

What is inheritance ?

Name the operator listed below

?:

String a[] = { “HELLO”, “HOW”, “ARE”, “YOU”,”ICSE” };

What will be the output of the following statements :

System.out.println(a[2]);

System.out.println(a[1].length());

What is the data type and value of the val after following is executed :

char ab = ‘j’;

val = Character.toUpperCase(ab);

Give the correct output of the following program segment and also mention the number of times the loop is executed ;

int a, b;

for (a = 7, b = 3; a < 49 ; a + = 7 )

{
if ( a % b == 0 )
break ;

}

System.out.println(a);

Write the output of the following code :

char ch = ‘T’;

int i = ch;

i += 5 ;

System.out.println(i+ ” ” +ch);

What is the value of the i if i = 6;

i = ++i -i++ +  – – i;

Write the output of the following :

String x = “Practice makes man perfect”;

System.out.println(x.indexOf(‘p’));

System.out.println(x.substring(0,8) + ” ” + “SUMMER”);

What are the values stored in the variables a, b and c :

1. double a = Math.abs(Math.min( -3.53 , -6.53));

2 double b = Math.sqrt(Math.floor( 25.5 ));

3 double c = Math.abs(Math.ceil( 6.45 ));

Give the output of the following code :

String A = “200”;

String B = “300”;

String C = A + B + “900”;

int a = Integer.parseInt(A);

int b = Integer.parseInt(B);

int c = a + b ;

System.out.println(“output1 = “+C);

System.out.println(“output2 = “+c);

Analyse the given java code and answer the following questions :

for (int i = 3; i <= 7; i ++)

for (int j = 2; j < i ; j++)

System.out.println();

System.out.print(“Success”);

1. How many times does inner loop execute ?

2. Write the output of the program segment ?

Name the type of error displayed for each of the statements ?

a. Math.sqrt(-9)

What will be the output for the following code ?

int [] a = { 10 , 9 , 8 , 7 , 6 , 5 , 4 , 3 , 2 , 1  };

System.out.println(a.length +”Hello World”+ a[2]+a[1]);

Convert the following while loop to the corresponding for loop :

int a = 3, i = 10 ;

while (i >=1)

{

System.out.println(a*i);

i– ;

}

Default values of primitive data type int and float are :

Which of the following is not the OOP’s principle ?

Evaluate the value of a if value of

int b = 10 , c = 20;

int a = ( b – c ) > ( c – b ) ? b – c : c – b ;

System.out.println(a);

Evaluate the output of the following code :

char ch ;

int x = 98;

do {

ch = (char) x;

System.out.print(ch +””);

if(x%10 == 0) break;

++x;

}while( x <= 105 );

Buffered reader class is stored in ___________ package.

void check( int a , int b )

{

a = a + b ;

b = a – b;

a = a – b;

System.out.println(a+ “,” +b);

}

What will be output of the code if a = 40 and b = 100

Evaluate the output of the following code :

String a = “America”;

String b = “India”;

String c = a.substring ( 2 , 5 );

String d = b.substring(2).toUpperCase();

System.out.println(d);

System.out.println(d.equalsIgnoreCase(a));

The access specifier which gives the most accessibility is _________________.

int y = 20;

int x = ( ++y  * ( y++ + 5 ) );

System.out.println(x);

What is the possible value of x in the output ?

String function trim() returns the following things.

__________________ is primitive data type 64 bit integer and is used when needed a range of values wider than those provided by int.

Identify the error in the following code :

int y [] = new int ( 5 );

for (int j =0; j<=5 ; j++)

y[j] =j;

When is the constructor invoked ?

Why is a class in JAVA known as composite data type?

A method which converts string to a primitive integer data type is ______________.

The default initial value of boolean variable data type is ____________________.

Simplify your answers and choose the correct option
 

Work out the following. Simplify your answers and choose the correct options

Work out the following and and simplify your answers where ever possible and choose the correct options. 
a)  8  × 7/8 
b)  10 × 3/5 
c)  16 ÷ 4/5 
d)  42 ÷ 7/8 

Work out the followings and choose the correct answers below : 
a) 46% of 50
b) 70% of 125
c) 90% of 90 
d) 36% of 180

An airline has a fleet of 120 planes . Of these, 20 are being serviced at any time. 
What percentage of the fleet is available for flights ?

A family sees the kitchen they want priced at $8000 but it is offered at a 
discount of 40% in a sale. What is the sale price ?

Calculate the tenth term for the following sequences and choose the appropriate answers : 
a) 8, 14, 20, 26, 32…
b) 12, 23, 34, 45, 56…
c) 11, 23, 35, 47…
d) 8, 12, 16, 20…

Write down the expression for the nth term for the following sequences and choose the correct options :

a) 2, 12, 22, 32, 42…
b) 5, 6, 7, 8, 9…  
c) 101, 201, 301, 401…
d) 4, 9, 14, 19, 24… 

Deduce the equation of the line shown in the graph below : 

Deduce the equation of the line from the linear graph shown below. And choose the correct option:

Find the angle a and b in the figure shown below for a Triangle. 

Find the value of angle x in the given quadrilateral shown below :

Find the area of the shape listed down in the figure below :