9th Class Mathematics Sample Paper

done Maths Olympiad Model Test Paper-16 Total Questions - 50    [Download]

• question_answer1)
  Which one of the following is a polynomial?
  A)
   \[\frac{{{x}^{3}}}{9}-\frac{3}{{{x}^{-3}}}+\sqrt{x}\]          
  done clear
  B)
   \[{{x}^{3}}-\frac{3{{x}^{{}^{7}/{}_{3}}}}{\sqrt[3]{x}}+\frac{{{x}^{{}^{-1}/{}_{2}}}}{{{x}^{{}^{1}/{}_{2}}}}\]
  done clear
  C)
   \[{{x}^{2}}-3\sqrt{5}x+\sqrt{2}+{{x}^{-1}}\]
  done clear
  D)
  \[\frac{{{x}^{{}^{3}/{}_{2}}}}{{{x}^{{}^{1}/{}_{2}}}}+\frac{2{{x}^{{}^{7}/{}_{5}}}}{{{x}^{{}^{1}/{}_{5}}}}+\frac{8{{x}^{2}}}{{{x}^{-1}}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer2)
  If\[x=17+12\sqrt{2},\] then the value of \[{{x}^{{}^{1}/{}_{4}}}-{{x}^{{}^{-1}/{}_{4}}}\] is equal to:
  A)
   0                                
  done clear
  B)
   1
  done clear
  C)
   2        
  done clear
  D)
   3
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer3)
  Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
  A)
   \[\frac{1}{2}\]                         
  done clear
  B)
   \[\frac{3}{4}\]
  done clear
  C)
   \[\frac{3}{8}\]                         
  done clear
  D)
   \[\frac{5}{16}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer4)
  Which one of the following relations is false?
  A)
   \[\frac{7\pi }{4}=315{}^\circ \]           
  done clear
  B)
   \[\frac{3\,\pi }{2}=270{}^\circ \]
  done clear
  C)
   \[\frac{4\pi }{16}=90{}^\circ \]
  done clear
  D)
   \[\frac{\pi }{3}=60{}^\circ \]   
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer5)
  In the figure given below \[\angle PAQ=59{}^\circ ,\] \[\angle APD=40{}^\circ \]then \[\angle AQB\] is equal of following?
  A)
   \[19{}^\circ \]                         
  done clear
  B)
   \[20{}^\circ \]
  done clear
  C)
   \[22{}^\circ \]             
  done clear
  D)
   \[27{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer6)
  In a quadrilateral with distinct sides, if diagonals AC and BD intersects at right angle, then which of the following is true?
  A)
   \[A{{B}^{2}}+B{{C}^{2}}=C{{D}^{2}}+D{{A}^{2}}\]
  done clear
  B)
   \[A{{B}^{2}}+C{{D}^{2}}=B{{C}^{2}}+D{{A}^{2}}\]
  done clear
  C)
   \[A{{B}^{2}}+A{{D}^{2}}+=B{{C}^{2}}+C{{D}^{2}}\]
  done clear
  D)
   \[A{{B}^{2}}+B{{C}^{2}}=2(C{{D}^{2}}+D{{A}^{2}})\]
  done clear
  E)
   None of these    
  done clear
  View Answer play_arrow

• question_answer7)
  On which dates of April, 2001, did Wednesday fall?
  A)
   1st, 8th, 15th, 22nd, 29th
  done clear
  B)
   2nd, 9th, 16th, 23rd, 30th
  done clear
  C)
   3rd, 10th, 17th, 24th
  done clear
  D)
   4th, 11th, 18th, 25th
  done clear
  E)
   None of these 
  done clear
  View Answer play_arrow

