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)