Model Test Paper - II.

Section - A
Section - B
Section - C

SECTION - A .

Question 1 to 15 carry 2 marks each.

  1. LCM of 2 polynomials p(x) and q(x) is ( x + 2 )( x + 3 )2( x - 5 ).
Their GCD is (x + 3), If p(x) = (x + 2) (x + 3)2.
Find q(x).
  2. Express in lowest terms ( x - 2 ) ( x2 + 9x + 20 )
                                       (x +4 ) (x2 + 11x + 30)
  3. Solve 15m2 + 2m - 8 = 0.
  4. If x2 + x = K(2 - 5x) then find the value of K.
  5. Prove that CosA + SecA = 2tan2A
                       CosA
  6. If A = 450 then show that : Cos2A = 1 - Sin2A.
  7. Find the median of the 1st 10 multiples of 3.
  8. The mean weight of 25 girls is 40 kgs. If the weight of man be included the mean weight increases by 500 grams.
Find the weight of man.

  9. Points P and R are the point of contact. S is the center of the circle. If m(arc PTR) = 110    0 then find ÐPQR.

  10. Area of 2 similar triangles DABC and DPQR are 36 cm2 and 25 cm2. If BC = 6.4. Find QR.

  11. Ð    PQR = ÐQSR = 900. PS = 10 , QS = 8. Find SR.     
  12. The diagonals of a rhombus are 24 cm and 10 cm. Find its area and perimeter.
  13. The volume of a cube is 1000 cu.cm. Find the total surface area.

  14. Find the radius of the circle shown in the figure, if the area of shaded region is 124 cm2.     
  15. Mayur bought a shirt of Rs. 583/- which included 6% sales tax.
Find list price of the shirt.

SECTION - B.

Question 16 to 25 carry 4 marks each.

  1. 
Find the missing figure :
    
      
    
        
    Class 
    		
        
    00 - 20
    		
        
    20 - 40
    		
        
    40 - 60
    		
        
    60 - 80
    		
        
    80 - 100
    		
      
    
      
    
        
    Frequency 
    		
        
    17
    		
        
    28
    		
        
    32
    		
        
    -
    		
        
    19
    		
      
    
    
  2. Simplify graphically the following system of linear equations.
3x - 4y = 12.
6x - 3y = 18.
  3. Construct a DABC in which AB = 4.4 cm , ÐC = 600 and the median 
through C equals 3.5 cms.
  4. Solve ( a + b + c )( ab + bc + ca ) - abc.
  5. In an equilateral DABC , the side BC trisected at D . Prove that 9AD2  = 7AB2. 
  6. If CosA / CosB = m and CosA / SinB = n
Show that ( m2 - n2 ) Sin2B = n2.
  7. Calculate the cost of living index number for the year 2000 taking 1996 as 
the base year from the following data.
    
    
      
     
         
          
    Commodity
    
            		
         
          
    Quantity
    
            		
         
          
     
            
    
Price in units(Rs.)
1996                     2000
    
          
    
      
     
         
          
    A
    		 
          
    10
    		 
          
    8.00
    		 
          
    12.00
    
      
     
         
          
    B
    		 
          
    15
    		 
          
    6.00
    		 
          
    8.00
    
      
     
         
          
    C
    		 
          
    12
    		 
          
    5.00
    		 
          
    6.50
    
      
     
         
          
    D
    		 
          
    20
    		 
          
    4.00
    		 
          
    55.00
    
      
     
         
          
    E
    		 
          
    25
    		 
          
    15.00
    		 
          
    20.00

  8. In the given figure the incircle of DABC, touches the side BC, CA and AB at D ,E and F respectively. Show that AF + BD + CE = AE + BF + CD = 1 / 2 (perimeter of DABC )     
  9. Two isoselas traingles have equal vertical angles and their area are 
in the ratio 9:16. Find the ratio of their corresponding heights(altitudes)
  10. How many bricks each of dimension 25cm x 16 cm x 10 cm will be needed to build
a wall 24 meters long, 6m height and 4m thick. What will be the cost of bricks at the rate of
 Rs. 3.50 per 1000 bricks, 10% of the wall is filled with mortar.

SECTION - C.

Question 26 to 30 carry 6 marks each.

  1. The angle of elevation of top of a tower from two points at a distance 'a' 
and 'b' from the base and in the same straight line with it are complementary.
Show that the height of the tower is Öab.
  2. 2(x2 + 1 / x2) - 3(x + 1/x )-1 = 0.

  3. AB is a line segment and M is its mid point on one side of AB, semi-circles have been drawn by taking AM, MB and AB as diameters. A circle has been drawn which touches each of the 3 semi-circles. Prove that the radius of circle = 1/6 AB.     
  4. During the year 1998-99, Mr. Sharma's income was Rs. 8300/- per month (HRA not included ) 
He contributes Rs. 9200/- towards PF during this year Rs. 100/- are deducted each month 
for 11 months from his salary as income tax. How much should invest in NSC so that he need 
not to pay any more tax in the last month of the year.
  5. 2 digit no. is such that the product of digit is 8, when 63 is subtracted  from the no. the digits
 interchange their places. Find the number.
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