• question_answer8)
  If \[{{\log }_{a}}(ab)=x,\] then \[{{\log }_{b}}(ab)\]is:
  A)
   \[\frac{1}{x}\]                         
  done clear
  B)
   \[\frac{x}{x+1}\]
  done clear
  C)
   \[\frac{x}{1-x}\]                       
  done clear
  D)
   \[\frac{x}{x-1}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer9)
  Which of the following quantity is an integer?
  A)
   \[[(\sqrt{2}+\sqrt{3})/(\sqrt{3}-\sqrt{2})]+\sqrt{6}\]
  done clear
  B)
   \[[(\sqrt{2}+\sqrt{3})/(\sqrt{3}-\sqrt{2})]+2\sqrt{6}\]
  done clear
  C)
   \[[(\sqrt{2}+\sqrt{3})/(\sqrt{2}-\sqrt{3})]+2\sqrt{6}\]
  done clear
  D)
   \[[(\sqrt{2}+\sqrt{3})/(\sqrt{2}-\sqrt{3})]+\sqrt{6}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer10)
  If the mean of 6 observations \[x,\]\[x+3,\,\]\[x+6,\]\[x+9,\]\[x+12,\]\[x+15\] is 18. Find the mean of first 4 observations.
  A)
   45                               
  done clear
  B)
   36
  done clear
  C)
   25                               
  done clear
  D)
   15
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer11)
  A tent of height 77 dm is in the form of a right circular cylinder of diameter 36 m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at Rs. 3.50 per \[{{m}^{2}}\].\[\left( use\,\pi =\frac{22}{7} \right)\].
  A)
   Rs. 5965.80                 
  done clear
  B)
   Rs. 6365.80
  done clear
  C)
   Rs. 6965.80                 
  done clear
  D)
   Rs. 5365.80
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer12)
  If \[a(x)=6{{x}^{4}}-3{{x}^{2}}-7x+4\] and \[b(y)=2{{y}^{4}}-3{{y}^{3}}-\,6y+3,\] then find the value of \[\left[ \frac{5}{2}.a\,(2)+\frac{7}{3}.b\,(3) \right]\].
  A)
   739                             
  done clear
  B)
   593
  done clear
  C)
   469                             
  done clear
  D)
   339
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer13)
  If \[x=\frac{5-\sqrt{21}}{2},\] then find the value of \[\left( {{x}^{3}}\,+\,\frac{1}{{{x}^{3}}} \right)\,-\,5\,\left( {{x}^{2}}\,+\,\frac{1}{{{x}^{2}}} \right)\,+\,\left( x\,+\,\frac{1}{x} \right)\]
  A)
   1                                
  done clear
  B)
   110
  done clear
  C)
   23                               
  done clear
  D)
   0
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer14)
  If \[\frac{4}{2+\sqrt{3}+\sqrt{7}}=\sqrt{a}+\sqrt{b}-\sqrt{c},\] then
  A)
   \[a=1,\,b=\frac{4}{3},\,c=\frac{7}{3}\]
  done clear
  B)
   \[a=1,\,b=\frac{2}{3},\,c=\frac{7}{9}\]
  done clear
  C)
   \[a=\frac{2}{3},\,b=1,\,c=\frac{7}{3}\]
  done clear
  D)
   \[a=7,\,b=\frac{4}{3},\,c=\frac{3}{7}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer15)
  The height of right circular cone is 20 cm and the radius of its base in 4.5 cm. It is cut off through the mid-point of its height parallel to the base. Find the ratio of the volume of the upper part to that of the lower part.
  A)
   3 : 7                            
  done clear
  B)
   7 : 3
  done clear
  C)
   7 : 1                            
  done clear
  D)
   1 : 7
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer16)
  The area bounded by y-axis, \[2x+3y=12\] and \[x-y=1\] is....
  A)
   7.5 square unit 
  done clear
  B)
   13.5 square unit
  done clear
  C)
   4.5 square unit 
  done clear
  D)
   75 square unit
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer17)
  A square of side a cm is cut from each corner of a square sheet of side 12 cm. The remaining sheet is folded to form a cuboid. If the minimum possible volume of the cuboid is M cubic cm & a is an integer, then M is
  A)
   20       
  done clear
  B)
   64
  done clear
  C)
   32                               
  done clear
  D)
   16
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer18)
  If\[\tan \theta =\frac{3}{4},\] then the value of \[{{(\tan \theta +\sec \theta )}^{2}}\] is:
  A)
   \[\frac{4}{5}\]                         
  done clear
  B)
   4
  done clear
  C)
   \[\frac{4}{3}\]                         
  done clear
  D)
   \[\frac{5}{4}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer19)
  Find the mean of the following frequency distribution:

