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SRI BHARATHI VIDHYASHRAM!!!!
MATRIC. HR. SEC. SCHOOL STD : IX TIME : 2 ½ Hrs
SUBJECT : MATHS MARK : 100
Section - A
I) Choose the correct Answer 15x1=15
1) If n(AXB) = 6 and A={1,3} then n(B) is ________
(1) 1 (2) 2 (3) 3 (4) 6
2) A={a,b,p}, B={2,3}, C={p,q,r,s} then n[(AUC)XB] is ________
(1) 8 (2) 20 (3) 12 (4) 16
3) If A={1,2}, B={1,2,3,4}, C={5,6} and D={5,6,7,8} then state which of the following statement is true.
(1) (AXC)⊂(BXD) (2) (BXD)⊂(AXC) (3) (AXB)⊂(AXD) (4) (DXA)⊂(BXA)
4) If there are 1024 relations from a set A={1,2,3,4,5} to a set B, then the number of elements in B is ______
(1) 3 (2) 2 (3) 4 (4) 8
5) The range of the relation R={(x,x2)/ x is a prime number less than 13} is ________
(1) {2,3,5,7} (2) {2,3,5,7,11} (3) {4,9,25,49,121} (4) {1,4,9,25,49,121}
6) If the ordered pairs (a+2,4) and (5,2a+b) are equal then (a,b) is ________
(1) (2,-2) (2) (5,1) (3) (2,3) (4) (3,-2)
7) Let n(A)=m and n(B)=n then the total number of non-empty relations that can be defined from A to B is _
(1) mn (2) nm (3) 2mn -1 (4) 2mn
8) For any two non-empty sets A and B, AXB is called as ________
(1) Cartesian product of A and B (2) Cartesian plane (3) Cartesian product of A, B and C (4) None of these
9) If A=φ or B=φ, then AXB = ________
(1) A (2) B (3) φ (4) None of these
10) The co-domain of the relation R is ________
(1) B (2) A (3) φ (4) None of these
11) Relations are subsets of ________
(1) Function (2) Cartesian product (3) Cartesian plane (4) Domain
12) If f(x) =x2+5, then f(-4) = ________
(1) 26 (2) 21 (3) 20 (4) -20 13) If f(a)=b, then b is called ________ of a under f and a is called a ________ of b.
(1) Image,image (2) Pre-image, image (3) Pre-image,pre-image (4) Image,pre-image
14) Let f(x)= 1 .Then what value of x the given f(x) is not defined,
(x-5)
(1) -5 (2) 5 (3) 15 (4) 25
15) If f={(6,3),(8,9),(5,3),(-1,6)}, then the pre-images of 3 are ________
(1) 5 and -1 (2) 6 and 8 (3) 8 and -1 (4) 6 and 5
Section - B
II) Answer any TEN of the following [Q.No :30 is compulsory] 10x2=20
16) If AXB={(3,2),(3,4),(5,2),(5,4)} then find A and B.
17) Let A={1,2,3} and B={a,b}. Find AXB and BXA.
18) Let A={x/x∈N, x ≤4}, B={y/y∈N, y<3}. Find AXB and BXB.
19) Let A={x∈W/3<x<7}, B={x∈N/0<x<3}, C={0,1} Find AX (B∩C).
20) Let A={1,2,3} and B={x/x is a prime number less than 10}. Find AXB and AXA.
21) If the ordered pairs (a+7,4) and (3,4a+b) are equal, then find a and b.
22) A Relation R is given by the set R={(x,y)/y=x+3, x∈{0,1,2,3,4,5}}. Determine its domain and range.
23) Let X={1,2,3,4} and Y={2,4,6,8,10} and R={(1,2),(2,4),(3,6),(4,8)}. Show that R is a function and find its
domain, co-domain and range. 24) Given f(x)=2x-x2, find (i) f(1) (ii) f(x+1) (iii) f(x)+f(1).
25) A relation f is defined by f(x)=x2-2, where x∈{-2,-1,0,3} (i) List the elements of f (ii) Is f a function?
26) Let f={(x,y)/x,y∈N and y=2x} be a relation on N. Find the domain, co-domain and range.
27) Define - Function.
