10th Class Mathematics Sample Paper

done Maths Olympiad Model Test Paper-3 Total Questions - 50    [Download]

• question_answer1)
  In the given figure, if AB || CD, find the value of x.
  A)
   \[104{}^\circ \]
  done clear
  B)
   \[105{}^\circ \]
  done clear
  C)
   \[110{}^\circ \]           
  done clear
  D)
   \[115{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer2)
  The solution for the system of linear equations, \[-3x+2y-6z=6;5x+7y-5z\]\[=6;+4y-2z=8,\] is:
  A)
   \[\left( -\,2,\,\,\text{3},\,\,1 \right)\]                      
  done clear
  B)
   (2, 4, 6)
  done clear
  C)
   (3, 3, 1)                       
  done clear
  D)
   \[\left( 4,\,\,7,-\,5 \right)\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer3)
  A girl of height \[90\,\,cm\] is walking away from the base of a lamp - post at a speed of 1.2 m/sec. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 sec.
  A)
   8 m                             
  done clear
  B)
   4.8 m
  done clear
  C)
   2.8 m              
  done clear
  D)
   1.6 m
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer4)

  Directions: In a group of 100 children 32% play hockey 64% play football and 40% play cricket. 14% play hockey and football 15% play football and cricket 13% play hockey and cricket. Only 6% play all the three games.

  How many children play only one game?
  A)
   70       
  done clear
  B)
   60
  done clear
  C)
   50                               
  done clear
  D)
   30
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer5)

  Directions: In a group of 100 children 32% play hockey 64% play football and 40% play cricket. 14% play hockey and football 15% play football and cricket 13% play hockey and cricket. Only 6% play all the three games.

  How many children play at least two games?
  A)
   41                               
  done clear
  B)
   35
  done clear
  C)
   30
  done clear
  D)
   28
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer6)

  Directions: In a group of 100 children 32% play hockey 64% play football and 40% play cricket. 14% play hockey and football 15% play football and cricket 13% play hockey and cricket. Only 6% play all the three games.

