# CBSE Sample Paper for Class 10 Maths

In this section, We have provided the latest sample paper for class 10 maths for the preparation of the final cbse board exams. Question has been taken from all the topics and as per exam syllabus ( CBSE Syllabus ). Still if it contains any error please do let us know. Please give your valuable feedback through the comment sections, Any type of suggestions will be highly appreciated.

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**Scheme of Examination**

Full Marks : 80

Time : 3 Hrs

Subject : Mathematics

**1) **Two coins are tossed simultaneously. Find the probability of getting at least one head.

**2)** All the three face cards of spades are removed from a well shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting (a) a black face card, (b) a queen, (c) a black card.

**3) **While boarding an areoplane, a passenger got hurt. The pilot showing promptness and concern, made arrangements to hospitalise the injured and so the plane started late by 30 minutes. To reach the destination, 1500 km away, in time, the pilot increased the speed by 100 km/hour. Find the original speed/hour of the plane. Do you appreciate the value shown by the pilot, namely, promptness in providing help to the injured and this effort to reach in time?

**4) **Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

Use the above for the following :

If the areas of two similar triangles are equal, prove that they are congruent.

**5) **The numerator of a fraction is one less than its denominator. If three is added to each of the numerator and denominator, the fraction is increased by * * . Find the fraction.

**6)** Draw a pair of tangents to a circle of radius 4 cm. Which are incline to each other at an angle of 60%?

**7) **A hemispherical bowl of internal diameter 36 cm is full of some liquid. This liquid is to be filled in cylindrical bottles of radius 3 cm and height 6 cm. Find the number of bottles needed to empty the bowl.

**8) ** A container open at the top and made up of metal sheet is the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the cost of metal sheet used the container, if it coast Rs 10 per 100 sq cm.

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

**10) **The 19th term of an AP is equal to three times its sixth term. If ii term is 19, find the AP.

**11) **For what value of k will the following system of linear equations have an infinite number of solutions : 2x + 3y = 2; (k + 2)x + (2k + 1)y = 2(k – 1) ?

**12) **What will be the ratio of perimeters of a square and a circle if their areas are equal?

**13) **Find the mean of the following distribution:

Class | Frequency |

0-10 | 8 |

10-20 | 12 |

20-30 | 10 |

30-40 | 11 |

40-50 | 9 |

**14)** A ceiling fan is marked at Rs. 970 cash or for Rs. 210 as cash down payment followed by three equal monthly installments of Rs. 260. Find the rate of interest charged under the installment plan.

**15) ** The length of the minute hand of a clock is 14 cm. Find the area swept by the minute band in 5 minutes

**16) **The salary of Hukam Singh is Rs. 42,000 per month (exclusive of HRA). He donates Rs. 30,000 to Prime Minister’s Relief Fund (100% exemption). He contributes Rs. 6,500 per month towards Provident Fund and Rs. 5,000 quarterly towards LIC premium. He also purchases NSC worth Rs. 10,000. He pays income tax of Rs. 5,100 per month for 11 months. Calculate the income tax he has to pay in the 12th month of the year.Use the following to calculate income tax :

(a) Savings 100% exemption for permissible savings upto Rs. 1,00,000

(b) Rates of Income tax lab Income tax

i. Upto Rs. 1,00,000 No tax

ii. From Rs. 1,00,001 to Rs. 1,50,000 10% of the taxable income exceeding Rs. 1,00,000

iii. From Rs. 1,50,001 to Rs. 2,50,000 Rs. 5,000 + 20% of the amount exceeding Rs. 1,50,000

iv. Rs. 2,50,001 and above Rs. 25,000 + 30% of the amount exceeding Rs. 2,50,000

(c) Education Cess 2% of Income tax.

**17)** A box contains 5 red balls, 4 green balls and 7 white balls. A ball is drawn at random from the box. Find the probability that the ball drawn is

(a) white.

(b) neither red nor white.

**18)** A loan of Rs. 2550 is to be paid back in two equal half-yearly installments. How much is each installment if interest is compounded half-yearly at 8% per annum.

**19)** In an A.P., the sum of its first n terms is n^{2}+2n. Find its 18^{th} term.

**20)** A card is drawn at random from a well shuffled pack of 52 cards. Find the probability that the card drawn is neither a red card nor a queen.

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