  Class Interval	50-70	70-90	90-110	110-130	130-150	150-170
  Frequency	18	12	13	27	8	22

  A)
   112.2  
  done clear
  B)
   113.2
  done clear
  C)
   114.5              
  done clear
  D)
   115.3
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer20)
  Find the median for the following frequency distribution:

  Height (in cm)	Frequency	Height (in cm)	Frequency
  160 - 162	15	169 - 171	118
  163 - 165	117	171 - 174	14
  166 - 168	136

  A)
   168 cm            
  done clear
  B)
   167 cm
  done clear
  C)
   189 cm            
  done clear
  D)
   198 cm
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer21)
  In a trapezium\[ABCD,\,AB\parallel DC\]. Find the possible values of x.
  A)
   6, 8                             
  done clear
  B)
   9, 6
  done clear
  C)
   7, 9                             
  done clear
  D)
   8, 9
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer22)
  In the given figure PQ, QR and RP touches a given circle respectively at point L, M and N. If \[\angle \,LMN=60{}^\circ \]and\[\angle \,MNL=45{}^\circ ,\] then find the value of \[(\angle P-\angle Q+\angle R)\].
  A)
   \[180{}^\circ \]           
  done clear
  B)
   \[120{}^\circ \]
  done clear
  C)
   \[60{}^\circ \]                         
  done clear
  D)
   \[0{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer23)
  Three points P, Q, R lie on the side BC of triangle ABC such that BP = PQ = QR = RC. If G be centroid of\[\Delta \,ABC,\] then what is ratio of areas of \[\Delta \,PGR\] and \[\Delta \,ABC\].
  A)
   \[\frac{2}{5}\]                         
  done clear
  B)
   \[\frac{3}{4}\]
  done clear
  C)
   \[\frac{1}{6}\] 
  done clear
  D)
   \[\frac{4}{7}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer24)
  The sides of a triangle measure 4 cm, 3.4 cm and 2.2 cm. Three circles are drawn with centres at A, B and C in such a way that each circle touches the other two. Then, the diameters of these circles would measure (in cm)                                             
  A)
   1.11, 1.7, 5.0   
  done clear
  B)
   1.6, 2.8, 5.2
  done clear
  C)
   1.5, 2.9, 5.2                 
  done clear
  D)
   1.6, 3.0, 5.0                   
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer25)
  ABC is a given triangle. AD, BE and CF are altitudes of\[\Delta \,ABC\].

  Assertion (A): \[(A{{B}^{2}}+B{{C}^{2}}+C{{A}^{2}})\] \[>\]\[(A{{D}^{2}}+B{{E}^{2}}+C{{F}^{2}})\]

  Reason (R): \[(A{{E}^{2}}-A{{F}^{2}})+(B{{F}^{2}}-B{{D}^{2}})\] \[+\]\[(C{{D}^{2}}-C{{E}^{2}})=0\]

  A)
   Both Assertion A and Reason R are correct and Reason R is a correct explanation of Assertion A.
  done clear
  B)
   Both Assertion A and Reason R are correct but Reason R is not the correct explanation of Assertion A.
  done clear
  C)
   Assertion A is correct, Reason R is wrong.
  done clear
  D)
   Assertion A is wrong. Reason R is correct.
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer26)
  In the shown figure, AD & BC are two chords of the circle with centre O, intersecting at E and AE = 6 cm, BE = 5 cm.

  Find the value of \[\frac{EC+ED}{EC-ED}\]

  A)
   11 cm 
  done clear
  B)
   5 cm
  done clear
  C)
   8 cm                           
  done clear
  D)
   10 cm
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer27)
  A owes B, Rs. 1573 payable \[1\frac{1}{2}\] years hence. Also B owes A, Rs. 1444.50 payable 6 months hence. If they want to settle the account forthwith, keeping 14 % as the rate of interest, then who should pay and how much?
  A)
   A, Rs. 28.50                 
  done clear
  B)
   B, Rs. 37.50
  done clear
  C)
   A, Rs. 50                     
  done clear
  D)
   B, Rs. 50     
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer28)
  Following are the marks obtained (Out of 50) by the students in a class.

