previous year examination questoins...2018/04/10 · maths made easy 1 previous years public...
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SET-6 : SET AND FUNCTION
2 Marks:
1. Given A={1,2,3,4,5}, B={3,4,5,6} and C={5,6,7,8}, Show That A∪(B∪C) =(A∪B)∪C.
2. If ACB, then find A∩B and A\B (Use Venn diagram).
3. Let P = {a, b, c}, Q = {g, h, x, y} and R = {a, e, f, s} find the following.
(i)P\R (ii)Q∩R (iii)R\(P∩Q).
Ans: {a, e, f, s}
4. A={4,6,7,8,9}, B={2,4,6}and C={1,2,3,4,5,6} then find (i)A∪(B∩C) (ii)A∩ (B∪C)
5. Given A={a,x,y,r,s}, B={1,3,5,7,-10}, Verify the commutative property of set Union.
6. Verify the commutative property of set intersection for A={l,m,n,o,2,3,4,7} and
B={2,5,3,-2,m,n,o,p}.
7. For A={x\x is a prime factor of 42}, B={x \ 5< x ≤ 12, x € N} and C={1,4,5,6}, Verify
A∪ (B∪C)=( A∪B) ∪C.
8. For A={5,10,15,20}; B={6,10,12,18,24} and C={7,10,12,14,21,28}, Verify whether
A\(B\C)=(A\B)\C. Justify your answer.
9. Draw Venn diagram of three sets A, B and C. Find A∪ (B∩C).
10. Let U = {4, 8, 12, 16, 20, 24, 28}, A = {8, 16, 24} B = {4, 16, 20, 28} find (A∪B)’
and (A∩B)’.
Ans: (A∪B)’ = {12} (A∩B)’ = {4, 8, 12, 20, 24, 28}
11. 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}.Find
A\(B∩C).
12. Given n(A) = 285, n(B) = 195, n(U) = 500, n(A∪B) = 410, find n(A’∪B’).
Ans: 430
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PREVIOUS YEAR EXAMINATION QUESTOINS
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13. Let A={1,2,3,4} and B={-1,2,3,4,5,6,7,9,11,12}. Let R={(1,3),(2,6),(3,10),(4,9)} be a
relation. Show that R is a function and find its domain, Co-domain and the range of R.
14. Let X={1,2,3,4}. Examine whether each of the relations given below is a function from X to
X or not Explain.
i) f={(2,3),(1,4),(2,1),(3,2),(4,4)}
ii) g={(3,1),(4,2),(2,1)}
iii) h={(2,1),(3,4),(1,4),(4,3)}
15. Which of the following relations are function from A = {1, 4, 9, 16} to
B = {-1, 2, -3, -4, 5, 6}? If it is function. Write down its range.
i) f1={(1,-1),(4,2),(9,-3),(16,-4)}
ii) f2={(4,2),(1,2),(9,2),(16,2)}.
16. 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.
Ans: {1, 4, 9, 16, 25}
17. For the given function F = {(1, 3) (2, 5) (4, 7) (5, 9) (3, 1)}, write the domain and
range.
Ans: Domain = {1, 2, 4, 5, 3} Range = {3, 5, 7, 9, 1}
18. If R = {(a, -2), (-5, 6), (8, c), (d, -1)} represents the identify function, find the values
of a, b, c and d.
Ans: a = -2 b = -5 c = 8 d = -1
19. Write the pre-image of 2 and 3 in the function f = {(12, 2), (13, 3), (15, 3), (14, 2),
(17, 17)}.
Ans: Pre-image of 2 is {12, 14} 3 is {13, 15}
20. The following table represents a function from A = {5, 6, 8, 10} to
B = {19, 15, 9,11} where f(x) = 2x - 1. For what values of a and b it represents a
one - one function?
X 5 6 8 10
F(x) A 11 B 19
Ans: 9 = a 15 = b.
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21. Let A={5,6,7,8}; B={-11,4,7,-10,-7,-9,-13} and f={(x,y): y=3-2x ; x € A, y € B}.
i) Write down the elements of f .
ii) What is the codomain?
iii) What is the range?
iv) Identify the type of function.
5 marks:
1. Verify this using Venn Diagram (A∩B)`= A`∪B`
2. Use Venn diagram, Verify the De Morgan’s Law for set Difference.
A\(B∩C) = (A\B)∪ (A\C).
