Class -IX
Subject :Higher Mathematics (Objective)
Time : 40 Minutes Marks 40
1. Which one of the following statements is correct?
a) QÇQ/ =R b) QUQ/ =f
b) QUQ/ =R
d) N={1,2,3,-3,4,-5,………}
2. 1 1 1 -2 -1 0 1 2
The interval of the above number line is-
a) [-2, 2[ b) ] -2, 2 [
c) ] -2, 2] d) [-2, 2]
3. A = [0,2] and B = ]1,3[ are the two intervals of real numbers. AUB =?
a) [0, 3[ b) [ 0, 3 ]
c) [ 0, 2] d) ]0, 2]
4. If C = ] 0, 2 [ and D = [ 1, 3 ] then CÇD=?
a) [1, 2] b) [ 1, 2 [
c) ] 1, 2] d) [1, 3]
5. If P(x) = 3x3 +3x2 -7x +8, then what is the value of P(O) =?
a) 8 b) 0
c) 3 d) 7
6. If D = { 1,2,3,4,5} is a set. The elements of P(D) will be-
a) 12 b) 16
c) 32 d) 64
7. P(x) = 8x2 -7x4 +5x3 -3x2+5x +7 what is the degree of P(x)?
a) 5 b) -7
c) 7 d) 4
8. Q(y) = 5y3- 3y2 +7y - 6 In the polynomial Q(y), what is the leading coefficient ?
a) 7 b) 6
c) -3 d) 5
9. R(x) = x2 -5x +6 Which one of the following factors is the factor of R(x).
a) x -2 b) x -1
c) x -5 d) x -6
10. If you divide 2x3 - 5x2 +6x -2 by x - 1, then you get remainder -
a) 0 b) 2 c) 1 d) 3
11. Given that Q (x,y) = x2 -2xy -y2 then what is the value of Q( 0, 6)?
a) 0 b) 36
c) -36 d) ¹36
12. If A = { -3, 0, 5}, B = { 0, 5, -3} and C={0, 5}, then which one of the following sets is correct?
a) A=B b) C Ì C
c) BÌ C d) B =C
13. Consider the polynomial P(x) where P(x)= x3+1. The value of P(s4) is -
a) S3 +1 b) S6 +1
c) S12 +1 d) S12
A= {3,4,5} and B= { 5, 6}
(From the above data, Answer the questions 14,15)
14. (A-B) Ç (B-A) Ç ( AUB) =?
a) f a) { 3,4,5,6}
c) { 3, 4,5} d) { 5}
15. Which one of the following is the total elements of the set A 
B.
B. a) 5 b) 6
c) 8 d) 9
16. If 5 = { x : x ÎR and x2 + 2 =0, what can you say about S?
a) S =R b) SËR
c) S =f d) S = S/
17. B A = ?
A = ? a) { (x,y) : x ÎB and y ÎA}
b) { (y,x) : y ÎA, x ÎB}
c) { (x,y) : x ÎB or y ÎA}
d) { (x,y) : x ÎA and y ÎB}
18. The closed interval from a to b is -
a) [ a, b[ b) ] a, b [
c) ] a, b ] d) [ a, b]
19. If x -2 is a factor of Q(x) = x2 -5x +6 then Q (2) =?
a) 0 b) 5
c) 2 d) 3
20. If a polynomial P(x) of positive degree is divided by ax +b, where a ¹ 0, the remainder will be-
a) P(a) b) P ( - 
)
) c) P (b) d) P(x)
21. a2 + b2 +c2 -ab -bc -ca =?
a) 
( a+b+c) { (a-b)2 + (b-c)2 +(c-a)2}
( a+b+c) { (a-b)2 + (b-c)2 +(c-a)2} b) {( a+b)2 + (b+c)2 + (c+a)2 }
{( a+b)2 + (b+c)2 + (c+a)2 } c) {( ab+bc)2 + (bc+ca)2 + (ab+ca)2 }
{( ab+bc)2 + (bc+ca)2 + (ab+ca)2 } d) {( a- b)2 + (b- c )2 + (c-a)2}
{( a- b)2 + (b- c )2 + (c-a)2}
22. The shaded region represents the set -
a) A/ b) AUB
c) A\B d) AÇB
23. Who is the deviser of the theory of sets?
a) Grorg cantor b) John Venn
c) Phthagorus d) Euclid
24. Given that A = { x : x ÎN, | < x < 10 } and B= { x: x ÎN, 2 <x < 6}then AÇB will be -
a) { 3,4,5} b) A
c) { 1,2,3, 4,5 } d) { 4, 5 }
25. N(x) = D (x) Q(x) + R(x), for all x, N(x) is called -
a) Dividend b) Divisor
c) Remainder d) Quotient
26. The terms of a polynomial in x, y, z are of the form -
a) Cxyz b) C xp yq zr
c) Cxp yq d) c xp.
