(Paper) Class X Math Sample Test Paper

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Class X Math Sample Test Paper

 Section A 

Q1) Find the value of k for which the system of equations has no solution :
 3x - 4y + 7 = 0
kx + 3y - 5 = 0 (Marks 2)


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

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

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

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)

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)

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

Q8) Simplify : (1 + tan2 )(1 - sinThita )(1 + sin ) (Marks 2)

Q9) Prove that : sin /(1 - cos ) = cosec + cot . (Marks 2)

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)

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 = 110o, find APB and ABQ. (Marks 2)

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)

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

 

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


Section-B 

 

Q16) Solve for the following system of equations graphically :
 2x + y - 3 = 0
2x - 3y - 7 = 0 (Marks 4)

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

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)

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

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)

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)

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)

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


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

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

 Section C

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

 

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)

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)

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)

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
(c) 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.

 

Exam Paper
Maths
Class-10