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

TEST PAPER -- 1(S)

            TEST PAPER - 1

             ( Marks 90)         

                  Section A

                   Attempt all 

1). (1x10= 10)

a) Express 15/56 as a decimal, correct to four decimal places.

b) Express 3.146146146.... as a vulgar fraction.

c) If √2= 1.414 and √3= 1732. Find the value of√72

d) What percentage of 2.5 is 1.21

e) If C. P=₹112, overheads= ₹14 and S. P=₹94.50. find Profit.

f) Factorize: 5a(b+c) -7b(b+c)

g) Insert a rational number between 3/5 and 5/7

h) Every real number is rational. True//false

i) x% of y = ?

j) 9x - 7= 6x +14

              SECTION- B.  

         Attempt all (10x2= 20)

2)

A) Show that √2 is not a rational number.

B) If 35% of a number is 26.6, what is 20% of that number?

C) If oranges are bought at 11 for ₹30 and sold at 10 for ₹31, find the loss or gain percentage.

D) At what rate percentage p.a. simple interest, would a sum double itself in 6 years?

E) Expand: (2x+ 1/3x)²

F) Solve: 7/(x-4) = 5/(x+2)

G) Simplify: (a+b)⁻¹ . (a⁻¹+b⁻¹)

H) Find the length of the longest rod that can be placed in a room 16m long, 12m broad and 32/3 m high.

I) Expand: (2p - 3q)³

J) Represent rational number on real line of - 1/4

              Section - C

    Attempt any six (6x5= 30)

3) A businessman sold 2/3 of his stock at a gain of 20% and the rest at a gain of 14%. Find the overall percentage of gain to the businessmen.

4) After getting two successive discount, a shirt with a list price of ₹150 is available at ₹105. If the second discount is 25/2%, find the first discount.

5) At a certain rate of simple interest, a sum amounts to ₹4760 in 3 years and Rs 5600 in 5 years. Find the sum and the rate percentage per annum.

6) Find the amount and the Compound Interest on ₹10000 for 4 years, if intrest is 5% p.a payable yearly.

7) If x - 1/x = 4, find

A) x² + 1/x². B) x⁴ + 1/x⁴

8) Factorize:

A) 3x² - 4x -7

B) 3x² - 48x

9) Solve: (5y-11)/4 + (3y-7)/2 = (4y-7)/3 + y - 1

10) A room is half as long again as it is broad. The cost of carpeting the room at ₹18 per m² is ₹972 and the cost of white washing the four walls at ₹ 6 per m² is ₹1080. Find the dimensions of the room.

                    Section - D

      Attempt any five (6x5= 30)

11) The dimensions of a metallic cuboid are 100cmx80cmx64cm. It is melted and recast into a cube. Find:

A) the edge of the cube

B) the surface area of the cube.

12) 

A) Simplify: {7²ⁿ⁺³ - (49)ⁿ⁺²}/[(343)ⁿ⁺¹]²⁾³

B) If 1960=2 ᵃ x 5ᵇ x 7ᶜ, find the values of a, b, c. Hence, Calculate the value of 1/(2 ᵃ x 5ᵇ x 7ᶜ)

13) If x = (k+1), find the value of k when, 1/2 (5x -3) - 1/2 (2+9k) = 1/4.

14) a) If a - 1/a =√5, find the value of I) a+ 1/a. II) a³ + 1/a³

15) The population of a town is 1764000. If it increases at the rate of 5% per annum, its population:

A) 2 years hence

B) 2 years ago

16) A man spends 80% of his income. His income increases by 20% and he increases his expenditure by 15%. Find the percentage increasein his savings.

17) a) Rationalize the denominator:

(√3+√2)/(√3 - √2)

b) Insert six rational numbers between 3 and 4.

TEST PAPER--2 Class -10

   MODEL TEST PAPER -2      (20/21)

            SECTION A (Marks 40)
            Attemptt all questions)

1) a) Amit needs ₹8000 after 3 years. What least money, in a multiple of 5 should be put in a Recurring deposit account to get the said amount, the rateof interest being 8% per annum.                     (5)

b) Using the remainder theorem, find the remainder when 7x²-3x+8 is divided by x-4.                                (2)

c) If x², 4 and 9 are in continued Proportion, find x.                         (1)

d) Find x if tan²x + cot²x= 2.        (2)

