X: Maths:High Scoring Questions: Pair of Linear Equations in Two Variables

X : Maths: Chapter: PAIR OF LINEAR EQUATIONS IN TWO VARIABLES	Type- 1
1. The pair 2x=3y-5 and 2y= 5x-4 of linear equations represents two lines which are	Ans(c)
(a) Parallel (b) coincident (c) intersecting (d) either parallel or coincident
2.  The pair x=p and y=q of the linear equations in two variables x and y graphically represents two    lines   which are	Ans(c)
(a) Parallel (b) coincident (c) intersecting at(p,q) (d) intersecting at(q,p)
3. If the lines represented by the pair of linear equations 2x+5y=3 and (k+1)x +2(k+2)y=2k are coincident, then  the value of k is	Ans(b)
(a) -3 (b) 3 (c) 1(d) -2
4. If the pair of linear equations (3k+1)x+3y-2=0 and (k2+1 )x+(k-2)y-5=0 inconsistent, then  the value of k is	Ans(b)
(a) 1 (b) -1 (c) 2 (d)-2
5. If the pair of linear equations 2x+3y=11 and 2px+(p+q)y=p+5q has infinitely many solution then   (a) p=2q (b)q=2p (c)p=-2q (d) q= -2p	Ans(b)
X : Maths: Chapter: PAIR OF LINEAR EQUATIONS IN TWO VARIABLES	Type- II
1. Find the value of k for which the given system of equations has unique solution:
2x+3y-5=0, kx-6y-8=0	[Ans k≠ -4]
2. For what value of k will the following system of linear equations have infinite number of solution?         2x+3y-5=2;                  (k+2)x+(2k+1)y=2(k-1)	[Ans k=4]
3. Find two numbers whose sum is 18 and difference is 6.	[Ans 12,6]
4. Solve for x and y.    X+6/y=6, 3x-8/y=5.	[Ans x=3, y=2]
5. The sum of the numerator and the denominator of a fraction is 20 if we subtract 5 from the numerator and 5 from denominator, then the ratio of the numerator and the denominator will be 1:4 .Find the fraction.	[Ans: 7/13]

X : Maths: Chapter: PAIR OF LINEAR EQUATIONS IN TWO VARIABLES	Type- III
1 Solve the following system of equations by using the method of elimination by equating the coefficient   x/10+y/5+1=15,              x/8+y/6=15.	[Ans x=80, y=30]
2. If two digit number is four times  the sum of its digits and twice the  product of digits. Find the number.	Ans: 36
3. Solve the following system of equations.
bx/a- ay/b +a +b=0                  bx –ay +2ab=0	Ans x= -3a, y= -b
4. Solve graphically the system of linear equations. 4x-3y+4=0,       4x +3y=20   also find the area of the region bounded by the lines and x-axis.	Ans x=2, y=4, Area=12 sq. unit]
5. The sum of two natural’s number is 8 and sum of their reciprocals is 8/15. Find the numbers	[Ans 5 and 3]
X : Maths: Chapter: PAIR OF LINEAR EQUATIONS IN TWO VARIABLES	Type- IV
1. Solve for x and y: 2/2x+y – 1/x-2y +5/9 =0                           9/2x+y – 6/x-2y +4    =0	Ans x=2 , y=1/2
2. Draw the graph the following equations:      2x+3y-12=0 and 7x-3y-15=0.Determine the coordinates of the vertices of the triangle formed by the lines and the y-axis	(0,4),(3,2),(0,-5)
3. The sum of the digits of a two- digit number is 12 the number obtained by interchanging the two digits exceed the given number by 18. Find the number.	Ans: 57
4. Abdul traveled 300km by train and 200km by taxi, it took him 5 hours 30 minutes. But if he travels 260 km by train and 240 km by bus he takes 6 minutes longer. Find the speed of the train and of the taxi	Ans 100 km/hr., 80 km/hr.
5. Solve the following pairs of equation for x and y. 15/x-y +22/x+y=5,         40/x-y + 55/x+y =13.	Ans x=8, y=3
6. Find the value of ‘p’ if (-3, p) lies on 7x+2y=14.	SELF
7. Solve the following system of linear equations using the method of cross-multiplication:                               ax +by  =1      and            bx +ay = (a+b)2 / a2+b2 =1	SELF
8. Solve for x and y.         bx +ay = a+b.       and   ax[1/a-b -1/a+b]+ by [1/b-a -1/b+a]=2	SELF

