**I MID TERM EXAMINATION – 2018**

STD: X MATHEMATICS MARKS: 50

__NOTE: This question paper contains 4 sections__

__Section: I (Marks: 6)__

- Choose the Correct Answer (6 X 1 = 6)

- If A = {p,q,r,s} B = {r,s,t,u} then A/B is
- {p,q} b) {t,u} c) {r,s} d) {p,q,r,s}

- If ACB, then AꓵB is
- B b) A/B c) A d) B/A

- If {(x,2), (4,y)} represents an identity functions, then (x,y) is
- (2,4) b) (4,2) c) (2,2) d) (4,4)

- If f: A->B is a bijective function and if n(A) = 5, then n(B) is equal to

- 10 b) 4 c) 5 d) 25

- The 8
^{th}term of the sequence 1,1,2,3,5,8 …… is

- 25 b) 24 c) 23 d) 21

- The sequence -3,-3,-3,……… is

- An A.P Only b) a G.P. Only c) Neither A.P nor G.P d) both A.P and G.P

__Section: II (Marks: 10)__

- Select any 4 Questions from the first 8 Questions (5 X 2 = 10)

Note: I) Answer 5 Questions ii) Question Number 15 is compulsory,

- If R= { (a,-2) (-5,b), (8,c) (d, -1) } Represent the identity function, find the values of a,b,c and d
- For the given functions F = { (1,3) (2,5) (4,7) (5,9) (3,1) } write the domain and range
- If A={4,6,7,8,9} B={2,4,6} C={1,2,3,5,6} then find AU(BꓵC)
- Find the common difference and 15
^{th}term of the A.P 125,120,115,110,………. - Find the Sn if a=50, n=25 and d=-4
- Let A={1,2,3,4,5} B=N and F:A- > B be defined by f(x) = x2. Find the range of f: Identify the type of function.
- Find the first five terms of the sequence given by a
_{1}= 2 a_{2}= 3+a_{1}and an = 2a_{n-1}+ 5 for n>2 - Let P= {a,b,c} Q = {g,h,x,y} and R = {a,e,f} find R | (pnq)
- How many two-digit numbers are divisible by 13?

**OR**

Which term of the G.P 1,2,4,8……. Is 1024?

__Section: III (Marks: 20)__

- Select any 4 Questions from the first 7 Questions (4 X 5 = 20)

Note: i) Answer 4 Questions ii) Question Number 23 is compulsory,

- Let A = {10,15,20,25,30,35,40,45, 50} B= {1,5,10,15,20,30} and C={7,8,15,20,35,45,48} verify A/(BꓵC) = (A|B) U (A|C)
- In a group of students, 65 play football, 45 play hockey, 42 play cricket, 20 play football and hockey. 25 play football and cricket, 15 play hockey and cricket and 8 play all the three games. Find the number of students in the group

- Let A= {4,6,8,10} and B={3,4,5,6,7} if f:A- > B is defined by f(x) = ½ x+1 then represent f by i) an arrow diagram ii) a set of ordered pair and iii) a table

- Find the sum of all-natural numbers between 300 and 500 which are divisible by 11

- Find he sum to n terms of the series 6+66+666+6666+________

- Use Venn diagrams to verify De morgan’s law for set difference

- The sum of three consecutive terms of a.A.P is 6 and their products is -120. Find the three numbers.

- A Sum of Rs.1000 is deposited every year at 8% simple interest. Calculate the interest at the end of each year. Do these interest amounts form an A.P? If so, find the total interest at the end of 30 years

OR

A function f: [ (1,6) > R is defined as follows

1 + x 1__<__ x < 2

F(x) = 2x – 1 2 __<__ x < 4

3×2 – 10 4__ <__ x < 6

Find the value of i) f(5) ii) f(3) iii) f(1) iv) f(2) – f(4) v) 2f(5)-3f(1)

__Section: IV (Marks: 14)__

- Answer both the question choosing either of the alternatives (2 X 7 = 14)

- Draw a circle of radius 3.2 cm. Take a point P on this circle and draw a tangent at P

**OR**

Draw a circle of radius 4.2 cm, and take any point on the circle Draw a tangent at the point using the centre

- Solve the equation graphically x
^{2}– 4= O

**OR**

Draw the graph of y=x^{2} and hence solve x^{2}-4x-5=0