MODEL TEST PAPER - retest (X) 20/21

      Suggestive Sample paper(1)         

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         SECTION A (40 Marks)

        (Answers all Questions)

1.(a) What least number should be added to each of the number 4,5,16 and 19 that the resulting numbers may be in proportion.

(b) Find the values of m if (x -m) is a factor of x²+m x -18.

c) Find the least value of n or which the sum of the first n terms of the series 12+20+28+... is greater than 1020 

d) The sum of the numerator and denominator of a fraction is 8, If 1 is added to both the numerator and denominator, the fraction is increased by 1/5. Find the fraction.

e) Solve the inequation and show

    the number lines. 3≥ (x -4)/2  + x/3 ≥ 2; x belongs  to R.

f) Find the remainder when 2x²-6x+4 is divided by (x+3).

g) if A = 1  -3    B = 2  -1    C = 2  0

               0   4           2   1           0  3

   Find X such that A + X = 2B - C.

h) Find the mean, the median and

   the mode of the following data:

   7,4,6,4,5,8,9,11,10,15,4,3.

I)) If 3 sin²x + 5 cos²x= 4, then find the value of sin 2x 

j) Shaikh has a cumulative time deposit account of Rs340 per month at 6% p.a. If she gets ₹7157 at the time of maturity. Find the total time for which the account was held.

     SECTION B(40 Marks)

 (Answer any four questions)

2.a) Manufacturer A sells a.       washing machine to a dealer B for 15000. The dealer B sells it to a consumer at a profit of ₹2000. If the sales are intra-state and the rate of GST is 12%, find

I) the amount of Tax (under GST)  paid by the dealer B to the Central Government.

II) the amount of Tax (under GST) received by the State Government.

III) the amount that the consumer pays for the machine.                  (5)

b) The nth term of an AP is (2n+1). Find the sum of first n terms is.     5                                 

3.a) A point P(a,b) is reflected in the x-axis to P' (2,-3). Write down the values of a and b. P" is the image of P, when reflected in y-axis. Write down the co-ordinates of P".       (5)

b) Solve: 4x² - 4ax+(a²-b²)=0.       (5)

4a) A ∆ RPQ, X and Y on the side RP and RQ respectively such that XY || PQ, If PX/XR = 5/2, and PQ= 7.7 cm. Find

I) YR/QR. II) XY.                             (5)

b) The horizontal distance between two towers is 200m. The angle of elevation of the top of the first tower seen from the top of the second tower is 30°. If the height of the second tower is 50m. Find the height of the first tower.               (5)

5a) Area of the two concentrated circle is 346.5 cm². The circumcentre of the inner circle is 88 cm. Calculate the radius of the outer circle.                                 (5)

b) Find the Equation of a straight line to y-axis and passing through the point (-3,5).                           (5)

6a) Using step deviation method, Calculate the mean :

Class         Frequency

50-60             9 

60-70            11

70-80            10

80-90            14 

90-100           8 

100-110        12 

110-120        11                           ( 7)

b) Prove: (1+cosA)/(1-cosA) = (cosec A - cotA)².                           3

7a) Draw a histogram and hence estimate the mode:

Class-interval          frequency

00-10                             2

10-20                             8 

20-30                            10

30-40                             5 

40-50                             4

50-60                             3                5

b) Prove: (cot x + cosec x -1)/ (cot x - cosec x+1)=(1+cot x)/sinx          5