MATHS PAPER OF STD 10

                             MATHS PAPER OF STD 10

                                    BY: – MEET K. DAVE

 

SECTION – A

1. Write a quadratic equation whose roots are 3+Ö3 and 3-Ö3.
2. Show that any positive odd integer is of the form 4q+1 or 4+3, where q is some integer.
3. If tanB = ¾, and A+B = 90°, then find the value of cotA.
4. If the zeros of the polynomial f(x) =x³-3x²+x+1 are (a-b) , a and (a+b)  find the value of and b.
5. A cylinder, a cone and a hemi-sphere have equal base and same height. What is the ratio of their volumes?
6. Give an example of polynomial p(x), g(x), q(x) and r(x), satisfying

      P(x) = g(x).q(x) + r(x), deg r(x) = 0

1. A die is thrown once. What is the probability of getting an even prime number?
2. Find the 20^th term of the sequence -2, 0, 2, 4 ————.
3. Find the perimeter of the sector whose base radius is 14 cm and central angle is 120°.
4.  For what value of ‘k’ the following pair of linear equations has infinitely many solutions?

      10x + 5y – (k-5) = 0 and 20x + 10y – k = 0.

                                                    

 

SECTION – B                                    [2marks each]

 

Q11.    Prove that unit place digit of 6ⁿ cannot be zero.

Q12.    Find the value of ‘k’ for which the points (8,1), (k, 4), (2, –5) are collinear.

Q13.    Two AP’s have the same common difference. The difference between their 100^th terms is 100, what is difference between 100000^th terms?

Q14.    Find the value(s) of ‘k’ for which ky(y–2) + 6 = 0 has two equal roots.

Or

Find the real roots of the equation 4x² +3x+5 = 0 by the method of completing square.

Q15.    If A, B, and are interior angles of a triangle ABC, then show that sin

 

SECTION C

 

1. Find the HCF of  426 and 576 using Euclid’s division algorithm

OR

      Prove that no number of the type  be perfect square

1. m and n are zeros of  . Find the values a and c   if
2. Draw the graph of  and  and show that there is a unique solution .Calculate the area bounded by these lines and x-axis
3. A polygon has 10 sides .The lengths of the sides starting with the smallest form an AP .If the perimeter of the polygon is 420 Cm and the length of the longest side is twice that of the shortest side .Find the first term and the common difference of the AP
4. Prove that

OR

      Prove that  , Using the identity

 

 

1. Observe the graph and state whether the quadrilateral ABCD is a parallelogram .Justify your answer .

 

 

 

 

 

 

 

 

 

 

 

 

1. Find the area of the triangle formed by joining the mid points of the sides of the sides of triangle whose vertices are
2. Draw a triangle ABC with side  ,  then  construct a triangle whose sides are  times the corresponding sides of
3. Prove that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle

 

 10. Define:-altitude,median,adjacent side.

 

 

 

 

 

 

 

 

 

 

                                                            SECTION- D

 

26.  In Birla auditorium the number of rows was equal to the number of seats in each row. When the number of rows was doubled and the number of seats in each row was   reduced by 10, the total no. of seats increased by 300. How many rows were there?

 

27 Two pillars of equal height stand on either side of a roadway which is180 m wide   From a point on the roadway between the pillars, the angles of elevations of the top of the pillars are 60˚ and 30˚. Find the height of the pillars and the position of the point.

 

                                                                                   

                                               

                                                                                                                                                                                

           28. State and prove the converse of Pythagoras theorem. Using it prove that triangle PQR is right angled if QS² =PS×SR and QS⊥PR.

 

29. Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level will rise by 21cm.

                                                                 

 

                                         

30. For the following frequency distribution draw the less than give and using it find the median.

 

Marks obtained	50-60	60-70	70-80	80-90	90-100
No. of students	4	8	12	6	6

                                             

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