3. Let U={-2,-1,0,1,2,……10}, A={-2,2,3,4,5} and B={1,3,5,8,9}. Verify Demorgan’s law of
complementation.
4. Let A={a,b,c,d,e,f,g,x,y,z},B={1,2,c,d,e}and C={d,e,f,g,2,y} verify A\(B∪C)=(A\B) ∩ (A\C)
5. Using venn diagram,verify the following. (i) A\(B∪C) = (A\B) ∩ (A\C) (ii) (A∪B)`= A`∩B`
6. A radio station 190 students to determine the types of music they liked. The survey revealed
that 114 liked rock music, 50 liked folk music, and 41 liked classical music, 14 liked rock
and folk music, 15 liked rock and classical music, 11 liked classical and folk music, and 5
liked all the three of music. find
i) How many did not like any of the 3 types?
ii) How many liked any two types only?
iii) How many liked folk music but not rock music?
7. In a town 85% of the people speak Tamil, 40% speak English and 20% speak
Hindi. Also, 32% speak English and Tamil, 13% speak Tamil and Hindi and
10% speak English and Hindi. Find the percentage of people who can speak
All the three languages.
Ans: All three languages speak Percentage = 30%
8. In a school of 4000 students, 2000 know French, 3000 know Tamil and 500 know Hindi,
1500 know French and Tamil, 300 know French and Hindi, 200 know Tamil and Hindi, and
50 know all the three languages. Find
i) How many do not know any of the three languages?
ii) How many at least know one language?
iii) How many know only two languages?
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9. Let |x|={x if x≥0
-x if x<0 where x€R. Does the relation {(x,y)\ y=|x|, x€R} define a function? Find
its range.
10. Let A = {0, 1, 2, 3} and B = {1,3,5,7,9} be two sets. Let f : A → B be a function
given by f(x) = 2x + 1. Represent this function as (i) a set of ordered pairs (ii) a
table (iii) an arrow diagram and (iv) a graph.
11. A function f : [1, 6) → R is defined as follows :
1+x, 1≤x<2
F(x)= 2x-1, 2≤x<4
3x2-10, 4≤x<6
Find the value of i) f(5) ii) f(3) iii) f(1) iv) f(2) - f(4) v) 2f(5) - 3 f(1)
Ans: i) 65 ii) 5 iii) 2 iv) -35 v) 124
12. If x={1,2,3,4,5}, Y={1,3,5,7,9}determine which of the following relations from x to y are
functions? Give reason for your answer. If it is a function, state its type.
i) R1={(x,y)\y=x+2,x€X, y€Y}
ii) R2={(1,1),(2,1),(3,3),(4,3),(5,5)}
iii) R3={(1,1),(1,3),(3,5),(3,1),(5,7)}
iv) R4={(1,3),(2,5),(4,7),(5,9),(3,1)}
13. Let A = {6, 9, 15, 18, 21}, B = { 1, 2, 4, 5, 6} and f : A → B be defined by
f(x) = x −3 Represent f by, (i) an arrow diagram (ii) a set of ordered pairs.(iii) a table
3
(iv)a graph.
14. Let A = {4, 6, 8, 10} and B = { 3, 4, 5, 6, 7}. If f : A → B is defined by f(x) = 1⁄2 (x+1)
then represent f by (1) an arrow diagram (2) a set of ordered pairs and (3) a
table.
15. A function f : [-3, 7] → R is defined as follows :
4x2-1; -3≤x<2
F(x)= 3x-2 ; 2 ≤x≤4
2x-3 ; 4<x<7
Find i)f(5)+f(6) ii)f(1)-f(-3)
iii)f(-2)-f(4) iv)f(3)-f(-1)
2f(6)-f(1)
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16. A function f:[-7,6) →R is defined as follows :
x2+2x+1; -7≤x< -5
F(x)= x+5 ; -5≤x≤ 2
x-1 ; 2<x< 6
Find (i) 2f(-4)+3f(2) (ii) f(-7)-f(-3) (iii) 4f(-3)+2f(4)
f(-6)-3f(1)
17. If f: N→N is defined by f(x)=x2-1, check whether f is not a function, find for what choice of
the co-domain, f will be a function?
18. Let A=z\{0} and f:A→R be defined by f(x)=|x|/x, x€A. Find the range and type of the
function. Is it one-to-one?