CBSE : IX : Subject: Mathematics assignment for term-II Chapter: Statistics

Class: IX               Subject: Mathematics          Assignment                Chapter: Statistics

1. Write the class size in each of the following:

(a) 0 – 4, 5 – 9, 10 – 14 (b) 10 – 19, 20 – 29, 30 – 39 (c) 5 – 5.01, 5.01 – 5.02, 5.02 – 5.03

2. Write class size and class limits in each of the following if the class marks are:

(a) 104, 114, 124, 134, 144, 154 (b) 47, 52, 57, 62, 67, 72, 77 (c) 12.5, 17.5, 22.5, 27.5, 32.5, 37.5

3. The monthly wages of 30 workers in a factory are given below:-

830, 835, 890, 810, 835, 836, 869, 894, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 836, 878, 840, 868, 890, 806, 840, 890

(a) Form frequency distribution table with class size 10

(b) Find cumulative frequency

(c) Draw histogram and frequency polygon

4. Draw histogram and frequency polygon:

Marks	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70
No. of students	5	10	4	6	7	3	2

5. The following are the scores of two groups of class IX students in a test.

Scores	Group A	Group B
50 – 52	4	2
47 – 49	10	3
44 – 46	15	4
41 – 43	18	8
38 – 40	20	12
35 – 37	12	17
32 - 34	13	22
Total	92	68

6. The mean of 40 observations was 160. It was detected on rechecking that the value of 165 was wrongly copied as 125 for computation of mean. Find the correct mean.

7. The mean monthly salary of 10 members of a group is Rs 1445, one more member whose monthly salary is Rs 1500 has joined the group. Find the mean monthly salary of 11 members.

8. If the mean of the following distribution is 6, find the value of P.

X	2          4          6          8          P + 5
F	3          2          3          1         2

10. Draw a histogram of the following distribution table:

Marks obtained	No of students
0 – 10	4
10 – 20	8
20 – 40	20
40 – 45	10
45 – 60	12
60 – 70	6
70 - 80	10
Total	70

11. The median of the following observations arranged in ascending order, is 25. Find x.

               
      11, 13, 15, 19, x + 2, x + 4, 30, 35, 39, 46

12.The mean of 1, 7, 5, 3, 4 and 4 is m. the numbers 3, 2, 4, 2, 3, 3, and p have mean m – 1 and median q. find p and q.

13. In the following groups of data, tell whether the mean or the median best describes the data:

       
 (i) 6, 4, 2, 12, 2 (ii) 31, 28, 24, 9, 23 (iii) 45, 51, 47, 65, 36 (iv) 10, 20, 30, 100, 9

14. Find the median of the first 10 natural numbers. Is it equal to their mean?

15. The following data has been arranged in ascending order:

         
     24, 27, 28, 31, 34, x, 37, 40, 42, 45.

16. If the median of the data is 35, find x. in the above data, if 45 is changed to 33, find the new median.

17. For what value of x, the mode of the following data is 5?

                2, 4, 3, 5, 4, 5, 6, 4, x, 7, 5

18. A boy scored the following marks in various class tests during a term, each test being marked out of 20:

                16, 10, 7, 17, 9, 16, 14, 19, 20, 18, 12

Find the mean, median and modal marks. Verify if the following relation holds true:

Mean – Mode = 3(Mean – Median)

21. 10 people were asked about the time they spent in a week in doing social work in their community. They said 10, 7, 13, 10, 20, 15, 10, 14, 12, 16 hours resp. Find the mean, mode, median time in a week  devoted by them for social work.

What value we draw from the above data ?

[(a) 91/00   (b) Society becomes aware to avoid accidents and save precious life.]

22.The class marks of a distribution are :8,14,20,26,32,38,44.50.Find the class size and class interval.