2a) If x belongs to Z, find the solution set for the inequation 5< 2x - 3 ≤ 14 and graph it on a number line.                                                  (3)

b) Find the values of p and q if g(x)= x+2 is a factor of f(x)= x³ - px + x +q and f(2)=4.                                    (3)

c) Given A= 1    -2. And B=  0
                    -3     4                 1
i) Find a matrix C such that A+C is a zero matrix
ii) Find the matrix D such that A+D = A
iii) Find AB.                                    (3)

3) a) AB and CD are two chords of a circle intersecting of at a point P inside the circle, such that AB= 12cm, AP= 2cm and DP= 4cm. Find PC.                                                 (3)

b) i) If 7 is the mean of 5, 3, 0.5, 4.5, b, 8.5, 9.5 find b.
ii) If each observations is decreased in value by 1 unit, what would the new mean be?             (3)

c) A die is thrown 3 times, find the probability of getting 6?              (3)

4) a) Find the value of m for which the Equation x² - 2(5+2m)x + 3(7+10m)= 0 will have equal roots.                                                         (4)

b) The surface area of a sphere 1256cm². It is cut into two hemispheres. Calculate:
i) the radius of the sphere
ii) the total surface area of a hemisphere
iii) volume of the hemisphere, correct to 2 d.p (π=22/7).            (4)

c) A piece of butter 3cm by 5cm by 12cm is placed in a hemispherical bowl of diameter 6.5cm. will the butter overflow when it melts completely.                                   (4)

           SECTION B (40 Marks)
   (Answer any four questions)

5) a) The first term of an AP is 9, last term is 96 and sum of the terms is 1575. Find the number of terms and common difference of the AP.                                            (5)

b) Mr. X purchased a T.V for₹25488, which includes 10% rebate on the list price and 18% tax(under GST) on the remaining price. Find the marked price of the TV.                 (5)

6)a) i) Point A(5,0) on reflection is mapped as A'(5,0). State the equation of the mirror line.
ii) Point B(4, -3) on reflection is mapped as B'(4,3). State the equation of the mirror line.
iii) Point C(-3,5) on reflection i y= 2 is mapped as C'. Find the Coordinates of C'.                         (3)

b) Solve x: (x+3)/(2x+3)= (x+1)/(3x+2).                                 (5)

c) Find the sum of 1+3+5+....n terms.                                             (2)

7) a) In what ratio does the point (5,3) divide the line segment joining the points (2,0) and (7,5) ?           (3)

b) Prove: (cosecx - sinx)(secx- cosx)= 1/(tanx+ cotx).                 (3)

c) Two dice are thrown simaltaneouly. Find the Probability that the sum of the numbers on two dice are not divisible by 3 or 5.     (4)

8a) A boy standing on a vertical cliff in a jungle observes two rest-houses in line with him on opposite sides deep in the jungle below. If their angles of depression are 30° and 60°& the distance between them is 222m, find the height of the cliff.                                                (5)

b) Find the Equation of the straight line which passes through the point (0,3) and is inclined at an angle 60° with the x-axis.                             (2)

c) A triangle having area 18cm² is enlarged. If the area of the image is 162cm², find the scale factor of enlargement.                                (3)

9a) A hollow cylindrical pipe 50cm long, whose external diameter is 7cm and the internal diameter is 5cm, is melted and recast into a right circular cone, whose base radius is 10cm. Calculate the height of the cone.                                    (4)
b) Insert 5 arithmatic means between (-5) and 7.                      (3)
c) Two dice are thrown simultaneously. Find the Probability of getting a multiple of 2 on one and a multiple of 3 on the other.  (3)

10. a) The midpoint of the line joining A(2,p) and B(q,4) is (3,5). Calculate the numerical values of p and q.                                              (3)

b) From the following table, find
i) The average wage of a worker. Give your answer, correct to the nearest paise.
ii) The modal class
Wages in ₹.      No of Workers
Below 10                15
Below 20                35
Below 30                60
Below 40                80
Below 50                96
Below 60               127
Below 70               190
Below 80               200                  (7)

11) a) If the nth term of an AP is p, then show that the sum of first (2n -1) terms is (2n-1) p.                    (4)

b) Prove: √{(1+cosa)/(1-cosa) = cosec a + cot a.                            (3)

c) Examine the Ogives given below which shows the marks obtained out of 100 by a set of students in an examination and Answer the following questions:
i) How many students are there in the set ?
ii) How many students obtained less than 40% marks?
iii) How many students obtained 90% and above?
iv) What is the median mark?      (4)