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The following frequency distribution table shows marks obtained by 180 students in Mathematics examination.
| Marks | No. of students |
| 0 – 10 | 25 |
| 10 – 20 | x |
| 20 – 30 | 30 |
| 30 – 40 | 2x |
| 40 – 50 | 65 |
Find the value of x. Also draw a histogram representing the above information.
Concept: Graphical Representation of Data as Histograms
The following table shows the number of students and the time they utilized daily for their studies. Find the mean time spent by students for their studies:
| Time (hrs.) | No. of. students |
| 0 - 2 | 8 |
| 2 - 4 | 14 |
| 4 - 6 | 18 |
| 6 - 8 | 10 |
| 8 - 10 | 10 |
Concept: Tabulation of Data
Find the value of determinant: `|[4,-2],[3,1]|`
Concept: Determinant of Order Two
If the value of determinant `|[m,2],[-5,7]|`is 31, find the value of m
Concept: Determinant of Order Two
If x + y = 5 and x = 3, then find the value of y.
Concept: Algebraic Methods of Solving a Pair of Linear Equations > Substitution Method
If the point (3, 2) lies on the graph of the equation 5x + ay = 19, then find a.
Concept: Algebraic Methods of Solving a Pair of Linear Equations > Substitution Method
A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?
Concept: Algebraic Methods of Solving a Pair of Linear Equations > Cross - Multiplication Method
A thief runs with a uniform speed of 100 m/minute. After one minute, a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief.
Concept: Algebraic Methods of Solving a Pair of Linear Equations > Cross - Multiplication Method
A thief, after committing a theft, runs at a uniform speed of 50 m/minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute every succeeding minute. After how many minutes, the policeman will catch the thief?
Concept: Algebraic Methods of Solving a Pair of Linear Equations > Cross - Multiplication Method
If the cost of bananas is increased by Rs. 10 per dozen, one can get 3 dozen less for Rs.600. Find the original cost of one dozen of bananas.
Concept: Simple Situational Problems
Solve the following simultaneous equations
`1/(3x)-1/(4y)+1=0`;
`1/(5x)+1/(2y)=4/15`
Concept: Algebraic Methods of Solving a Pair of Linear Equations > Substitution Method
Find the value of following determinant.
`|(-1,7),(2,4)|`
Concept: Equations Reducible to a Pair of Linear Equations in Two Variables
Two numbers differ by 3. The sum of twice the smaller number and thrice the greater number is 19. Find the numbers.
Concept: Simple Situational Problems
Solve the following word problem.
To find number of notes that Anushka had, complete the following activity.
Concept: Simple Situational Problems
Solve the Following Word Problem.
Sum of the present ages of Manish and Savita is 31. Manish’s age 3 years ago was 4 times the age of Savita. Find their present ages.
Concept: Simple Situational Problems
Solve the Following Word Problem.
Places A and B are 30 km apart and they are on a st raight road. Hamid travels from A to B on bike. At the same time Joseph starts from B on bike, travels towards A. They meet each other after 20 minutes. If Joseph would have started from B at the same time but in the opposite direction (instead of towards A) Hamid would have caught him after 3 hours. Find the speed of Hamid and Joseph.
Concept: Simple Situational Problems
Select the correct alternative and write it.
What is the degree of the determinant `|[a ,b],[c,d]|`
Concept: Determinant of Order Two
Solve the following simultaneous equations by Cramer's method.
`x+y=7,2x-3y=9`
Concept: Algebraic Methods of Solving a Pair of Linear Equations > Substitution Method
The sum of a two digit number and the number obtained by reversing its digits is 121. Find the number if its units place digit is greater than the tens place digit by 7.
Concept: Simple Situational Problems
If `|( 4,5), (m , 3)|` = 22, then find the value of m.
Concept: Algebraic Methods of Solving a Pair of Linear Equations > Cross - Multiplication Method
