Sample General Mathematics Question 3 for Class-X

Mymensingh Girls' Cadet College

Subject Code - 109

Progress Test examination-2009

Class-X

Subject : General Mathematics

Time :  3 hrs.                                                                                                                           Marks: 100

1.         If A = { a, b, c } , B = { p, q }, then find A´B and B´A.                                                                    4

Or,       Determine the following sets in Roster method:  { xÎN : x² >15  and x³ < 225}.

2.         Find the solution sets :     =3,  x ¹ -5.                                                                                          4

3.         Answer any three:                                                                                                                               5x3 =15

            a)         If 2x -  = 3, then prove that  8 ()  = 63.

            b)         Resolve into factors :  a³ - 9b³ + (a + b)³

            c)         Find the H. C. F. and  L.C.M of   x² - x ( a -c ) - ac ; x² - x ( a +c) + ac and ax³ - a³ x.

            d)         Salary of Matin is x% higher than that of Jalil. As a result Jalils salary is y% less than that of             Matin. Express y in terms of x.

            e)         Resolve into factors:     2a³ - 3a² + 3a - 1.

4.         Simplify :        7 log  + 5 log   + 3 log   .                                                                                 5

Or,                              Log   + log   + log   - 3log b²c.

5.         If  , then prove that, a, b, c are in continued proportion.                                      5

Or,       If the length of each  side of a square is increased by 10%, then what is the percentage of increase in        the area enclosed by the square?  

           

6.         Solve :                                                          4

           

Or,       The digits in tens place of a number consisting of two digits is twice the digits in the ones place. Show that the number is seven times the sure of the digits.

7.         If  f(y) = ,  then prove that  f (  ) = f (y² ).                                                                      4

Or,       If x ay and y aZ, then show that x² + y² +z² a yz + zx + xy.

8.         By the method of cross multiplication find the solution ( x, y) and verify:

             x - y

             + 2y = 10

Or,       Find the solution ( if there by any) by grafical method of     5x - 3y =10

                                                                                                            10x - 6y = 1

9.         If in a geometric series 1st and 2nd terms are respectively 125 and 25, find the 5th and the 6th term.        5

Or,       If the sum of n -terms of the series 9+7+5+ ............ is -144, then find the value of n.

Answer any two of the following :                                                                                                                 6x2=12

10.       a)         If the square on one side of a triangle is 1 to the sum of the squares on the other two sides, the             angle continued by these two sides is a right angle. Prove it.

            b)         The locus of a point equidistant from two intersecting straight lines is the bisectors of the terminal             angles between the two given straight lines. Prove with your hypothesis.

            c)         The sum of the two opposite angles of a quadrilateral inscribed in a circle is two right angles.              Prove with the help of diagram.

11.       Answer any two :                                                                                                                    4x2= 8

            a)         DABC is a right angled isoceles triangle . P is a point on BC, its hypotenuse, prove that

            PB² + PC² = 2PA². 

            b)         Prove that, three bisectors of the angles of a triangle are concurrent.

            c)         Two circles touches internally at the point P. The chord AB of the greater circle touches the             smaller circle at C. show that, the line PC bisects ÐAPB.

12.       To construct a trapezium when two parallel sides of trapezium and the angles adjacent to the greater side             are given. [ sign of diagram and description is must.]                                                                                    5

Or,       To draw circle inscribed in a triangle [ sign of the diagram and explanation is essential.]

13.       Construct an equilateral triangle whose perimeter are given.                                                                         5

Or,       Draw a tangent to a circle which is parallel to a given straight line.

14.       Prove that :  = = SecA - tan A.                                                                                                 4

Or,       If Sin A + cosA = a and secA + cosesA = b, then prove that b(a²-1) = 2a.

15.       Solve :    2cos²q + 2 sin q = 3.

Or,       If   q = 30⁰,  then show that Cos 3q = 4 cos³q - 3 cosq.

16.       A man standing at a place or the bank of a river of a river observes that the angle of elevation of a tower exactly opposite to him on the other bank is 60⁰. On moving 25 metres. in the backward direction he observed that the angle of elevation of the tower is 30⁰. Find the height of the tower and the width of the river.                        4

Or,       The shadow of a tower on the ground is increased by 44 metres, when the anlge of elevation of the sun is changed from 60⁰ to 45⁰. What is the height of the tower?    

17.       The area, of a rectangular region is 160 sq.m. The region becomes a square if its length is reduced by 6 metres. Find the length and breadth of the rectangular region.                                                                                  4

Or,       The length of the base of an isosceles triangles is 60 cm. If its area is 1200 sq. cm. Find the length of the equal sides.

18.       The outer measurements a rectangular box are 8 cm, 6 cm and 4 cm respectively and the area of the whale inner surface is 88 sq.cm. Find the thickness of the wood.               

Or,       The height of a right circular cylinder and a cone is x and they stand on the same base. If the areas of their curved surfaces are in the ratio 4:3, show that the radius of the base is   .