Sample General Mathematics Question 5 for Class-X

              Class : X

Time : 2.5 hrs.                                                                                                Full marks: 75

1.      If P , Q & R are be the subsets of the universal set U , Then prove that ,

                                                               or

Prove that ,     A ×  = ( A × B)  ( A×C) .

2. Answer any two .                                                                                           3×2 = 6

  a) Factorise , (x + y + z) (xy + yz + zx) – xyz

  b) If  a^-3 + b^-3 + c^-3 = 3(abc)^-1 , then prove that ,

      a^-1 + b^-1 + c^-1 =0 or a^-1 = b^-1 = c^-1 

  c) Simplify , …… 

3. If S  then prove that , S = N ,                            4

                                                               or

  Prove by Mathematical Induction Formula , 

a + ar + ar² + ar³ +………+ ar^n-1 =

4.         If a² + 2 = ; then prove that   3a³ + 9a – 8 = 0              5

                                                  or

If a^(3-x).b^5x = a^(5+x).b^3x  ; then prove that , xlog_k = log_ka     

5.         Findout the domain & range of F(x) = (1 – x)²  & prove that F(x) is one -one or not ?                                                                                 4                                                or

If S = ; then find out from the graph that S is a function or not ?

6.         Solve & verify : 6                                         4

                                                  or

Solve & show the solution set on the number line ; < 0

7.         Solve:  ; .

                                                  or

Sketch the graph of  > 0 & 2x – y – 6  0 ;

8.         Impose a condition on x so that

will have a sum & also find its sum .                                                   4

9.         State & prove that Apolloneous theorem .                              6

                                                   or

State & prove that the Ptolemy’s  theorem .

     10.                  If AD, BE & CF are three medians of the ∆ABC intersects at O then,           prove that  .                               4                                                          or

           In the ∆ABC , AB = AC , AD BC & R be the circum radius of the

          ∆ABC ; then peove that ,  .

P.T.O

::  2  ::

 11.    Draw a triangle where the base , vertical angle & difference of two sides are given . (Sign of construction & description are essential)                             4

Or,    Draw a circle which passes through the two fixed point & whose centre lies on the given st. line .  (Sign of construction & description are essential)

12.     If a , b & c are the position vectors of the point A ,B & C & the point C divides the line AB into m : n then prove that the position vector of C is

c =                                                                                                  4

                                                              or

If AD , BE & CF are the three medians of the ∆ABC then prove that by vector method AD + BE + CF = O ;

13. The volume of a rt. circular cone is V , area of a curved circle S ,radius of a base is r & the semi – vertical angle is Ф ; then prove that , S =     4                                                         or

If the curved surface & the volume of a cylinder are 100 m² & 150 m³      ; then  find its height & radius .

14. Answer any three .                                                                 3 × 4 = 12               a) Define radian angle . Prove that radian is a constant angle .

b) Prove that ,  

c) Prove that cosA - sinA = sinA ; when cosA + sinA = cosA .

d) If tan =   & sin is negative then find the value of

e) Solve : ;              

15.     Find the mean deviation or sketch an curve from the given data :    5

Class Interval	10 - 14	15 - 19	20 - 24	25 – 29	30 - 30	35 - 39
Frequency	8	12	15	11	9	5

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