Tuesday, December 9, 2014

Model Questions of Higher Mathematics Objective Sample Question for Class-IX



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.
            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)  { (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}
            b)   {( a+b)2 + (b+c)2 + (c+a)2 }
            c)   {( ab+bc)2 + (bc+ca)2 + (ab+ca)2 }
            d)  {( a- b)2 + (b- c )2 + (c-a)2}
Text Box: A       B22.                               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.
Text Box:    A   B
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?
            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?
            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)
           A
34.      
             B                   C
In the 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)
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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