27. The shaded region represents the set which is -
a) A\B b) B\A c) AUB d) AÇB
28. In the triangle ABC? Which of the following is/are correct?
i) If ÐC is obtuse, AB2 > BC2 + CA2
ii) If ÐC is a right angle, AB2= BC2 + CA2
iii) If ÐC is acute, AB2 < BC2 + CA2
a) (i) b) (i) and (ii) (c) (i) and (iii)
d) (i), (ii) and (iii).
y B
A 29.
x/ x y C D
In the above figure AC and BD are perpendiculars respectively from A and B on xx/. Therefore the length of the projection of AB is -
a) AB b) CD
c) AC d) BD
A 
30. B D C
In the above 
ABC, ÐB is an acute angle and AD ^ BC. Which one of the following is true?
ABC, ÐB is an acute angle and AD ^ BC. Which one of the following is true? a) AC2= AB2 -BC2-2BC.BD
b) AC2= AB2 +BC2-2BC.CD
c) AC2= AB2 +BC2+2BC.BD
d) AC2= AB2 +BC2-2BC.BD
31. A 
B C D
In the above ABC, ÐC is an obtuse angle and AD is perpendicular to produced BC. Which one of the following is correct?
ABC, ÐC is an obtuse angle and AD is perpendicular to produced BC. Which one of the following is correct? a) AB2 = AC2 +BC2 -2BC.CD
b) AC2 = AB2 +BC2 +2BC.BD
c) AB2 = AC2 +BC2 +2BC.CD
d) AB2 = AC2 +BC2 +2BC.BD
y B 
32. x/ x A D
y
In the above figure, BD^xx/. Therefore the length of the projectionof AB on xx/ is -
a) BD b) AB
c) AD d) xx/
A
33. B D C
In the above triangle ABC, AD is a median of BC By Apollonius theorem, Which one of the following is true?
a) AB2 + BC2 = 2 ( AD2 +BD2)
b) BC2 + CA2 =2AD2 +2CD2
c) AB2 + BC2 =2 (AD2 -BD2)
d) AB2 - BC2 =2(AD2 +BD2)
A34.
B C
In the ABC, ÐB is a right angle, then which one is true?
ABC, ÐB is a right angle, then which one is true? a) AC2 > BC2 +CA2 b) AC2 = AB2 +BC2
c) AB2 = AC2 +BC2 d) BC2 = AB2 +CA2
35. Which one of the following formula is correct?
a) a3 +b3 +c3-3abc=( a+b+c) (a2+b2+c2-ab-bc -ca)
b) a3 +b3 +c3-3abc=( a+b+c) (a2+b2+c2+ab+bc+ca)
c) a3 +b3 +c3-3abc=(a-b-c) (a2+b2+c2-ab-bc -ca)
(a-b-c) (a2+b2+c2-ab-bc -ca)d) a3 +b3 +c3-3abc=(a-b-c) (a2+b2+c2-ab-bc -ca)
36. bc (b -c) + ca ( c -a) + ab ( a -b) =? Which is correct?
a) (a - b) ( b -c ) ( c-a)
b) (a + b) ( b +c ) ( c +a)
c) -(a - b) ( b -c ) ( c-a)
d) -(a + b) ( b -c ) ( c-a)
37. Which one of the following represents the number line? 1 1 1 a b
a) a £ x £ b b) a £ x <b
c) a < x £ b d) a < x < b
38. P ( x, y) = 8x3 + y3 -4x2 + 7xy + 2y -5 then P ( 1, 0) =?
a) 2 b) -1 c) 1 d) -2
39. P(x)=x4-5x3+7x2-a is a polynomial for what value of a x-2 is a factor of P(x) ?
a) 2 b) 3 c) 4 d) 5
40. If a3 +b3 +c3 = 3abc, where a+b+c ¹0 which one of the following is right?
a) a = b =c b) a = b =c =0
c) a< b < c d) a > b > c
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