  How many children play hockey or football but not cricket?
  A)
   45                               
  done clear
  B)
   60
  done clear
  C)
   70                               
  done clear
  D)
   85
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer7)
  If zeros of a quadratic polynomial are \[(-\,3+\sqrt{3})\]and \[(-\,3-\sqrt{3}),\] find the polynomial.
  A)
   \[{{x}^{2}}+6x+6\]  
  done clear
  B)
   \[{{x}^{2}}-6x+6\]
  done clear
  C)
   \[{{x}^{2}}+2x+4\]              
  done clear
  D)
   \[{{x}^{2}}+6x-6\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer8)
  The zeros of the cubic polynomial \[\left( -\,2,\,\,3 \right)\] are in A.P. Find its zeros.
  A)
   \[-\,2,\,\,3\,\,and\,\,7\]                
  done clear
  B)
   \[-\,1,\,\,2\,\,and\,\,5\]
  done clear
  C)
   \[-\,3,\,\,2\,and\,\,7\]      
  done clear
  D)
   \[-\,4,\,\,2\,and\,\,5\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer9)
  If \[x=\frac{2}{3}\] and \[x=-\,3\] are the roots of the equation\[a{{x}^{2}}+7x+b=0,\] find the value of a and b.
  A)
   \[a=3,\,\,b=-\,6\]          
  done clear
  B)
   \[a=3,\,\,b=+\,6\]
  done clear
  C)
   \[a=2,\,\,b=-\,5\]          
  done clear
  D)
   \[a=3,\,\,b=-\,2\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer10)
  A two - digit number is seven times the sum of its digits and is also equal to 12 less than three times the product of its digits. Find the number.
  A)
   84       
  done clear
  B)
   36
  done clear
  C)
   34                               
  done clear
  D)
   93
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer11)
  There are two examination rooms A and B. If 10 students are sent from A to B, then the number of students in each room is same. If 20 students are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
  A)
   20                               
  done clear
  B)
   80
  done clear
  C)
   100     
  done clear
  D)
   200
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer12)
  A body falls 16 meters in the first second of its motion, 48 metres in the second, 80 metres in the third and so on. How long will it take to fall 4096 metres?
  A)
   16 seconds       
  done clear
  B)
   18 seconds
  done clear
  C)
   12 seconds                   
  done clear
  D)
   20 seconds
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer13)
  The charges of boring a well are Rs. 5 for the first metre and increase by Rs. 0.50 for every subsequent metre. Find the cost of boring the 10th metre and also the total cost of boring a well 60 metres deep.
  A)
   Rs. 5.50, Rs. 1085        
  done clear
  B)
   Rs. 8.50, Rs. 1185
  done clear
  C)
   Rs. 9.50, Rs. 1185
  done clear
  D)
   Rs. 9.50, Rs. 1200
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer14)
  The HCF of two polynomials is \[{{x}^{2}}-1\] and their LCM is\[{{x}^{4}}-10{{x}^{2}}+9\]. If one of the polynomials is \[{{x}^{3}}+3{{x}^{2}}-x-3,\] then the other polynomial is
  A)
   \[{{x}^{3}}-3{{x}^{2}}-x+3\]
  done clear
  B)
   \[{{x}^{3}}+3{{x}^{2}}+x+3\]
  done clear
  C)
   \[{{x}^{3}}-3{{x}^{2}}-x-3\]
  done clear
  D)
   \[{{x}^{3}}+3{{x}^{2}}-x-3\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer15)
  Find the value of 'x' in the following figure, if DE || BA.
  A)
   \[\frac{5}{2}\,\,cm\]                 
  done clear
  B)
   \[\frac{3}{2}\,\,cm\]
  done clear
  C)
   \[\frac{5}{3}\,\,cm\]                 
  done clear
  D)
   \[\frac{5}{4}\,\,cm\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer16)
  The angles of depression of the top and the bottom of a building 50 metres high as observed from the top of a tower are \[30{}^\circ \] and \[60{}^\circ \]respectively. Find the height of the tower and also the horizontal distance between the building and the tower.