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MATHS MADE EASY
1
PREVIOUS YEARS PUBLIC EXAMINATION QUETIONS
SET-1 : 2. SEQUENCE AND SERIES
2marks:
1. Give an example for a function which is not a sequence.
2. Find the 12thterm of the A.P. √2, 3√2, 5√2…….
3. Find the first term and common difference of the A.P. 1/2 , 5/6 , 7/6 ,
3/2 , ……….,17/6
4. Find the 17th term of the A.P: 4, 9, 14…….
5. In an A.P 5 times of the fifth term is equal to 7 times of the seventh
term. Prove that 12th term is 0.
6. Write the first three terms of the sequence whose nth term is given by
an= n (n-2)/3.
7. In a flower garden, there are 23 rose plants in a first row, 21 in the
second row and 19 in the third row and so on. There are 5 rose plants in
the last row. How many rows are there in the flower garden?
8. If -2/7, m,-7(m+2)/2 are in G.P. Find the values of m.
9. Find the number of terms in the arithmetic series 5+11+17+……+95.
10. In an arithmetic series Sn=1275. First term a=3, common difference d=4.
Find n.
11. How many two digit numbers are divisible by 13?
12. Find the sum of the arithmetic series 5+11+17+……..+95.
13. Find the sum of the series 31+33+35+………. +53?
14. Find the sum of the series 13+23+33+……….+203.
15. Find the sum of the first 10 terms of the series 12-22+32-42+………
5marks:
1. If 7 times the 7th term of an Arithmetic progression is equal to 11 times
its 11th term, show that its 18th term is zero. Can you find the first term
and the common difference? Justify your answer.
2. If the 10th and 18th terms of an A.P. are 41 and 73 respectively. Find the
27th term.
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MATHS MADE EASY
2
3. The sum of four consecutive terms of an A.P. is 20 and the sum of their
squares is 120. Find those numbers.
4. The 4th term of a geometric sequence is 2/3 and the seventh term is
16/81. Find the geometric sequence.
5. If a, b, c and d are in geometric sequence, then prove that,
(b-c)2+(c-a)2+(d-b)2=(a-d)2.
6. If the 4th and 7th terms of a G.P. are 54 and 1458 respectively, find the
G.P.
7. A gardener plans to construct a trapezoidal shaped structure in his
garden. The longer side of trapezoid needs to start with a row of 97
bricks. Each row must be decreased by 2 bricks on each end and the
construction should stop at 2500th row. How many bricks does he need
to buy?
8. If 1/x+y, 1/2y, 1/y+z are three consecutive terms of an A.P. then prove
that x, y, z are three consecutive terms of a G.P.
9. In an arithmetic series, the sum of the first 14 terms is -203 and the sum
of the next 11 terms is -572. Find the arithmetic series.
10. The ratio of the sums of first m and first n terms of an arithmetic series is
m2:n2. Show that the ratio of the mth and nth terms is (2m-1):(2n-1).
11. Find the sum of all 3 digit natural numbers is divisible by 9.
12. Find the sum to n terms of the series 6+66+666+………..
13. Find the sum to first n terms of the series 7+77+777+………..
14. Find the sum of the first 2n terms of the series 12-22+32-42+………
15. Find the sum of the series 122+132+142+…..+352.
16. Find the sum of all natural numbers between 300 and 500 which are
divisible by 11.
17. Find the sum of the series 2+4(3)2+6(5)2+8(7)2+…….+22(21)2.
18. Find the total area of 14 squares whose sides are 11cm, 12cm, 13cm,
………24cm.
19. Find the total volume of 15 cubes whose edges are 16 cm, 17cm, 18cm,
…………..,30cm respectively.
20. If s1, s2 and s3 are the sum of first n, 2n and 3n terms of a geometric
series respectively, then prove that s1(s3-s2)=( s2-s1)2.
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MATHS MADE EASY
PREVIOUS YEARS PUBLIC EXAMINATION QUESTIONS
SET-4 : ALGEBRA
2MARKS:
1. Solve by Elimination Method:
3x-5y= -16
2x+5y= 31
2. Solve by Elimination Method:
13x+11y=70
11x+13y=74
3. Solve: 3x+5y=25
7x+6y=30
4. Form a quadratic equation whose roots are 3,4.
5. Form a quadratic equation whose roots are 3+√7, 3-√7.
6. Form a quadratic equation where sum and product of the roots are -4 and 3.
7. If -5 is a root of the quadratic equation 2x2+px-15=0. Find the value of p.
8. Form a quadratic equation whose roots are 7+√3,7-√3.
9. Solve x and y if 2x+y 5
x-3y = 13
10. Solve: 3x-8/x = 2
11. Solve : x+ 1 = 26
x 5
12. Form a quadratic equation with zeros at x=1/4, -1.
13. Find the value of k for which the roots are real and equal in 12x2+4kx+3=0.
14. If α and β are the roots of the equation 3x2-6x+4=0.Find α
2 +β
2?
