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Guess Paper 7

Guess Paper 7 - 2009


Class - X


Subject - Mathematics


 


Time:3hrs                                                                                                                                     Max.Marks:80


 


General Instructions             




  1. All questions compulsory
  2. The question paper consist of thirty questions divided in to 4 sections A,B,C and D. Section A comprises of ten questions of  1 marks each ,Section B comprises of five questions of 2 marks each, Section C comprises of  ten questions of 3 marks each and section D comprises of five questions of 6 marks each
  3. All questions in section A are to be answered in one word , one sentence or as per the exact requirement of the question
  4. there is no overall choice .However internal choice has been provided in one question of 2 marks each ,three question of three marks each and two questions of 6 marks each .You have to attempt only one of the alternatives in all such questions.
  5. In question on construction ,drawings should be neat and exactly as per the given measurements
  6. Use of calculators is not permitted .However you may ask for mathematical tables

 


SECTION A


1.              Given H.C.F ( 306, 657 )  =  9, find L.C.M ( 306, 657 )


2.                       For which value of ‘P’ does the pair of equations has unique solutions.


      4x + Py + 8 = 0


      2x + 2y + 2 = 0


3.              For the polynomial, what is the sum of zeros?


4.         Find the discriminant of the quadratic equation



5.                     Write down the empirical relationship between the three measures of central


           tendency.


6.              One card is drawn from a well-shuffled deck of 52 cards.  Calculate the probability that the card will not be a joker.


7.              If  tan 2A   =   cot ( A – 180 ),  where  2A  is  an  acute  angle,  find the value of A.


8.              Find  the  length  of  the  arc  of  a  circle  with  radius  6cm  if  the  angle of  sector  is 600.


9.              In fig. DE // BC. Find EC.


                          A


                   1.5cm         1cm


                        D             E             


              3cm


                  B                        C


10.              Prove that the tangents drawn at the ends of a diameter of a circle are parallel.


 


SECTION B


 


11.               Find the zeros of the quadratic polynomial x2 + 7x + 10 and verify the                relationship              between the zeros and the coefficients.



A


       R


B


C


Q


 


   O


     P

12.              The adjacent figure PQ||AB and PR||AC Prove that QR||BC.


 


 


 


13.              If maths_linear_image318find the value of maths_linear_image320


14.              The co-ordinates of the mid-point of the line joining the points (3p, 4) and (-2, 2q) are (5, p). Find the values of p and q.


15.              A coin is tossed  three times. Find the probability of getting


                         (a)  atleast two heads


                         (b)  atmost one head


                         (c)  exactly one tail                 


 


SECTION C


16.              Prove that 2+  is irrational.


17.              Draw the graph of x-y+1=0 and 3x+2y-12=0 calculate the area bounded by these lines and x-axis.


18.              Find all the zeroes of x4 – 5x3 + 3x2 + 15x -18, if two of its zeroes are √ 3 and                -√3.


19.              Determine the A.P whose 5th term is 15 and the sum of its 3rd and 8th terms


                     is 34.


20.              In given figure PQR is a right angled triangle with PQ = 12 cm and QR = 5 cm. A circle with centre O and radius x is inscribed in. Find the value of x.


                                                  


21.              Construct a D similar to a given triangle ABC with its sides 7/5 th of the corresponding side of D ABC. It is given that AB= 6cm, angle BC =7 cm, and angle CA = 8cm.Write the steps of contraction also.


22.              If cosθ + sinθ = √2 cosθ , show that  cosθ – sin θ = √2 sinθ


OR


If image820find the value of image822


23.              Determine the ratio in which the points P (m, 6) divides the join of A (-4, 3) and               B (2, 8). Also find the value of m.


24.              Find the value of p for which the points (-1, 3), (2, p) and (5,-1) are collinear.


25.              In given figure, ABCD is a square whose each side is 14 cm. APD and BPC are semicircles. Find   


       the area of the shaded region.


 


 


 


SECTION D


26.              The sum of the digits of two digits number is 9. Also, nine times this number     is twice the number obtained by reversing the order of the digits of the number Find the number.


OR


              A motor boat whose speed is 15km/hr in still water, goes 30km downstream and comes back in a total time of 4 hours 30 minutes. Find the stream


27.              State and prove Pythagoras Theorem. Using it , if ABC is a triangle in which AB = AC and D is any point in BC, Prove that:  AB2--AD2=BD.CD                                                                             


28.              If the angle of elevation of a cloud from a point h              meters above a lake is a and the angle of depression of its reflection in the lake is b, prove that the distance of the cloud from the point of observation is             


                                                                                   


                                                       

 

                                                                                                                                                                      Or                                                           


              From the top of a church spire 96 m high the angles of depression of two vehicles on a road, at the same level as the base of the spire and on the same side of it are x° and y°, where tan x° = 1/4 and tan y° = 1/7. Calculate the distance between the vehicles.


29.              Water flows out through a circular pipe, whose internal diameter is 2cm, at the rate of 0.7m per second into a cylindrical tank, the radius of whose base is 4cm. By how much the water level will rise.


                                                                                    Or


              A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered in to water and its size is such that when it touches the sides, it is just immersed. What fraction of water overflows?


30.              If the median of the distribution given below is 28.5, find the values of x and y.   


      


                      Class:                         0-10     10-20   20-30    30-40   40-50   50-60   total


                      Frequency   :                  5           x         20       15        y           5         60


 


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