  A)
   \[73\,\,m,\,\,43.3\,\,m\]  
  done clear
  B)
   \[43.3\,\,m,\,\,75\,\,m\]
  done clear
  C)
   \[75\,\,m,\,\,41.3\,\,m\]  
  done clear
  D)
   \[75\,\,m,\,\,43.3\,\,m\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer17)
  Find the ratio in which the point \[\left( -\,3,\,\,k \right)\] divides the line segment joining the points \[\left( -\,5,\,-\,4 \right)\] and \[\left( -\,2,\,\,3 \right)\].
  A)
   \[3:1\]                          
  done clear
  B)
   \[1:1\]
  done clear
  C)
   \[2:1\]              
  done clear
  D)
   \[2:2~\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer18)
  In the adjoining figure, ABCD is a parallelogram in which \[DC=10\,\,cm\] and \[\left( -\,2,-\,1 \right)\]. AP is perpendicular to DC. If \[\angle ADC=60{}^\circ ,\] find the length of AP.
  A)
   6 cm   
  done clear
  B)
   8 cm
  done clear
  C)
   4 cm                           
  done clear
  D)
   12 cm
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer19)
  If \[\left( -\,2,-\,1 \right),\] (a, 0), (4, b) and (1, 2) are the vertices of a parallelogram, find the value of a and b.
  A)
   a = 1, b = 3
  done clear
  B)
   a = 1, b = 5
  done clear
  C)
   a = 3, b = 1                
  done clear
  D)
   a = 2, b = 4
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer20)
  The inner circumference of a circular track is 440 m and the track is 14 m wide. Calculate the cost of leveling the track at \[25\,\,paise/{{m}^{2}}\]. Also find the cost of fencing the outer boundary of the track at Rs. 5 per metre.
  A)
   Rs. 1600, Rs. 2640        
  done clear
  B)
   Rs. 1594, Rs. 2640
  done clear
  C)
   Rs. 1694, Rs. 2110        
  done clear
  D)
   Rs. 1694, Rs. 2640
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer21)
  In the adjoining figure, \[DE\parallel BC,\] AD = 2 cm, BD = 2.5 cm, AE = 3.2 cm, DE = 4 cm. Determine AC and BC.
  A)
   6.2 cm, 5 cm               
  done clear
  B)
   7.2 cm, 9 cm
  done clear
  C)
   5.2 cm, 9 cm               
  done clear
  D)
   6.2 cm, 8 cm
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer22)
  In the adjoining figure, ABC is a right angled triangle with AB = 5 cm and AC = 12 cm. A circle with centre O has been inscribed inside triangle. Calculate the value of r, the radius of the inscribed circle.
  A)
   8 cm                           
  done clear
  B)
   5 cm
  done clear
  C)
   3 cm                           
  done clear
  D)
   2 cm
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer23)
  In\[\Delta \,ABC,\]\[\angle B=90{}^\circ ,\] AB = 16 cm, AC = 20 cm. D and E are points on AB and AC respectively such that \[\angle AED=90{}^\circ \] and \[DE=4\,\,cm\]. Find the value of \[\frac{\text{area}\,\,\text{of}\,\,\text{quadrilateral}\,\,\text{BCED}}{\text{area}\,\,\text{of}\,\,\Delta \,\text{ABC}}\]
  A)
   \[\frac{10}{3}\]                        
  done clear
  B)
   \[\frac{3}{10}\]
  done clear
  C)
   \[\frac{8}{9}\] 
  done clear
  D)
   \[\frac{9}{8}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer24)
  In the figure given below, P is a point on the side BC of \[\Delta \,ABC\] such that \[MP||AB\] and\[NP||AC\]. If \[MN\]and\[CB\]are produced to meet in\[Q\], then
  A)
   \[P{{Q}^{2}}=QB\times QC\]
  done clear
  B)
   \[P{{Q}^{2}}=Q{{B}^{2}}\times Q{{C}^{2}}\]
  done clear
  C)
   \[P{{B}^{2}}=QC\times QB\] 
  done clear
  D)
   \[P{{B}^{2}}=PQ\times QB\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer25)
  The mean of the following frequency table is 50. But the frequencies \[{{f}_{1}}\] and \[{{f}_{2}}\] in class 20 - 40 and 60 - 80 are missing. Find the missing frequencies