  Marks	Numbers of Students
  10 - 20	8
  20 - 30	X
  30 - 40	9
  40 - 50	6

  One student from the class is selected at random. If the probability that his marks is 20 or more but less than 40, is \[\frac{5}{7},\] then the value of x is
  A)
   13                               
  done clear
  B)
   18
  done clear
  C)
   6                                
  done clear
  D)
   26
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer29)
  Find the cube root of\[72-32\sqrt{5}\].
  A)
   \[3-\sqrt{5}\]
  done clear
  B)
   \[5-\sqrt{5}\]
  done clear
  C)
   \[2\sqrt{2}-3\sqrt{5}\]               
  done clear
  D)
   \[(3-\sqrt{5})(5-\sqrt{5})\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer30)
  The LCM & HCF of the polynomials \[p\,(x)=51{{x}^{2}}\,{{(x+3)}^{3}}\,{{(x-2)}^{2}}\]and \[q\,(x)=34x\,{{(x-1)}^{5}}\,{{(x-2)}^{3}}\] are respectively.
  A)
   \[102{{x}^{2}}{{(x-1)}^{5}}{{(x-2)}^{3}}{{(x+3)}^{3}}\,and\,17{{x}^{2}}{{(x-2)}^{2}}\]
  done clear
  B)
   \[204{{x}^{2}}{{(x-1)}^{5}}{{(x-2)}^{3}}{{(x+3)}^{3}}\,and\,17x(x-2)\]
  done clear
  C)
   \[102{{x}^{2}}{{(x-1)}^{5}}{{(x-2)}^{3}}{{(x+3)}^{3}}\,and\,17x{{(x-2)}^{2}}\]
  done clear
  D)
   \[102{{x}^{2}}{{(x-1)}^{5}}{{(x-2)}^{2}}{{(x+3)}^{3}}\,and\,17x{{(x-2)}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer31)

  Directions: Study the following information carefully and answer the question which follow-

  'X # Y' means 'X is mother of Y'

  'X @ Y' means 'X is brother of Y'

  'X = Y' means 'X is wife of Y'

  'X $ Y' means 'X is father of Y'

  'X % Y' means 'X is son of Y'

  If the statement 'T#P%O@C$I' is true, then which one of the following relations is false?
  A)
   P is nephew of C
  done clear
  B)
   C is brother-in-law of T
  done clear
  C)
   P is cousin of I
  done clear
  D)
   I is nephew of T
  done clear
  E)
   More than one of the above     
  done clear
  View Answer play_arrow

• question_answer32)

  Directions: Study the following information carefully and answer the question which follow-

  'X # Y' means 'X is mother of Y'

  'X @ Y' means 'X is brother of Y'

  'X = Y' means 'X is wife of Y'

  'X $ Y' means 'X is father of Y'

  'X % Y' means 'X is son of Y'

  If the statement 'B$T=I%O#N@J' is true then which one of the following relations is true?
  A)
   B is father of N
  done clear
  B)
   I is son-in-law of B
  done clear
  C)
   B is father-in-law of N    
  done clear
  D)
   O is wife of B
  done clear
  E)
   J is brother-in-law of T
  done clear
  View Answer play_arrow

• question_answer33)
  A is older than B and D. C is older than B but younger than E. D is older than E. Who among them is second youngest?
  A)
   D                                
  done clear
  B)
   A
  done clear
  C)
   C        
  done clear
  D)
   E
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer34)
  In a family of 6 members A, B, C, P, Q and R, father of B is elder than P. A is younger than only three members of the family. Q, wife of B is elder than C, who is not the youngest. P is second eldest. Who is third eldest among them?
  A)
   R                                
  done clear
  B)
   Q
  done clear
  C)
   B                                
  done clear
  D)
   C
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer35)
  Among 6 persons, Ravi is elder than Mohan but younger than Rohit. Arpit is elder than only 1 person. Sachin is younger than Deepak, who is third eldest among them while Mohan is not the youngest. If they are arranged in descending order of their age then how many persons are in between Rohit and Sachin?
  A)
   One                            
  done clear
  B)
   Two
  done clear
  C)
   Three              
  done clear
  D)
   Four
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer36)

  Directions: Each of the questions below consists of a question and two statements numbered I and II. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and answer.

