(Paper) Class X Math Sample Test Paper
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Class X Math Sample Test Paper
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 - sin
)(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)
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)
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 |
No tax |
| (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.