  Class Interval	0-20	20-40	40-60	60-80	80-100	Total
  Frequency	17	\[{{f}_{1}}\]	32	\[{{f}_{2}}\]	19	120

  A)
   \[28,\,\,24\]
  done clear
  B)
   \[26,\,\,24\]
  done clear
  C)
   \[27,\,\,20\]                  
  done clear
  D)
   \[30,\,\,28\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer26)
  If \[\alpha ,\]\[\,\beta \] and \[\gamma \] are the zeros of the polynomial \[2{{x}^{3}}-3{{x}^{2}}-23x+12,\] then the value of \[\frac{1}{\alpha }+\frac{1}{\beta }+\frac{1}{\gamma }\] is
  A)
  \[\frac{23}{12}\]          
  done clear
  B)
  \[-\,6\]
  done clear
  C)
  \[\frac{3}{2}\]                         
  done clear
  D)
  \[\frac{-\,23}{12}\]
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer27)
  Divide the polynomial \[f(x)={{x}^{4}}-2\] by the polynomial \[g(x)=5x-{{x}^{2}}+1\] and find the quotient and remainder.
  A)
   \[q(x)=-{{x}^{2}}-5x-26,\] \[r(x)=130x+20\]
  done clear
  B)
   \[q(x)=-{{x}^{2}}-5x-26,\] \[r(x)=135x+24\]
  done clear
  C)
   \[r(x)=-{{x}^{2}}-5x-25,\] \[q(x)=135x+24\]
  done clear
  D)
   \[q(x)=-x-2x-26,\] \[r(x)=135x+22\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer28)
  Find the coordinates of the points which divide the line segment joining the points \[(-\,2,\,\,0)\] and\[(0,\,\,8)\] in four equal parts.
  A)
   \[\left( \frac{2}{3},\,\,2 \right),\,\,(1,\,\,3),\,\,\left( -\frac{2}{1},\,\,5 \right)\]
  done clear
  B)
   \[\left( \frac{2}{3},\,\,2 \right),\,\,(1,\,\,3),\,\,\left( -\frac{2}{1},\,\,6 \right)\]
  done clear
  C)
   \[\left( -\frac{3}{2},\,\,2 \right),\,\,(-1,\,\,4),\,\,\left( -\frac{1}{2},\,\,6 \right)\]
  done clear
  D)
   \[\left( -\frac{3}{2},\,\,2 \right),\,\,(-1,\,\,3),\,\,\left( \frac{1}{1},\,\,6 \right)\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer29)
  Find the term of the Arithmetic Progression 9, 12, 15, 18,... which is 39 more than its 36th term.
  A)
   49th     
  done clear
  B)
   43th
  done clear
  C)
   47th                             
  done clear
  D)
   48th
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer30)
  Evaluate\[\frac{2}{3}\,\,({{\cos }^{4}}30{}^\circ -{{\sin }^{4}}45{}^\circ )-3\,\,({{\sin }^{2}}60{}^\circ -{{\sec }^{2}}45{}^\circ )\]\[+\frac{1}{4}{{\cot }^{2}}30{}^\circ \].
  A)
   \[4\,\,\frac{17}{24}\]
  done clear
  B)
   \[3\,\,\frac{17}{24}\]
  done clear
  C)
   \[4\,\,\frac{-17}{24}\]               
  done clear
  D)
   \[5\,\,\frac{17}{24}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer31)
  Which one of the given responses would be a meaningful order of the following words in ascending order?

  1. Atomic Age

  2. Metallic Age

  3. Stone Age

  4. Alloy Age

  A)
   1, 3, 4, 2                     
  done clear
  B)
   3, 2, 4, 1
  done clear
  C)
   2, 3, 1, 4                     
  done clear
  D)
   4, 3, 2, 1
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer32)
  Replace the question mark with the correct number. 81 : 63 :: ? : 93
  A)
   27                               
  done clear
  B)
   12
  done clear
  C)
   144     
  done clear
  D)
   1728
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer33)
  Six students - A, B, C, D, E and F are sitting in a ground. A and B have come from Delhi while other from Bangalore. D and F are tall and all others are short. A, C and D are girls while other are boys. Who is the taller girl hailing from Bangalore?
  A)
   C                                
  done clear
  B)
   D
  done clear
  C)
   E                                
  done clear
  D)
   F
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer34)
  Select the answer figure in which the question figure is hidden/embedded. Question figure: Answer figures:
  A)
                  
  done clear
  B)
   
  done clear
  C)
                   
  done clear
  D)
   
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer35)
  Six persons A, B, C, D, E and F are standing in a circle. B is between F and C; A is between E and D, F is to the left of D. Who is between A and F?
  A)
   E                                
  done clear
  B)
   B
  done clear
  C)
   C                                
  done clear
  D)
   D
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer36)
  P, Q, R, S, T, U are 6 members of a family in which there are two married couples. T, a teacher is married to a doctor who is mother of R and U. Q, the lawyer is married to P. P has one son and one grandson. Of the two married ladies one is a housewife. There is also one student and one male engineer in the family. Which of the following is true about the grand - daughter of the family?
  A)
   She is a student.
  done clear
  B)
   She is a lawyer.
  done clear
  C)
   She is an engineer.        
  done clear
  D)
   She is a doctor.
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer37)
  Which one set of letters when sequentially placed at the gaps in the given letter series shall complete it? a _ b _ ca _ b _ c _ a _ cc
  A)
   a b a b a c                   
  done clear
  B)
   a c b c a b
  done clear
  C)
   a b a b c a                   
  done clear
  D)
   a c a c a b
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer38)

