Mathematics Class X Model Test Paper
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12/18/2011
CBSE
Section 
A
Question 1 15 carry 2
marks each.
Solve 17x + 31y = 113 and 31x + 17y = 127.
Find the sum and product of the roots of the following equation without actually
solving them. 6x^{2}  11x + 3 = 0.
Write a rational expression whose numerator is a quadratic polynomial with 0 , 2 ,3
and whose denominator is a cubic polynomial with 0 , 2 , 1 , and 4.
Express x^{2}  3x  4 / x^{2}  9 X x^{2} x 6 / x^{2} + 3x +2 as a rational expression.
Find H.C.F of 2x^{3} + 3x^{2} + 3x +1 and 3x^{3} + x^{2} + x  2.
The sides of ( are 25 cm, 17 cm, 12 cm. Find its area and the length of the altitude on the longest side.
A rectangular sheet of area 176 cm^{2} and length 16 cm is rolled along its breadth to make
a hollow cylinder. Find the volume of cylinder.
If V is the volume of a cuboid of dimension a , b , c and s is its surface area , then
prove that : 1 /v = 2 /5 [ 1/a + 1/b + 1/c ].
If 5 tan A = 12. Find value of 2CosA + SinA
SinACosA.
A man goes 15 m west and then 8m due north. Find his distance from starting point.
Prove that any 2 angles in the same segment of a circle are equal.
2 tangent segment BC, BD are drawn to a circle c(o, x) such that ÐDBC = 120^{0}.
Prove that BO = 2BC.
Population of 2 towns are given as 768942 and 609272 respectively and their respective death rates
as 1.56 and 1.28 per 100. Find to the nearest whole number the death rate for the 2 towns taken together.
The mean of 40 observations was 160. It was detected on rechecking that the value 165 was wrongly
copied as 125 for the computation of mean. Find the correct mean.
DABC ~ DDEF. A(D)ABC = 36cm^{2} and A(D)DEF = 64 cm^{2}. If DE = 6.2 cm Find AB.
SECTION 
B.
Question 16  25 carry 4
marks each.
One fourth of a herd of camels was seen in forest. Twice the square root of the
herd had gone to the mountain, and remaining 15 camels were on the bank of
the river. Find the total number of camels.
Solve graphically : 2x  6y = 12. ; 3x  6y = 24.
A page from the pass book of Snehal is given below. Find the interest
for the period Jan to Dec, 99 @ 5% p.a.
DateBalance(Rs.)Jan 21250Feb 6700Mar 32700Mar 103275Nov 41775Dec 44775
If x sin^{3} + y cos^{3} = sinq . cosq
xsinA = y cosA
S.T => x^{2} + y^{2} = 1.
Find the radius of circle of a regular polygon of 18 sides each of length 60 cm.
(cot 10^{0} = 5.671).
State and explain the Basic proportionality Theorem.
Construct a D ABC in which BC = 5 cm. ÐA = 65^{0} & median through A = 3.6 cm.
How many such triangles are possible.
The total surface area of a hollow cylinder which is open from both sides is 4620 cm^{2}
area of base ring is 115.5 cm^{2} and height is 7 cm. Find the thickness of the cylinder.
2 parallel sides of a trapezium are 60 cm and 77 cm, and the other sides are 25 cm
and 26 cm. Find area of the trapezium.
The annual income of Ramlal is 185000(excluding HRA). He contributes Rs.3000/ per month
in his P.F. and pays an annual pre of 32000 towards his LifeInsurance Policy.
Calculate the income tax paid by Ramlal in the last month of the year
if his earlier deduction for first 11 months for income tax were @ Rs. 1000/ per month.
Assume the following for calculating income tax.
a) Standard deduction : 1/3 of total income subject to a max. of Rs. 20000/
b) Rates of income tax .
Slab Tax
i) upto Rs . 50000 10% of amt.exceeding Rs. 50000.
ii) Rs. 50001  Rs. 6000 Rs. 1000 + 20% of the amt. exceeding Rs. 60000/
iii) Rs. 60001  Rs. 150000 Rs. 19000 + 30% of the amt. exceeding Rs. 150000/
iv) Rebate in tax. 20% of the total saving subject to a max. of Rs. 12000/
SECTION 
C
Question 26  30 carry 6
marks each.
Factories a( b  c )^{3} + b ( c  a )^{3} + c ( a  b )^{3} .
If Pragnesh had walked 1 km. Per hour faster then Anurag, Pragnesh would have taken 10 minutes
less to walk 2 km to meet Aarti. Find the rate of Pragnesh walking.
The horizontal distance between 2 towers is 70 m. The angles of depression of the top of the 1^{st}
tower when seen from the top of the second tower is 120 m. Find the height of the 1^{st} tower.
PP^{1} and QQ^{1} are 2 direct common tangents to 2 circles intersecting points A and B.
The common chord produced intersects PP^{1} in R & QQ^{1} in S. Prove that RS^{2} = (PP^{1})^{2} + AB^{2}.
For the given standardized population of a city shown in the table, find the standardized death rate.
Age GroupPopulationNo. of DeathsStandardised Populationunder 10300004502400010  25400001003200025  50300001803000050  804000020020000above 80250002505000