Find next two terms of an A.P.
4, 9, 14, ......
Concept: Arithmetic Progression
State whether the given equation is quadratic or not. Give reason.
`5/4m^2 - 7 = 0`
Concept: Quadratic Equations
if `D_x = 25`, D = 5 are the values of the determinants for certain simultaneous equations in x and y, find x
Concept: Cramer'S Rule
If S = {2, 4, 6, 8, 10, 12} and A = {4, 8, 12}, find A'
Concept: Probability - A Theoretical Approach
Write any one solution of equation x + 2y = 7.
Concept: Linear Equations in Two Variables Applications
If `S_5 = 15` and `S_6 = 21`, Find `t_6`.
Concept: Arithmetic Progression
Find n if the nth term of the following A.P. is 68
5, 8, 11, 14, ..........
Concept: Arithmetic Progression
If one of the roots of the quadratic equation x^{2} - 11x + k = 0 is 9, then find the value of k
Concept: Quadratic Equations Examples and Solutions
A box contains 20 cards marked with numbers 1 to 20. One card is drawn at random. Event A is the number of the card which is multiple of 5. Write S, n(S), A and n(A).
Concept: Concept Or Properties of Probability
Find the value of x- y if 4x + 3y = 25, 3x + 4y = 24
Concept: Linear Equations in Two Variables Applications
Form the quadratic equation if its roots are –3 and 4.
Concept: Nature of Roots
For a certain frequency distribution, the values of mean and median are 72 and 78 respectively. Find the value of mode.
Concept: Median of Grouped Data
For an A.P., find S_{7} if a = 5 and d = 4.
Concept: Arithmetic Progression
Solve the following quadratic equation by using formula method :
2x^{2} - 3x = 2
Concept: Quadratic Equations
Solve the following simultaneous equations using Cramer’s rule :
3x - 2y = 3
2x + y = 16
Concept: Cramer'S Rule
A die is thrown, find the probability of the event of getting a number less than 3.
Concept: Sample Space
The marks obtained by a student in an examination out of 100 are given below. The total marks obtained in various subjects are as follows:
Subject | Marks |
Marathi | 85 |
English | 85 |
Science | 90 |
Mathematics | 100 |
Total | 360 |
Represent the above data using pie diagram
Concept: Pie Diagram
If α + β = 5 and α^{3} +β^{3} = 35, find the quadratic equation whose roots are α and β.
Concept: Quadratic Equations
Two dice are thrown. Find the probability of getting :
1) The sum of the numbers on their upper faces is at least 9.
2) The sum of the numbers on their upper faces is 15.
3) The number on the upper face of the second die is greater than the number on the upper face of the first die.
Concept: Probability Examples and Solutions
Frequency distribution of daily commission received by 100 salesmen is given below :
Daily Commission (in Rs.) |
No. of Salesmen |
100-120 | 20 |
120-140 | 45 |
140-160 | 22 |
160-180 | 09 |
180-200 | 04 |
Find mean daily commission received by salesmen, by the assumed mean method.
Concept: Mean of Grouped Data
A boat takes 10 hours to travel 30 km upstream and 44 km downstream, but it takes 13 hours to travel 40 km upstream and 55 km downstream. Find the speed of the boat in still water and the speed of the stream.
Concept: Linear Equations in Two Variables Applications
If the 9th term of an A.P. is zero, then prove that 29th term is double of 19th term.
Concept: General Term of an Arithmetic Progression
Draw histogram and frequency polygon on the same graph paper for the following frequency distribution
Class | Frequency |
15-20 | 20 |
20-25 | 30 |
25-30 | 50 |
30-35 | 40 |
35-40 | 25 |
40-45 | 10 |
Concept: Histograms, Frequency Polygon and Frequency Curve