  Direction: Read the following information carefully and answer the questions given below it:

  The sum of the incomes of A and B is more than that of C and D taken together. The sum of the incomes of A and C is the same as that of B and D taken together. Moreover, A earns half as much as the sum of the incomes of B and D.

  Whose income is the highest?
  A)
   A                                
  done clear
  B)
   B
  done clear
  C)
   C                                
  done clear
  D)
   D
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer39)

  Direction: Read the following information carefully and answer the questions given below it:

  The sum of the incomes of A and B is more than that of C and D taken together. The sum of the incomes of A and C is the same as that of B and D taken together. Moreover, A earns half as much as the sum of the incomes of B and D.

  Which of the following statements is not correct?
  A)
   A earns more than B.
  done clear
  B)
   B earns more than D.
  done clear
  C)
   C earns more than D.
  done clear
  D)
   B earns more than C.
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer40)

  Direction: Read the following information carefully and answer the questions given below it:

  The sum of the incomes of A and B is more than that of C and D taken together. The sum of the incomes of A and C is the same as that of B and D taken together. Moreover, A earns half as much as the sum of the incomes of B and D.

  If A?s income be Rs. 80, 000 per annum and the difference between the incomes of B and D be the same as A's income, B's income is
  A)
   Rs. 40,000                   
  done clear
  B)
   Rs. 60,000
  done clear
  C)
   Rs. 80,000                   
  done clear
  D)
   Rs. 1,20,000
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer41)
  Match the columns

  Column - Ist		Column - IInd
  (A)	A and B are two events such that P(A) = 0.3 and \[P\,(A\bigcup B)=0.8.\] If A and B are independent, then P(B) is	(P)	\[\frac{4}{13}\]
  (B)	A single card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a king or a club?	(Q)	\[\frac{2}{5}\]
  (C)	If A and B be two mutually exclusive events in a sample space such that \[P(A)=\frac{2}{5}\] and \[P\,(B)=\frac{1}{2},\] then \[P\,(A\bigcap \overline{B})\] is	(R)	\[\frac{5}{7}\]
  (D)	A natural number is chosen at random from amongst the first 300. What is the probability that the number, so chosen is divisible by 3 or 5?	(S)	\[\frac{7}{15}\]

   
  A)
  A\[\to \]P, B\[\to \]Q, C\[\to \]R, D\[\to \]S
  done clear
  B)
  A\[\to \]Q, B\[\to \]P, C\[\to \]R, D\[\to \]S
  done clear
  C)
  A\[\to \]R, B\[\to \]P, C\[\to \]S, D\[\to \]Q
  done clear
  D)
  A\[\to \]R, B\[\to \]P, C\[\to \]Q, D\[\to \]S
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer42)
  Match the columns

  Column I		Column II
  (A)	If all the dimensions of a cuboid are increased by 100%, by what percent does the volume of cuboid increase?	(p)	15.76%
  (B)	If side of a cube is increased by 10%, by how much percent its volume will increase?	(q)	21%
  (C)	If radius of a cylinder is increased by 10%, while height remains unchanged, by cylinder will increase?	(r)	33.1%
  (D)	When each radius and height of a cone are increased by 5%, by what percent its volume will increase?	(s)	700%