  Mohan is shorter than Kapil and David is taller than Manav. Who is the shortest among them?

  Statements:

  I. Kapil is taller than David.

  II. Manav is taller than Kapil.

  A)
   The data in statement I alone is sufficient to answer the question while the data in statement II is not sufficient to    answer the question.
  done clear
  B)
   The data in statement II alone is sufficient to answer the question while the data in statement I is not sufficient to   answer the question.
  done clear
  C)
   The data in either statement I alone or statement II alone is sufficient to answer the question.
  done clear
  D)
   The data even in both the statements 1 and II together is not sufficient to answer the question.
  done clear
  E)
   The data in both the statements I and II together is necessarily to answer the question.
  done clear
  View Answer play_arrow

• question_answer37)

  Directions: Each of the questions below consists of a question and two statements numbered I and II. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and answer.

  A, B, C, D and E are sitting around a circular table facing the centre. Who is on the immediate right of A?

  Statements:

  I. E is seated immediate left of B and E is not near to C.

  II. Only D is seated between A and C.

  A)
   The data in statement I alone is sufficient to answer the question while the data in statement II is not sufficient to answer the question.
  done clear
  B)
   The data in statement II alone is sufficient to answer the question while the data in "statement I is not sufficient to answer the question.
  done clear
  C)
   The data in either statement I alone or statement II alone is sufficient to answer the question.
  done clear
  D)
   The data even in both the statements I and II together is not sufficient to answer the question.
  done clear
  E)
   The data in both the statements I and II together is necessarily to answer the question.
  done clear
  View Answer play_arrow

• question_answer38)

  Directions: Each of the questions below consists of a question and two statements numbered I and II. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and answer.

  What is the code for 'GOLD' in the code language?

  Statements:

  I. 'ka dik fu' means 'gold and silver', 'do lu ka" means 'diamond and pearl' and 'lu fig fu' means "silver or diamond"

  II. 'na pik la" means 'stone and pearl?, 'dik ni la? means "gold is stone' and 'dik la fa? means ?it is stone?

  A)
   The data in statement I alone is sufficient to answer the question while the data in statement II is not sufficient to answer the question.
  done clear
  B)
   The data in statement II alone is sufficient to answer the question while the data in statement I is not sufficient to answer the question.
  done clear
  C)
   The data in either statement I alone or statement II alone is sufficient to answer the question.
  done clear
  D)
   The data even in both statements I and statement II together is not sufficient to answer the question.
  done clear
  E)
   The data in both statements I and statement II together is necessarily to answer the question.
  done clear
  View Answer play_arrow

• question_answer39)
  Which number would replace the question mark (?) in the series 64, 55, 47, 40, 34, ?, 25.
  A)
   33                               
  done clear
  B)
   30
  done clear
  C)
   29       
  done clear
  D)
   27
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer40)
  Find the next term in the series: BMO, EOQ, HQS, ?
  A)
   KSU    
  done clear
  B)
   LMN
  done clear
  C)
   SOV                           
  done clear
  D)
   SOW
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer41)
  If \[{{\log }_{10}}2=0.30103,\] \[{{\log }_{10}}3=0.47712,\] the number of digits in \[{{3}^{12}}\times {{2}^{8}}\] is
  A)
   7                                
  done clear
  B)
   8
  done clear
  C)
   9        
  done clear
  D)
   10
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer42)
  If \[x=\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}},\,y=\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}},\] then \[3{{x}^{2}}+4xy-3{{y}^{2}}=\]
  A)
   \[\frac{1}{3}\,\,[56\,\sqrt{10}-12]\]        
  done clear
  B)
   \[\frac{1}{3}\,\,[56\,\sqrt{10}+12]\]
  done clear
  C)
   \[\frac{1}{3}\,\,[56+12\,\sqrt{10}]\]       
  done clear
  D)
   \[\frac{1}{5}\,\,[56+10\,\sqrt{15}]\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer43)
  Find the value of a and b so that following system of equation has infinitely many solutions

  \[2x-(a-4)y=2b+1\]

  \[4x-(a-1)y=5b-1\]

