CBSE Maths Sample Question Paper – Year 96

Maths Class X (CBSE)
You are on Set no 1 Qno. 1 to 20Time allowed : 3 hours
Maximum Marks : 100

General Instructions :

(i) Question number 1 to 15 carry 2 marks each.
(ii) Question number 16 to 25 carry 4 marks each.
(iii) Question number 26 to 30 carry 6 marks each.
(iv) Write the serial number of the question before attempting it.
(v) Use of logarithmic and trignometric tables is permitted. Use of calculator is not permitted.

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Section – AQ1) Find the value of k for which the system of equations has no solution :
3x – 4y + 7 = 0
kx + 3y – 5 = 0 (Marks 2)

Answer
Q2) Find the g.c.d. of the following polynomials :
2x² – x – 1 and 4x² + 8x + 3 (Marks 2)
Answer

Q3) If A = (x + 1)/(x – 1), find A – 1/A in the simplified form. (Marks 2)
Answer

Q4) Form the quadratic equation in x whose roots are 2 + 5 and 2 – 5. (Marks 2)
Answer

Q5) The base radii of two right circular cones of the same height are in the ratio 3 : 5. Find the ratio of their volumes. (Marks 2)
Answer

Q6) A colour T.V. is available for Rs. 13,440 inclusive of sales tax. If the original cost of T.V. is Rs. 12,000 find the rate of sales tax. (Marks 2)
Answer

Q7) Evaluate : cot 54^o/tan 36^o + tan 20^o/cot 70^o – 2 (Marks 2)
Answer

Q8) Simplify : (1 + tan² )(1 – sin )(1 + sin ) (Marks 2)
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Q9) Prove that : sin /(1 – cos ) = cosec + cot . (Marks 2)
Answer

Q10) In Fig. 1, ABC and DEF are similar. The area of ABC is 9 sq.cm and area of DEF is 16 sq.cm. If BC = 2.1 cm, find the length of EF. (Marks 2)

Answer

Q11) In Fig. 2, O is the centre of the circle and AB is a chord of the circle. Line QBS is a tangent to the circle at B. If AOB = 110^o, find APB and ABQ. (Marks 2)

Answer

Q12) In Fig. 3, chords AB and CD intersect at P. If AB = 5 cm, PB = 3 cm and PD = 4 cm, find the length of CD. (Marks 2)

Answer

Q13) Calculate the median of the following data :
83, 37, 70, 29, 45, 63, 41, 70, 30, 54 (Marks 2)

Q14) Find the Crude Death Rate (CDR) for the following data: (Marks 2)

Age group (in years)	Population	Number of Deaths
0 – 10	5000	250
10 – 25	2000	120
25 – 45	8000	150
45 – 70	7000	80
Above 70	3000	250

Answer

Q15) Flow Chart. Omitted being out of Syllabus. (Marks 2)

Section – B
AnswerQ16) Solve for the following system of equations graphically :
2x + y – 3 = 0
2x – 3y – 7 = 0 (Marks 4)
Answer

Q17) Factorise. Omitted, being out of Syllabus. (Marks 4)
Answer

Q18) A man has only 20 paise coins and 25 paise coins in his purse. If he has 50 coins in all totaling Rs. 11.25, how many coins of each does he have? (Marks 4)
Answer

Q19) Divide 29 into two parts so that the sum of the squares of the parts is 425. (Marks 4)
Answer

Q20) The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of 28 cm diameter. Find the length of the wire. (Marks 4)
Answer

Q21) �In a triangle, a line drawn parallel to one side, to intersect the other side in distinct points, divides the two sides in the same ratio”. Prove. (Marks 4)
Answer

Q22) The perpendicular AD on the base BC of a ABC intersects BC at D so that DB = 3CD. Prove that
2AB² = 2AC² + BC² (Marks 4)
Answer

Q23) Find the mean of the following data : (Marks 4)

Class Interval	Frequency
0 – 10	8
10 – 20	10
20 – 30	9
30 – 40	12
40 – 50	11

Answer

Q24) Algorithm. Omitted, being out of Syllabus. (Marks 4)
Answer

Q25) Flow Chart. Omitted, being out of Syllabus. (Marks 4)

Section – C
Answer

Q26) Solve for x :
4(x2 + 1/x2) + 8(x – 1/x) – 29 = 0 (Marks 6)

Answer

Q27) A tower in a city is 150 m high and a multistoried hotel at the city centre is 20 m high. The angle of elevation of the top of the tower at the top of the hotel is 5o. A building, h metres high, is situated on the straight road connecting the tower with the city centre at a distance of 1.2 km from the tower. Find the value of h if the top of the hotel, the top of the building and the top of the tower are in a straight line. Also find the distance of the tower from the city centre.
(Use tan 5o = 0.0875; tan 85o = 11.43) (Marks 6)
Answer

Q28) �The degree measure of an arc of a circle is twice the angle subtended by it at any point of the alternate segment of the circle with respect to the arc.� – Prove. (Marks 6)
Answer

Q29) Construct ABC in which BC = 6 cm, A = 60o and the altitude through A is 4.5 cm. Measure the length of the median through A. Write the steps of construction. (Marks 6)
Answer

Q30) The total salary of Manjeet Singh is Rs. 1,25,500 (excluding HRA) during a year. He pays a premium of Rs. 10,800 annually towards LIC and contributes Rs. 2,000 per month towards G.P.F. Rs. 250 are deducted each month from his salary as income tax. Calculate the income tax Manjeet Singh is to pay in the last month of the financial year. (Marks 6)
Assume the following for calculating income tax :

(a) Standard Deduction	1/3 of the total income subject to a maximum of Rs. 20,000 (Rs. 25,000 if income is less than Rs. 1 lac)
(b) Rates of Income tax Slab (i) Upto Rs. 50,000 (ii) From Rs. 50,001 to 60,000 (iii) From Rs. 60,001 to Rs. 1,50,000	� Income Tax No tax 10% of the amount exceeds Rs. 50,000 Rs. 1,000 + 20% of the amount exceeding Rs. 60,000
� Rebate in Tax	20% of the total savings subject to a maximum of Rs. 12,000
(d) Surcharge	10% of the tax payable

OR
A page from the pass book of Ram Lal�s Saving Bank Account in a particular year is given below :-

Date	Particulars	Amt. Withdrawn Rs.� P.	Amt. Deposited Rs.� P.	Balance Rs.� P.
Jan. 1	By Balance			1200.00
Jan. 5	By Cash		500.00	1700.00
Feb. 20	By Cash		700.00	2400.00
Feb. 25	To Cheque	500.00		1900.00
May, 8	By Cash		1000.00	2900.00
July, 12	By Cash		1500.00	4400.00
July, 20	To Cheque	1000.00		3400.00
Sept. 1	By Cash		1200.00	4600.00
Oct. 5	To Cheque	2000.00		2600.00
Dec. 15	By Cash		500.00	3100.00

Assuming the rate of interest is 5% p.a. and interest is paid once in a year, at the end of December, calculate the interest earned by Ram Lal at the end of the year.

Note: Question done according to the latest syllabus.
Total salary of Manjeet Singh taken as Rs.125,500 in place of Rs.120,500.