  A)
              A-s, B-r, C-p, D-q         
  done clear
  B)
   A-s, B-p, C-r, D-q
  done clear
  C)
   A-s, B-r, C-q, D-p
  done clear
  D)
   A-p, B-q, C-r, D-s
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer43)
  Find the wrong number in the given series. 2, 11, 38, 197, 1172, 8227, 65806
  A)
   11                               
  done clear
  B)
   38
  done clear
  C)
   197                             
  done clear
  D)
   1172
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer44)
  Consider the following equations

  (i) \[{{\operatorname{cosec}}^{2}}x+{{\sec }^{2}}x={{\operatorname{cosec}}^{2}}x.{{\sec }^{2}}x\]

  (ii) \[{{\sec }^{2}}x+{{\tan }^{2}}x={{\sec }^{2}}x{{\tan }^{2}}x\]

  (iii) \[{{\operatorname{cosec}}^{2}}x+{{\tan }^{2}}x={{\cot }^{2}}+{{\sec }^{2}}x\]

  Which of the following equations are correct?

  A)
   (i) and (ii)                     
  done clear
  B)
   (ii) and (iii)
  done clear
  C)
   (i) and (iii)        
  done clear
  D)
   (i), (ii) and (iii)
  done clear
  E)
   None of these
  done clear
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• question_answer45)
  A word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as in the two matrices given below. The coloumns and rows of Matrix - I are numbered from 0 to 4 and that of Matrix - II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g., 'D' can be represented by 02, 14 etc., and 'R' can be represented by 57, 76 etc. Similarly, you have to identify the set for the word. "BEST"  
  A)
   24, 22, 77, 96  
  done clear
  B)
   24, 22, 76, 97
  done clear
  C)
   24, 21, 77, 97  
  done clear
  D)
   24, 22, 77, 97
  done clear
  E)
   None of these
  done clear
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• question_answer46)
  Find the sum of the natural numbers between 300 and 900 which are multiples of 11.
  A)
   35173             
  done clear
  B)
   34373
  done clear
  C)
   33376             
  done clear
  D)
   32373
  done clear
  E)
   None of these
  done clear
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• question_answer47)
  For what value of k will the following pair of linear equations have no solution? \[3x+y=1,\]\[(2k-1)\,x+(k-1)\,\,y=2k+1\]
  A)
   1                                
  done clear
  B)
   2
  done clear
  C)
   3                                
  done clear
  D)
   \[\frac{1}{4}\]
  done clear
  E)
   None of these
  done clear
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• question_answer48)
  A cylindrical bucket, 32 cm high and base radius 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.
  A)
   \[16,\,36\,\sqrt{3\,}\,cm\]           
  done clear
  B)
   \[36,12\,\sqrt{3\,}\,cm\]
  done clear
  C)
   \[25,8\,\sqrt{17\,}\,cm\]             
  done clear
  D)
   \[48,\,12\,\sqrt{13\,}\,cm\]
  done clear
  E)
   None of these
  done clear
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• question_answer49)
  The roots of the equation \[{{3}^{2x}}-{{10.3}^{x}}+9=0\] are
  A)
  1, 2                             
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  B)
  0, 2
  done clear
  C)
  0, 1     
  done clear
  D)
  1, 3
  done clear
  E)
  None of these
  done clear
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• question_answer50)
  If a round balloon of radius 'a' metres subtends an angle \[\theta \] at the eye of an observer while the angle of elevation of its centre is\[\phi \], then the height of the centre of the balloon is
  A)
   \[a\,\,\sin \,\,\frac{\phi }{2}\,\,\,\operatorname{cosec}\theta \]       
  done clear
  B)
   \[\frac{a}{2}\,\,\sin \phi \,\,\operatorname{cosec}\,\,\frac{\theta }{2}\]
  done clear
  C)
   \[\frac{a}{2}\,\,\sin \,\,\frac{\phi }{2}\,\,\operatorname{cosec}\theta \]      
  done clear
  D)
   \[a\,\,\sin \,\,\phi \,\operatorname{cosec}\,\,\frac{\theta }{2}\]
  done clear
  E)
   None of these
  done clear
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