model test paper

           M.M 90                 Math Test Class X                     Time: 3 Hrs

No	nsyQuestions
	General Instructions:  All questions are compulsory. The question  paper consists of 34 questions Question No’s. from 1 to 8 , 1  mark  each, Question No’s. from 9 to 14 , 2  mark  each, Question No’s. from 15 to 24 , 3  mark  each, Question No’s. from 25 to 34, 4 mark each.
1.	Find the co-ordinate of the centroid of the triangle whose vertices are (2, 3), (-4, 6) and (8, 3).
2.	Find the 19th term of AP: 15, 22, 29….
3.	What is the distance of the point (-5, 3) from the origin.
4.	If PQ and PR are the tangents to a circle with center O and radius 4 from point P then find the perimeter of Quadrilateral PQOR. If PQ=11cm.
5.	If one of the root of the quadratic equation           x²-7x+k=0 is 5. Find the value of k.
6.	Find  the distance of the point (2,-3) from the mid point of the line joining (1,4) and (5,3)
7.	What is the probability of having 53 Sunday in a non leap year.
8.	A circle is inscribed in a triangle with sides 8, 15 and 17cm. Find the radius of the circle.
9.	If the points (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of the parallelogram. Find the value of x and y.
10.	A die is tossed then find the probability of getting (i) a Prime no. (ii) a Multiple of 5.
11.	Find the 20th term from the end of AP:5,12,19………….215
12.	A box containing tickets numbered from 11 to 25 find the probability of getting (i) a prime number (ii) a odd number.
13.	Solve the quadratic equation: 9x² - 16x -4=0
14.	Find the co-ordinate of a point on y-axis that is equidistant from the points (4,-3) and (5, 2).
15	Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that

MATHEMATICS MODEL TEST PAPER FOR CLASS X SA2

 

CLASS X MODEL TEST PAPER SA2 FOR MATHEMATICS MAXIMAM MARKS 90

Add caption

X mathematics solutions chapter 1 exercise 1.3

EXERCISE 1.3

1.    Prove that √5 is irrational.

                             Let take √5 as rational number

                        If   a and b are two co prime number and b is not equal to 0.

                                     We can write √5      = a/b

                        Multiply by b both side we get

                                                            b√5     = a

                        To remove root, Squaring on both sides, we get

                                                            5b^2    = a^2    ……………(1) 

      Therefore, 5 divides a^2 and according to theorem of rational number, for any prime number p which is divides a^2 then it will divide a also.

                                    That means 5 will divide a. So we can write

                                                            a          = 5c

                        and plug the value of  a in equation (1) we get

                                                            5b^2    = (5c)^2

                                                            5b^2    = 25c^2

                        Divide  by 25 we get

                                                            b^2/5   = c^2

            again using same theorem we get that b will divide by 5

            and we have already get that a is divide  by 5

            but  a and b are co prime number. so it is contradicting .

                                    Hence √5  is a non rational number    

2.    Prove that 3 + 2√5 is irrational.

       Let take that 3 + 2√5 is a rational number.

      So we can write this number as

                                    3 + 2√5           = a/b

      Here a and b are two co prime number and b is not equal to 0

      Subtract 3 both sides we get

                                    2√5                 = a/b – 3

                                    2√5                 = (a-3b)/b

      Now divide by 2 we get

                                    √5                    = (a-3b)/2b

      Here a and b are integer so (a-3b)/2b is a rational number so √5 should be a rational number But √5 is a irrational number so it contradict the fact   

                                    Hence result is 3 + 2√5 is a irrational number

3. Prove that the following are irrationals:

      (i) 1/√2 (ii) 7√5 (iii) 6 + √2

     

      (i)   Let take that 1/√2  is a rational number.

            So we can write this number as

                                    1/√2                = a/b

            Here a and b are two co prime number and b is not equal to 0

            Multiply by √2 both sides we get

                                    1                      = (a√2)/b

            Now multiply by b

                                    b                      = a√2

            divide by a we get

                                    b/a                   = √2

      Here a and b are integer so b/a is a rational number so √2 should be a rational number But √2 is a irrational number so it is contradict  

                                                            Hence result is 1/√2 is a irrational number

(ii)        Let take that 7√5 is a rational number.

            So we can write this number as

                                    7√5                 = a/b

            Here a and b are two co prime number and b is not equal to 0

            Divide by 7 we get

                                    √5)                  =a/(7b)

      Here a and b are integer so a/7b is a rational number so √5 should be a rational number but √5 is a irrational number so it is contradict  

                                                            Hence result is 7√5 is a irrational number.

(iii) Let take that  6 + √2 is a rational number.

      So we can write this number as

                                     6 + √2            = a/b

      Here a and b are two co prime number and b is not equal to 0

      Subtract 6 both side we get

                                    √2                    = a/b – 6

                                    √2                    = (a-6b)/b

Here a and b are integer so (a-6b)/b is a rational number so √2 should be a rational number But √2 is a irrational number so it is contradict  

                                                            Hence result is 6 + √2 is a irrational number