Sample Question Paper for class 10 Mathematics (Annual Examination)

 Sample Question Paper for class 10 

Mathematics (Annual Examination)

Pre Board Examination 2020-21

Class – X

Subject – Mathematic  

Time: 3 Hours                                                                                 M: M 80

 

 

General Instructions:       

Question 1- 20 (1 mark), 21 – 26 (2 mark), 27-34 (3 mark),  35-40 (4 mark).

                                                                        Section – A 

Q.1     In an A.P if a = 35, d= 0, n= 101, then a_n = 

(a)       0                      (b)       3.5                  (c )      104.5                         (d)       103.5

Q. 2    At some time, the length of a shadow of a tower is √3 times its height, then the angle 

of elevation of the sun, at that times is …

(a)       15`                  (b)       30`                  (c )      45`                  (d)       60` 

Q. 3    The surface area of sphere is 616cm². Its radius is …..

            (a)       19                   (b)       7                      (c )      -7                    (d)       14 

Q. 4    the number of Zeroes that polynomial f(x) = (x-2)² +4  can have.

            (a)       2                      (b)       1                      (c )      0                      (d)       3

Q. 5    the pair of eq. 2x-3y=1 and 3x-2y=4 has…… solution 

            (a)       one                 (b)       two                 (c )      no                   (d)       many 

Q. 6    if tan ɵ =1 then ɵ = 

            (a)       45`                  (b)       30`                  (c )      135`               (d)       60`

Q. 7    A cube of edge 4cm. is cut in to cubes of side 1cm. then total surface area of all small cube.

            (a)       384cm²                    (b)       316 cm²                  (c )      380 cm²         (d)       388 cm²

            fill in the blanks:

Q. 8    If a line intersects a circle in two distinct points then it is known as a ……..

Q. 9    The two figures having same shape but having same size are called ……. Figures.

Q. 10 If Sin ɵ= Cos ɵ then ɵ = …….

Q. 11 A pair of dice is thrown once. The probability of getting the same number on each dice is ….

Q. 12 find the ratio in which the joining of points (-3,10) and (6, -8) is divided by the point (-1, 6).

Q. 13 Find the area of the quadrant of a circle whose circumference is 44cm.

Q. 14 The areas f two similar triangles are 196cm² and 169cm². If the median of first  triangle in 4cm. find the median of other triangle.

Q. 15 Find the root of quadratic equations x²+5x+6=0 

Q. 16  What is the probability of an impossible event and a sure event.

Q. 17 The list of numbers -10,-6,-2,2 is an A.P. with d=

Q. 18 The class marks of the class 35-55 and 75-95 are _________ and ________

Q. 19 Sin (90-ɵ). Cos ɵ + Cos (90-ɵ). Sin ɵ ______

Q. 20 The line touching the circle at a point is called ______ to a circle.

                                                            Section- B 

Q. 21 Using Euclid’s  division algorithm, find the H.C.F of 252 and 198.

Q. 22 How many terms of the A.P 9, 17, 25,…….. must be taken to give a sum of 636.

Q. 23 If the points A (4,3) and B (x,5) lie on the circle with centre O (2, 3 ). Find the value of x ?

Q. 24 Find the mode of the following data 

Class interval	1-3	3-5	5-7	7-9	9-11
Frequency	14	16	4	4	2

Q. 25 If  tan ɵ = a/b, find                         a Sin ɵ - b Cos ɵ 

                                                                        a Sin ɵ + b Cos ɵ

 

Q. 26 A solid metallic cuboid 18cm X 15cm X 4.5cm is melted and recast into solid cubes what is the edge of cube.

                                                           

Section – C

Q. 27 find the zeroes of the quadratic polynomial x²-2x-8 and verify the relationship between the zeroes  and its coefficients 

Q. 28  Divide 39 into two parts such that their product is 324.

Q. 29 Determine the A.P. whose third term is 16 and the 17^th term exceeds the 5^th term by 12

Q. 30 Construct a triangle similar to       ABC with side BC = 6cm and AB = AC = 4cm such that each of its sides is 3/5 times of the corresponding sides of      ABC.

Q.31 State and prove the Pythagoras theorem.

Q.32   Find the length of the median through the vertex A (5, 1) draw to the triangle ABC, where other two vertices are B (1, 5 ) and C(-3, -1).

Q. 33 Prove that 

            (Sin A + Cosec A)² + (Cos A + Sec A)² = 7 + tan² A + Cot² A.

Q. 34  Find the mean of the following data.

 

Class Interval	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Frequency	2	6	12	16	13	20	5	1	4	1

Section – D

Q. 35 To prove that √3 is an irrational number.

Q. 36 The angle of elevation of the top of a tower from a point on the ground is 45` on walking 30 meters towards the tower the angle of elevation becomes 60`. Find the height of the tower and the original distance from the foot of the tower.

 

Q. 37 Find the area of the shaded region in the given figure. If ABCD is a square of side 20cm and APD and BPC are semicircles. 

Q.38   One curd is drawn from a well shuffled deck of 52 cards. Find the probability of getting 

(i) a king of red colour     

(ii)       a face card              

(iii)      a diamonds             

(iv)      a club 

Q. 39 Solve for x and y 

Q. 40 Prove that opposite sides of a quadrilateral circumscribing a circle subtend 

Supplementary angles at the center of the circle.