10th Maths model question paper

                                   FULL TEST - I (2017)                             

             

 

SECTION - A

Note: (i) Answer all the 15 questions  (ii) Choose the correct answer in each question.  Each of these questions contains four options with just one correct option   (iii) Each question carries one mark.

Choose the correct answer from the given alternatives:-                                    15 x 1 = 15

1.      For two sets A and B, if and only if

          a)               b)               c)                d)

2.       If 1 + 2 + 3 + …. + n = k, then 1³ + 2³ + …… + n³ is equal to ________

          a) K²                     b) K³                    c)             d) (K + 1)³

3.       The number of terms in the A.P 7, 13, 19, ……. 97 is ________

          a) 97                     b) 17                    c) 16                     d) 15

4.       If one root of the equation is negative of the other in the equation ax² + bx + c = 0, then _______

          a) c = 0                 b) a = 0                c) b = 0                d) a = 0 and c = 0

5.       The G.C.D of (x³ + 1) and (x⁴ – 1) is ______

          a) x³ – 1                b) x³ + 1               c) x + 1                 d) x – 1

6.       If A is of order 3 x 4 and B is of order 4 x 3, then the order of BA is

          a) 3 x 3                 b) 4 x 4                c) 4 x 3                 d) not defined

7.       Slope of the line through the points (1, 2) (4, 2) is ________

          a) 0                       b) 1                      c) 2                       d)

8.       If (1, 2), (4, 6), (x, 6) and (3, 2) are the vertices of a parallelogram taken in order, then the value of x is _______

          a) 6                       b) 2                      c) 1                       d) 3

9.       The sides of two similar triangles are in the ratio 2 : 3, then their areas are in the ratio

          a) 9 : 4                  b) 4 : 9                 c) 2 : 3                  d) 3 : 2

10.     In ∆ABC, DE//BC, meeting AB and AC at D and E.  If AD = 3 cm, DB = 2 cm and AE = 2.7 cm, then AC is equal to ______

          a) 6.5 cm              b) 4.5 cm             c) 3.5 cm              d) 5.5 cm

11.     9 tan²θ – 9sec²θ = ________

          a) 1                       b) 0                      c) 9                       d) -9

12.     A man is 28.5 m away from a tower.  His eye level above the ground is 1.5 m.  The angle of evelvation of the tower from his eyes in 45.  Then the height of the tower is _______

          a) 30 m                b) 27.5 m             c) 28.5 m              d) 27 m

13.     If the radius of a sphere is 2 cm, then the curved surface area of the sphere is equal to

          a) 8p cm²             b) 16 cm²             c) 12p cm²            d) 16p cm²

14.     If the variance of a data is 12.25, then the S.D is

          a) 3.5                    b) 3                      c) 2.5                    d) 3.25

15.     Probability of sure event is

          a) 1                       b) 0                      c) 100                   d) 0.1

SECTION - B

Note:            (i) Answer any Ten question:-                                                            10 x 2 = 20

          (ii) Answer any 9 questions from the first 14 questions.  Question No: 30 is

       compulsory.  (iii) Each question carries two marks.

16.     If , then find and A\B (Use Venn diagram).

17.     If R = {(a, -2), (-5, b), (8, c), (d, -1)} represents the identity function, find the values of an b, c and d.

18.     Which of the following sequences are geometric sequences

          (i) 5, 10, 15, 20 ………

          (ii)

19.     Find the quotient and remainder when (x³ + x² – 3x + 5) is divided by (x-1).

20.     Simplify the rational expression into lowest form: .

21.     Find the product of the matrices if exists,

22.     Find the midpoint of the line segment joining the points (3, 0) and (-1, 4).

23.     Find the equation of the straight line whose x-intercept and y-intercept on the axes are 2 and 3.

24.     In ∆PQR, given that s is a point on PQ such that ST//QR and   If PR = 5.6 cm then find PT.

25.     Prove the identity .

26.     A kite is flying with a string of length 200 m.  If the thread makes an angle 30° with the ground, find the distance of the kite from the ground level.  (Here, assume that the string is along a straight line).

27.     A solid right circular cylinder has radius of 14 cm and height of 8 cm.  Find its curved surface area and total surface area.

28.     The smallest value of a collection of data is 12 and the range is 59.  Find the largest value of the collection of data.

29.     Two unbiased dice are rolled once.  Find the probability of getting

          (i) a sum 8           (ii) a doublet

30.     If , then find A^T and (A^T)^T.   (OR)

          The volume of a solid right circular cone is 4928 cu. cm.  If its height is 24 cm, then find the radius of the cone.  .

         

SECTION - C

Note:     (i) Answer any Nine question:                                                                   9 x 5 = 45

              (ii) Answer any 8 questions from the first 14 questions.  Question No 45 is

          compulsory.

31.     Verify  (Using Venn diagram).

32.     Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets.  Let f : A→B be a function given by f(x) = 2x + 1.  Represent this function as (i) a set of ordered pairs

(ii) a table (iii) an arrow diagram and (iv) a graph.

33.     Find the sum of first n terms of the series 7 + 77 + 777 + ……. .

34.     Find the value of k, if 1³ + 2³ + 3³ + …. + k³ = 4356.

35.     Divide the following and write your answer in lowest term.

         

36.     Find the square root 4x⁴ + 8x³ + 8x² + 4x + 1.

37.     If  then show that A² – 4A + 5I₂ = 0.

38.     Find the area of the quadrilateral formed by the points (-4, -2), (-3, -5), (3, -2) and (2, 3).

39.     The vertices of a ∆ABC are A(1, 2), B(-4, 5) and C(0, 1).  Find the slopes of the attitudes of the triangle.

40.     State and prove thales theorem.

41.     The angle of elevation of an aeroplane from a point A on the ground is 60°.  After a flight of 15 seconds horizontally, the angle of elevation changes to 30°.  If the aeroplane is flying at a speed of 200 m/s, then find the constant height at which the aeroplane is flying.

42.     Base area and volume of a solid right circular cylinder are 13.86 sq.cm and

69.3 cu.cm respectively.  Find its height and curved surface area. 

43.     An iron right circular cone of diameter 8 cm and height 12 cm is melted and recast into spherical lead shots each of radius 4mm.  How many lead shots can be made?

44.     A card is drawn at random from a well – shuffled deck of 52 cards Find the probability that it will be a spade or a king.

45.     a) Factorize x³ – 3x² – 10x+24.

          b) A group of 45 house owners contributed money towards green environment of their street. The amount of money collected is shown in the table below.

Amount Rs.	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100
No of house owners	2	7	12	19	5

          Calculate the variance and standard deviation.

           

SECTION – D

Note:-  (i) This section contains two questions, each with two alternatives.

  (ii) Answer both the questions.  Choosing either of the alternatives.

                                                                                                                        2 x 10 = 20

46.     a) Draw a circle of radius 3 cm.  From an external point 7 cm away from its

   centre, construct the pair of tangents to the circle and measure their lengths.

(OR)

b) Construct a cyclic quadrilateral ABCD when AB = 6 cm, BC = 5.5 cm  and AD = 4.5 cm.

47.     a) Solve graphically 2x² + x - 6=0.

(OR)

          b)  The following table gives the cost and number of note books bought.

No.of ntoe books x	2	4	6	8	10	12
Cost (Rs y)	30	60	90	120	150	180

          Draw the graph and hence

(i)               Find the cost of seven note books.

(ii)            How many notebooks can be bought for Rs. 165.