16.doc

 

SAMPLE PAPER - 2009

Class - X

SUBJECT - MATHEMATICS

 

Time: 3Hrs.                                                                                                                              Marks:  80

(SECTION-A-10marks;Section-B-10marks,Section-C-30marks,Section D-30marks)

                                            

SECTION-A

 

1) Using Euclid’s division algorithm find HCF of 216 and 1176.     (24

2) Given below are 3 equations. Two of them have infinite solutions and two have unique solutions .State the two pairs.                                        (U-1,2,  I- 1,3.)

       4x-5y=3, 5x-4y=5, 8x-10y=6.

3) Draw the graphs of 3x=3  and   x-2y= -4.Shade the area of the regions bounded by the lines and x-axis.

4) If -1 is one of the zero of the polynomial p(x)=3x3 -5x2-11x-3, find the other two zeros                                                                                           (3,  -1/3)

5) Find the roots of equation a2x2-3abx+2ab2=0.                   (2b/a, b/a)

6) Determine whether the given quadratic equation has roots .If so find it. 1/(x+1)+2/(x+2)=4/(x+4) .                                                                2(1±-√3)

7) P.t. 5+√2 is irrational.

8) Find the volume of  ‘m’ so that m+2, 4m-6, 3m-2 are three consecutive terms of AP.   

                                                                                                                                   (3)

9) Three unbiased coins are tossed. What is the probability of getting

a) two heads  b) at least two heads  c) at most two heads  d) one head or 2 heads.

                           (3/8, 1/2,  7/8,  3/4)

10) Find the value of cos220+cos270   +sin2 64+ cos64  sin26          (2)                                                                                                                 

                                     Sin231+sin259

                                      SECTION-B

11) S.t. Sinθ – 2Sin3θ  = tanθ.

             2cos3θ – cosθ                                                                              

12) A rocket is in the form of a cylinder closed at the lower end with a cone of the same radius attached to the top. The cylinder is of the radius 2.5m,and height21m and cone has a slant height 8m.Calculate TSA.                                              (4125m2)

13) Find the sum of 51+50+49+…….+21.                                      (1116)

14) Find the sum of all multiples of 4 lying between 50 and 250.    (7500)

15) Find the point on the ‘x’axis which is equidistant from the points (2, --5) and (-2,9)

                                                                                                                            (-7, 0)

                                   SECTION-C

16) Find the area of the quadrilateral ABCD formed by the pth

      A(-3,5),   B((3,0),  C(3,0),  D(-1,4)     (25sq units) 

F

A  AA

E

B

D

C

 

 

17) In the adjoining fig.E is a point on side CB produced of an isoscles ∆ABC with AB=AC.If AD ┴ BC, EF ┴ AC, p.t. ∆ABC  ~  ∆ECF

18) A wooden article was made by scooping out hemispheres from each end of a cylinder as shown in the figure.Find its TSA                (374)

                                                                                                       

10cm

 

 

7mm

 

19) Two customers are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as on the another. What is the probability that both with visit the shop on a) the same day

b) different days     c) consecutive days                          (1/6,   5/6,    5/18)

20) Using division algorithm find the quotients and reminder on dividing 8x4+14x3-2x2+8x-12 by 4x2+3x-2.         (Q=2x2+2x-1  R=15x – 4)

21) The vertices of a triangle are A(3,4), B(7,2),  C(-2,-5).Find the length of median through vertex A.                                                                      (√61)

22) A train covered a certain distance at a uniform speed.If the train would have been 6 km/hr,it would have taken 4 hours less than the sheduled time and if the train were slower by6 km/hour,it would have taken 6 hours more than the sheduled time.Find the length of the journey.                                                                           (720 km)

R

23) In the fig.∆PQR is a right ∆ with PQ=12cm,QR=5cm.A circle with centre O and radius x is inscribed in ∆ PQR.Find the value of x.             (2cm)

P

B

Q

                  

O

C

       

A

 

24) Determine graphically the vertices of a triangle,the equations of whose sides are given below.   

         2y – x =8,    5y – x = 14,   - 2x + 7 = 0.                                  (-4,2), (1,3),(2,5)

25) At the foot of a mountain the angle of elevation of a summit is 450.After ascending 1km towards the mountain up an inclination of 300,the elevation changes to 600.Find the height of the mountain.                                        (1.366km)

                                               SECTION-D

26) A man on the deck of a ship is 12m above the water level. He observes that the angle of elevation of the top of a cliff is 450 and the angle of depression of the base is 300.Calculate the distance of the cliff from the ship and height of the cliff.

                                              (20.784m)                    (32.784m)                                    

27) A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder.The diameter of hemisphere is 14cm and total height of vessel is 13cm.Find inner surface area of vessel.                                                                                       (572cm2)

28) Prove that the tangent at any point of a circle is ┴ to radius through the point of contact. Using this theorem do the following.

Point A is 13cm from the centre of a circle. The length of tangent drawn from A  to the circle is 12cm.Find the radius of the circle.                                  (8cm)

29) From a pointP,2 tangents PA and PB are drawn to a circle with centre O. If OP is equal to diameter of the circle, to the ∆ PAB is equilateral.

B

A

Q

P

O

 

 

 

30) The following table gives the weekly consumption of electricity of 56 families.

 

 

Weekly consumption	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50
No: of families	16	12	18	6	4

 

 

 

      Find the mean.                                                           (20)