  A)
   (2, 6)               
  done clear
  B)
   (3, 7)
  done clear
  C)
   (7, 3)
  done clear
  D)
   (4, 5)
  done clear
  E)
   None of these
  done clear
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• question_answer44)
  Express \[\frac{{{(4+\sqrt{15})}^{\frac{3}{2}}}+{{(4-\sqrt{15})}^{\frac{3}{2}}}}{{{(6+\sqrt{35})}^{\frac{3}{2}}}-{{(6-\sqrt{35})}^{\frac{3}{2}}}}\] in rational form.
  A)
   \[\frac{13}{7}\]                        
  done clear
  B)
   \[\frac{7}{15}\]
  done clear
  C)
   \[\frac{7}{13}\]
  done clear
  D)
   \[\frac{2}{5}\]
  done clear
  E)
   None of these
  done clear
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• question_answer45)
  ABCD is a trapezium in which\[AB\parallel CD\]. Then \[A{{C}^{2}}+B{{D}^{2}}\] is equal to:
  A)
   \[A{{D}^{2}}+B{{C}^{2}}-2AB.CD\]
  done clear
  B)
   \[A{{D}^{2}}+B{{C}^{2}}+2AB.CD\]
  done clear
  C)
   \[A{{D}^{2}}-B{{C}^{2}}+2AB.CD\]
  done clear
  D)
   \[A{{D}^{2}}-B{{C}^{2}}-2AB.CD\]
  done clear
  E)
   None of these
  done clear
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• question_answer46)
  For what values of a and b points (1, 1), (2, 3), (3, a) and (b, 7) are collinear?
  A)
   (4, 5)               
  done clear
  B)
   (5, 4)
  done clear
  C)
   (5, 7)               
  done clear
  D)
   (2, 5)
  done clear
  E)
   None of these
  done clear
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• question_answer47)
  Factorise : \[{{a}^{4}}(b-c)+{{b}^{4}}(c-a)+{{c}^{4}}(a-b)\]
  A)
   \[(a-b)(b-c)(c+a)({{a}^{2}}+{{b}^{2}}+{{c}^{2}}+ab-bc-ca)\]
  done clear
  B)
   \[-(a-b)(b-c)(c-a)\]\[({{a}^{2}}+{{b}^{2}}+{{c}^{2}}+ab+bc+ca)\]
  done clear
  C)
   \[-(b-a)(c-b)(a-c)\]\[({{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ca)\]
  done clear
  D)
   \[(a+b)(b+c)(c+a)\]\[({{a}^{2}}+{{b}^{2}}+{{c}^{2}}+ab+bc+ca)\]
  done clear
  E)
   None of these
  done clear
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• question_answer48)
  If \[a-b=3,\] \[a+b+x=2,\] then the value of \[(a-b)\,\,[{{x}^{3}}-2a{{x}^{2}}+{{a}^{2}}x-(a+b)\,{{b}^{2}}]\]
  A)
   32                               
  done clear
  B)
   36
  done clear
  C)
   48       
  done clear
  D)
   84
  done clear
  E)
   None of these
  done clear
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• question_answer49)
  Find n, if \[{{2}^{200}}-{{2}^{192}}.31+{{2}^{n}}\] is a perfect square.
  A)
   97                               
  done clear
  B)
   138
  done clear
  C)
   198     
  done clear
  D)
   218
  done clear
  E)
   None of these
  done clear
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• question_answer50)
  If \[a:b=\frac{2}{9}:\frac{1}{3},\] \[b:c=\frac{2}{7}:\frac{5}{14}\] and \[d:c=\frac{7}{10}:\frac{3}{5},\] then a : b : c : d is
  A)
   4 : 6 : 7 : 9                  
  done clear
  B)
   16 : 24 : 30 : 35
  done clear
  C)
   8 : 12 : 15 : 7   
  done clear
  D)
   30 : 35 : 24 : 16
  done clear
  E)
   None of these
  done clear
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