15. If α and β are the roots of the equation 3x2-5x+2=0.Find the value of α + β
β α
16. If the sum and product of the roots of the quadratic equation ax2-5x+c=0 are both equal to
10. Then find the value of a and c.
17. Determine the nature of the roots of the equation (x-2a)(x-2b)=4ab.
18. Find L.C.M of 3(a-1),2(a-1)2,(a
2-1).
19. Find L.C.M of x2y+xy
2, x
2+xy
20. Find G.C.D of m2-3m-18, m
2+5m+6.
21. Simplify 6x2+9x
3x2-12x
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MATHS MADE EASY
22. Simplify x3 + 8
x-2 2-x
23. Simplify 5x+20
7x+28
24. Simplify x2-4 x a
3-a
a2-1 x
3+2x
2
25. Find the quotient and remainder when 3x3-17x
2+31x+12 is divided by (3x-2).
26. If the product of two consecutive even numbers is 24. Find the numbers?
27. If the sum of two consecutive odd numbers is 20. Find the numbers?
28. The base of a triangle is 4cm longer than its altitude. The area of triangle is 48cm2. Then
find its base and altitude.
5marks:
1. The cost of 11 pencils and 3 erasers is Rs.50 and the cost of 8 pencils and 3 erasers is
Rs.38. Find the cost of each pencil and each eraser.
2. Factorize: x3-3x
2-10x+24
3. Factorize: x3-23x
2+142x-120
4. Factorize: x3-5x
2-2x+24
5. Factorize: 2x3-3x
2-3x+2
6. Find the G.C.D of 3x4+6x
3-12x
2-24x and 4x
4+14x
3+8x
2-8x
7. Find the L.C.M of x3+y
3, x
3-y
3, x
4+x
2y
2+y
4
8. If P= x/x+y , Q=y/x+y then find 1/P-Q – 2Q/P2-Q
2
9. Simplify 1/x2+3x+2 + 1/x
2+5x+6 – 2/x
2+4x+3
10. Which rational expression should be subtracted from 4x3-7x
2+5 to get 2x
2-5x+1 ?
2x-1
11. Simplify a2-16 x 2a
2-3a-2 ÷ 3a
2-11a-4
a3-8 2a
2+9a+4 a
2+2a+4
12. Find the square root of x4-10x
3+37x
2-60x+36
13. Find the square root of 4+25x2-12x-24x
3+16x
4
14. Find the square root of x4-6x
3+19x
2-30x+25
15. Find the square root of 4x4+8x
3+8x
2+4x+1
16. If m-nx+28x2+12x
3+9x
4 is a perfect square, then find the values of m and n.
17. If 16x4-12x
3+(a-1)x
2+(b+1)x+49 is a perfect square. Find a,b.
18. If 4x4-12x
3+37x
2+ax+b is a perfect square. Find a,b.
19. If x4-4x
3+10x
2-ax+b is a perfect square. Find a,b.
20. Solve x + x+1 = 61
x+1 x 30
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MATHS MADE EASY
21. Sum of two numbers is 24 and sum of their reciprocals is 1/6 , find the numbers.
22. The sum of the numerator and denominator of a fraction is 12. If 3 is added to the
denominator, it is 2 times of the numerator. Find the fraction.
23. One year ago, a man was 8 times as old as his son. Now his age is equal to the square of
the his son’s age. Find their present ages.
24. Speed of a boat in still water is 15km/hr. it goes 30km upstream and return downstream
to the original point in 4hr 30 min. Find the speed of the stream.
25. The length of a verandah is 3m more than its verandah. The numerical value of its area is
equal to the numerical value of its perimeter. Find the length and breadth of the verandah.
26. The train covers a distance of 90km at a uniform speed. Had the speed been 15km/hr
more, it would have taken 30 minutes less for the journey. Find the original speed of the
train.
