# CBSE Maths Sample Paper for Class 10

Central Board of Secondary Education conducts Board Exams every year in the month of March. To get excellent marks every appearing students need to prepare well before the day of exam. Thus for this purpose, here in this section you will find out **CBSE Maths Sample Paper for Class 10** for better preparation of Board Examination. Choice of questions are made as per the latest Board pattern to get students idea of type of questions asked in the exam. So practice well and secure good marks. For more help you can also take help from **Chemistry **and** ****Maths Formulas **for more practice.

**CBSE Sample Paper for Class 10 Maths**

Class X Duration: 3 Hour Marks: 80 Marks

**General Instructions:**

**a)** This paper consist of three sections i.e: A,B and C.

- Section-A: Question 1 to 10
- Section-B: Question 11 to 20
- Section-C: Question 21 to 25

**b)** All questions are compulsory.

**Section-A[ 30 marks]**

**1)** If the point C (1, 2) divides internally the line segment AB in the ratio 3 : 4, where the coordinates of A are (2, 5), find the coordinates of B.

**2)** Find the value of a and b so that the polynomials p(x) and q(x) have (x + 1)(x – 2) as their HCF. p(x) = (x2 + 3x + 2)(x2 + x + a) q(x) = (x2 – 3x + 2)(x2 – 3x + b).

**3)** Draw a circle of radius 5.5 cm. At a point A on it,draw a tangent to the circle without using the centre.

**4)** Three consecutive vertices of a parallelogram are (2,1);(1,0) and (4,3).Find the coordinates of the fourth vertex.

**5)** An integer is chosen from 1 to 50 at random. Find the probability that the number is:

(i) Divisible by 5

(ii) A perfect cube

(iii) A prime number.

**6)** A bay has a toy which is in the form of a cone mounted on a hemisphere with the same radius. The base diameter of the conical portion is 6 cm and the total height of the toy is 15 cm. Find the volume of the toy.

**7)** The annual income of Sheena (excluding HRA) is Rs. 1,50,000. She contributes Rs. 4000/-month to her mother fund and pays a half yearly insurance premium of Rs. 4000. Calculate the income tax along with surcharge Shenna has to pay in the last month of the year if her earlier deductions as income tax for the first 11 months were at rate is of Rs. 200/- month.

**(a)** Standard Deduction 2/3 of the total income subjected to a max. of Rs. 10,000

**(b)** Rates of Income tax Slab

(i) Upto Rs. 40,000

(ii) From Rs. 40,001 to 50,000

(iii) From Rs. 50,001 to Rs. 1,40,000

**(c)** Rebate in Tax 10% of the total savings subject to a max. value of Rs. 11,000

**(d)** Surcharge 20% of the tax is payable

**8)** A part of monthly charges in a college are fixed and the remaining depends on the number of days one has taken food in the mess. When a student S takes food for 10 days, he has to pay Rs. 500 as charges where as a student S’, who takes food for 13 days, pays Rs. 5900 as charges. Find the fixed charge and the cost of food per day.

**9)** The slant height of a frustum of a cone is founded as 4 cm. If the difference between the radii of its two circular ends is 2 cm, find the actual height of present frustum.

**10)** Write all the values of k for which the quadratic equation 2×2+kx+8+0, has equal roots. Also find roots.

**Section-B[30 marks]**

**11)** If the points A (4, 3) and B(x, 5) are on the circle with the centre O (2, 3), find the value of x.

**12)** The product of a two digit number is 18. If 5 is added to the number, both the digits interchange their places then Find the numbers.

**13)** Find the locus of centers of circle which touch two interesting lines.

**14)** For what value of p are 2p, p + 10 and 3p + 12 in A.P.?

**15)** Evaluate without using trigonometric table: cos 75o/sin 15o + sin 12o/cos 78o – cos 18o/sin 72o

**16)** Find the value of a for which the system of equation 8x + 5y = 9, ax + 10y = 15 has unique solution.

**17)** Draw a pair of tangents to a circle of radius 5 cm. Which are incline to each other at an angle of 60%?

**18)** All the three face cards of spades are removed from a well shuffled pack of 52 cards. A card is then drawn at random then find the probability of getting

(a) a red face card,

(b) a king,

(c) a diamond queen.

**19)** Find the area of the quadrilateral whose vertices are taken in order (–4, –2), (–3, –5), (3, –2) and (2, 3)

**20)** When tangents are drawn at the ends of a diameter of a circle become parallel. Name the theorem and prove it.

**Section-C[25 marks]**

**21)** A quadrilateral PQRS is drawn to circumscribe a circle. Prove that PQ+RS=PS+QR.

**22)** Draw a triangle ABC with side BC = 6 cm AB = 5 cm and / ABC = 600 , then construct a triangle whose sides are ¾ of the corresponding sides of the triangle ABC.

**23)** A bus travels 150 km at a uniform speed. If its speed is increased by 4 km per hour then it would take half hour less to complete the same journey. Find the speed of bus.

**24)** **(a)** The height of a right triangle is 5 cm less than its base. If the hypotenuse is 12 cm, find the remaining sides.

**(b)** How many multiples of 5 lie between 20 and 300.

**25)** Two coins are tossed one after other. Find the probability of getting at least one tail.

**For pdf of CBSE Maths Sample Paper for Class 10, follow: **

**Related links for CBSE Sample Papers for Class 10 :**

**Mathematics:**

**Sample Paper of Mathematics for Class 10th****CBSE Sample Paper for Class 10 Maths****Maths Sample Paper for Class 10**

**Science:**

**CBSE Sample Papers for Class 10 Science****Sample Papers for Class 10 Science****CBSE 10th Science Model Question Paper**

**Other:**

**CBSE Sample paper for English Class 10****Sample Paper of Class 10 Social Science****Foundation of IT CBSE Class X Sample Papers**

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