CBSE SAMPLE QUESTION PAPER Mathematics (Theory) - Class X (Code C)

 

 

Time : 3 Hours                                                                                                                                        Max. Marks : 80

 

General Instructions :

 

1.         The questions are compulsory.

2.         The question paper consists of thirty questions divided into 4 sections A, B, C and D. Section A comprises of ten questions of 1 mark each, section B comprises of five questions of 2 marks each, section C comprises of ten questions of 3 marks each and section D comprises of five questions of 6 marks each.

3.         All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.

4.         There is no overall choice. However, internal choice has been provided in one question of 2 marks each, three questions of 3 marks each and two questions of 6 marks each. You have to attempt only one of the alternatives in all such questions.

5.         In question on construction, drawings should be neat and exactly as per the given measurements.

6.         Use of calculators is not permitted. However you may ask for mathematical tables.

 

 SECTION – A

 

1.         What do you know about lemma?

2.         The graph y = f(x) is shown in the figure. Write the number of zeros of f(x).

 

3.         For what value of k, the following pair of linear equations has infinitely many solutions?

                        10x + 5y – (k – 5) = 0

                        20x + 10y – k = 0

4.         For what value of k, the equation 2x2 + kx + 3 = 0 have two equal roots?

 

5.         What is the maximum value of     ?

 

6.         If      and A + B = 90°, then what is the value of cos B?

 

7.         Two tangents TL and TM are drawn from an external point T to a circle with centre O, as shown in the figure. If they are inclined to each other at an angle of 150°, then what is the value of Ð LOM?

 

8.         Find the area  of the sector of a circle with radius 4 cm and of angle 30°.

 (Use p = 3.14)

9.         Find the mean of the following distribution:

 

10. When a die is thrown, then what is the probability of getting a number greater than 4?

 

SECTION – B

 

11.       Determine the A.P whose 3rd term is 5 and the 7th term is 9.

12.       Find the distance between the points A (3 sin x, –cos x) and B (–sin x, 3cos x).

13.       If  tan(A+B)=v3  and ; 0° < A + B < 90°; A > B, find A and B.

OR

 

            Prove the identity

 

14.       In the following figure, DE || BC, AD = 2.4 cm, DB = 3.6 cm and AC = 5 cm, Find AE.

 

15.       All cards of ace, jack and queen are removed from a deck of playing cards. One card is drawn at random from the remaining cards. Find the probability that the card drawn is

            (i)  A face card.

            (ii) Not a face card.

 

 

SECTION – C

 

16.       Show that   is irrational.

17.       Solve the following pair of equations by reducing them to a pair of linear equations  and 

 

 

18.       Find the roots of the equation

OR

            Solve ,     x ¹ –2.

 

19.       If the sum of first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.

20.       If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, find the value of p.

21.       Find the value of k if points A(2, 3), B(4, k) and C(6, –3) are collinear.

22.       Prove that

23.       Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculations.

24.       In the following figure,  and         ?1= ?2. Show that ?PQS ~ ?TQR.

 

 

OR

In the given figure, PT touches the circle whose centre is O, at R. Diameter SQ produced meets PT at P. Given ?SPR = xº and ?QRP = yº.

>

 

 

            (i) Prove ?ORS = yº

            (ii) Write down the expression connecting x and y.

25.       In the following figure, ABCD is a square of side 14 cm, with centres A, B, C and D four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.

 

OR

In the following figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region.

 

SECTION – D

 

26.       The ages of two friends Rohit and Mohit differ by 3 years. Rohit’s father Ram is twice as old as Rohit and Mohit is twice as old as his sister Shalini. The ages of Shalini and Ram differ by 30 years. Find the ages of Rohit and Mohit.

OR

            Draw the graphs of the following equations

                        2x – y – 2 = 0

                        4x + 3y – 24 = 0

            Hence, find the area of the region bounded by

                        x = 0, y = 0 and 4x + 3y – 24 = 0.

27.       The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it complementary. Prove that the height of the tower is 6 m.

OR

A man standing on the deck of a ship which is 10 m above the water level, observes the angle of the elevation of the top of a hill as 60° and angle of depression of the base of the hill as 30°, find the distance of the hill from the ship and height of the hill.

28.       Prove that in a right angle triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Using this results, also prove that the perpendicular from the vertex A on the side BC of a DABC intersects BC at point D such that DB = 3CD. Prove that 2AB² = 2AC² + BC².

29.       A circus tent of total height 50 metres is to be made in the form of a right circular cylinder surmounted by a right circular cone. If the height and radius of the conical portion of the tent are 15 m and 20 m respectively. Find the cost of the cloth required, at the rate of Rs. 14 per square metre to make the tent.

30.       If the mean of the following distribution is 19.92, find the missing frequencies f1 and f2.