27. A car left 30 minutes later than the scheduled time. In order to reach its destination
150km away in time, it has to increase its speed by 15km/hr from its usual speed. Find its
usual speed.
28. If one root of the equation 2x2-ax+64=0 is twice the other, then find the value of a.
29. If α and β are roots of 3x2-6x+1=0.then form an equation whose roots are:
i) α2β, β
2α ii)2α+β,2β+α iii)1/α , 1/β
30. If the equation (1+m2)x
2+2mcx+c
2–a
2=0 has equal roots, then P.T c
2=a
2(1+m
2).
31. If α and β are the roots of the equation x2-3x+1=0 then form a quadratic equation whose
roots are 1/ α+β and 1/ αβ .
32. If α and β are the roots of the equation 3x2-4x+1=0 form a quadratic equation whose
roots are α2 / β and β
2/ α .
33. If α and β are the roots of the equation 3x2-6x+4=0 find the values of α
2+β
2 .
34. if a quadratic equation is divided by (x-2) and (x+1) leaves the remainder 11 and 1
respectively. Find the polynomial.
35. Person A takes 6 days less than time taken by person B finish a work. If both A and B
together can finish it in 4 days. Find the time taken by B to finish that work by himself.
36. The sum of the reciprocals of (x+2) and (x-2) is equal to 6 times the reciprocal of 4x+7.
Find x.
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MATHS MADE EASY
1
4.MATRICES
2MARKS:
1. Construct a 2x3 matrix A=[aij] whose elements area given by aij=|2i-3j|.
2. If A= 8 5 2 then find AT
and (AT )
T .
1 -3 4
3. A matrix consist of 30 elements. What are the possible order it can have?
4. Construct a 2x2 matrix A=[aij] whose elements are given by
i) aij =2i-j
ii) aij = i-j/i+j
5. If A= 5 6 -2 3 and B= 3 -1 4 7 ,then find A+B?
1 0 4 2 2 8 2 3
6. Solve for x and y if 2x+y = 5
x-3y 13
7x+y
7. Find = 9Y+zx,y and z if
z- 05
8. If A= 2 3 _ 1 5 then find the additive inverse of A.
-9 5 7 -1
9. 8and B=23Let A= -1 find the matrix C if C=2A+B.
5 1 34
10) If A= 4 -2 and B= 8 2 find 6A-3B.
5 -9 -1 -3
PREVIOUS YEARS PUBLIC EXAMINATION QUETIONS
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MATHS MADE EASY
2
11) Determine whether each matrix product is defined or not. If the product is
defined, state the dimension of the product matrix.
i) A2x5 and B5x4 ii) A1x3 and B4x3
12. Solve 3 2 x = 8
4 5 y 13
13. If A= 1 3 , then verify AI=IA=A, where I is the unit matrix of order 2.
9 -6
14. Find the product of the matrices, if exists,
i) 3 -2 4 1 ii) 2 9 -3 4 2
5 1 2 7 4 -1 0 -6 7
-2 1
iii) 6 2 -7
-3
2MARKS:
1. If A= a b and I2= 1 0 then show that A2-(a+d)A=(bc-ad)I2.
c d 0 1
2. If A= 3 2 B= -2 5 and C= 1 1 verify that A(B+C)=AB+AC.
-1 4 6 7 -5 3
-2
3. If A= 4 and B= 1 -3 6 , then verify that (AB)T=BTAT.
5
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3
4) If A= 1 -1 then show that A2-4A+5I2=0
2 3
5) If A= 5 2 and B= 2 -1 verify that (AB)T=BTAT.
7 3 -1 1
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MATHS MADE EASY
PREVIOUS YEARS PUBLIC EXAMINATION QUESTIONS
SET-5 : TRIGONOMETRY
2MARKS:
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5 MARKS:
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PREVIOUS YEARS PUBLIC EXAMINATION
QUESTIONS
SET-3 : MENSURATION
2marks: 1. 2. 3. 4.
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6. 7.
8.
9.
10.
11.
12.
13.
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14.
15.
16.
17.
18.
19.
20.
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21. 22. 23. 24. 25. 26.
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5marks: 1. 2. 3. 4. 5. 6.
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7. 8. 9.
10.
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11. 12. 13. 14. 15.
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16. 17. 18. 19. 20. 21. 22.
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23. 24. Facebook Link: https://www.facebook.com/mathsmadeeasyforyou/
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