28) A function f is defined by f(x)=3-2x. Find x such that f(x2)=[f(x)]
2.
29) A plane is flying at a speed of 500 km per hour. Express the distance d travelled by the plane as function of time
t in hours.
I MID TERM EXAMINATION 2019 -20!!!!
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30) (a) If A={5,6}, B={4,5,6}, C={5,6,7}, show that AXA=(BXB)∩(CXC).
(or)
(b) Let f(x)=2x+5. If x≠0, then find f(x+2)-f(2)
x
Section - C
III) Answer any NINE of the following [Q.No :45 is compulsory] 9x5=45
31) Find AXB, AXA and BXA
(i) A={2,-2,3} and B={1,-4} (ii) A=B={p,q} (iii) A={m,n}, B=φ
32) Let A={x∈N/1<x<4}, B={x∈W/0≤x<2} and C={x∈N/x<3}. Then verify that AX(BUC)=(AXB)U(AXC).
33) Given A={1,2,3}, B={2,3,5}, C={3,4} and D={1,3,5}, check if (A∩C)X(B∩D)=(AXB)∩(CXD) is true?
34) Let A={ x∈W/x<2}, B={x∈N/1<x≤4} and C={3,5}. Then verify that AX(B∩C)=(AXB)∩(AXC).
35) Given A={2,3,5}, B={1,2,3}, C={2,5}, D={2,3,5}, check if (A∩C)X(B∩D)=(AXB)∩(CXD) is true?
36) Let A={3,4,7,8} and B={1,7,10}. Which of the following sets are relations from A to B?
(i) R1={(3,7), (4,7),(7,10),(8,1)}
(ii) R2={(3,1),(4,12)}
(iii) R3={(3,7),(4,10),(7,7),(7,8),(8,11),(8,7),(8,10)}
37) Represent the given relation by (a) an arrow diagram (b) a graph (c) a set in roster form, wherever possible
R={(x,y)/y=x+3, x,y are natural numbers <10}
38) Given the function f:x→x2-5x+6, evaluate (i) f(-1) (ii) f(2a) (iii) f(2) (iv)f(x-1)
39) If A={1,3,5} and B={2,3}then
(i) find AXB and BXA
(ii) Is AXB=BXA? If not why?
(iii) show that n(AXB)=n(BXA)=n(A)Xn(B).
40) Let A=The set of all natural numbers less than 8, B=The set of all prime numbers less than 8, C=The set of even
prime number. Verity that (A∩B)XC=(AXC)∩(BXC).
41) Let A={1,2,3,.....,45} and R be the relation defined as "is square of " on A. Write R as a subset of AXA. Also, find
the domain and range of R.
42) If X={-5,1,3,4} and Y={a,b,c}, then which of the following relations are functions from X to Y?
(i) R1={(-5,a), (1,a),(3,b)}
(ii) R2={(-5,b),(1,b),(3,a),(4,c)}
(iii) R3={(-5,a),(1,a),(3,b),(4,c),(1,b)}
43) Let X={3,4,6,8}. Determine whether the relation R={(x,f(x))/x∈X, f(x)=x2+1} is a function from X to N? Also,
find domain, co-domain and range.
44) A function f is defined by f(x)=2x+8
(i) find f(4)+f(2)
7
(ii) find x such that f(x)=10
(iii) find x such that f(x)=x
45) (a) Let A={x∈W/3<x<7}, B={x∈N/0<x<3}, C={x∈W/x<2}. Then verify that AX(B∩C)=(AXB)∩(AXC).
(or)
(b) A function f is defined by f(x)=2x-3
(i) find f(0)+f(1) (ii) find x such that f(x)=0
2
(iii) find x such that f(x)=x (iv) find x such that f(x)=f(1-x).
Section - D
IV) Answer the following questions 2x10=20
46) (a) Draw a circle of radius 3cm. Take a point P on this circle and draw a tangent at P.
(or)
(b) Draw a circle of radius 4cm. At a point L on it draw a tangent to the circle using the alternate segment theorem.
47) (a) Draw the graph of the quadratic equation x2+x-12=0 and discuss the nature of solution.
(or)
(b) Draw the graph of the quadratic equation x2-8x+16=0 and discuss the nature of solution.
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