Mathematics Class X Model Test Paper

12/18/2011 CBSE


Section -
A


Question 1 -15 carry 2
marks each.


  1. Solve 17x + 31y = 113 and 31x + 17y = 127.

  2. Find the sum and product of the roots of the following equation without actually 
    solving them. 6x2 - 11x + 3 = 0.

  3. 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.

  4. Express x2 - 3x - 4 / x2 - 9 X x2 -x -6 / x2 + 3x +2 as a rational expression. 

  5. Find H.C.F of 2x3 + 3x2 + 3x +1 and 3x3 + x2 + x - 2.

  6. The sides of ( are 25 cm, 17 cm, 12 cm. Find its area and the length  of the altitude on the longest side.

  7. A rectangular sheet of area 176 cm2 and length 16 cm is rolled along its breadth to make 
    a hollow cylinder. Find the volume of cylinder.

  8. 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 ].

  9. If 5 tan A = 12. Find value of 2CosA + SinA 
    SinA-CosA.

  10. A man goes 15 m west and then 8m due north. Find his distance from starting point.

  11. Prove that any 2 angles in the same segment of a circle are equal.

  12. 2 tangent segment BC, BD are drawn to a circle c(o, x) such that ÐDBC  = 1200. 
    Prove that BO = 2BC.

  13. 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.

  14. 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.

  15. DABC ~ DDEF. A(D)ABC = 36cm2 and A(D)DEF = 64 cm2. If  DE = 6.2 cm Find AB.

SECTION -
B.


Question 16 - 25 carry 4
marks each.


  1. 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.

  2. Solve graphically : 2x - 6y = 12. ; 3x - 6y = 24.

  3. A page from the pass book of Snehal is given below. Find the interest 
    for the period Jan to Dec, 99 @ 5% p.a.

    Date
    Balance(Rs.)
    Jan 2
    1250
    Feb 6
    700
    Mar 3
    2700
    Mar 10
    3275
    Nov 4
    1775
    Dec 4
    4775


  4. If x sin3 + y cos3 = sinq . cosq
    xsinA = y cosA
    S.T => x
    2 + y2 = 1.

  5. Find the radius of circle of a regular polygon of 18 sides each of length 60 cm. 
    (cot 10
    0 = 5.671).

  6. State and explain the Basic proportionality Theorem. 

  7.  Construct a D ABC in which BC = 5 cm. ÐA = 650 & median through A = 3.6 cm.
    How many such triangles are possible.

  8. The total surface area of a hollow cylinder which is open from both sides is 4620 cm2 
    area of base ring is 115.5 cm2 and height is 7 cm. Find the thickness of the cylinder.

  9. 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.

  10. 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.


  1. Factories a( b - c )3 + b ( c - a )3 + c ( a - b )3 .

  2. 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.

  3. The horizontal distance between 2 towers is 70 m. The angles of depression of the top of the 1st 
    tower when seen from the top of the second tower is 120 m. Find the height of the 1
    st tower.

  4. PP1 and QQ1 are 2 direct common tangents to 2 circles intersecting points  A and B.
    The common chord produced intersects PP
    1 in R & QQ1 in S. Prove that RS2 = (PP1)2 + AB2.

  5. For the given standardized population of a city shown in the table, find  the standardized death rate.

    Age Group
    Population
    No. of Deaths
    Standardised Population
    under 10
    30000
    450
    24000
    10 - 25
    40000
    100
    32000
    25 - 50
    30000
    180
    30000
    50 - 80
    40000
    200
    20000
    above 80
    25000
    250
    5000


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