SAMPLE PAPER- 2010
CLASS – X th
MATHEMATICS
SECTION A (40 MARKS )
Answers all questions.
1.(a) The polynomial kx3+3x2+8 when divided by x-2 leaves a remainder which
is double the remainder left by the polynomial x2-10x + 2k when divided
by x-2 . Find the value of k. (3)
(b) Given X =
, Y=
(i) Find a matrix Z such that X + Z is a zero
, Y= (i) Find a matrix Z such that X + Z is a zero matrix.
(ii) Find the matrix M such that X + M = X.
(iii) Find XY. (4)
(c) A piece of butter 3cm by 5cm by 12 cm is placed in a hemispherical bowl of
radius 3.25 cm. Will the butter overflow when it melts completely . (3)
2. (a) If x2, 4 and 9 are in continued proportion , find the value of x. (3)
(b) Find the equation of a line that passes through (1,3) and is parallel to the
line y= -3x + 2. (3)
(c) On a map drawn to a scale of 1: 125,000, a triangle plot of land has the
following measurements: AB = 10cm, BC = 8cm, Ð ACB = 90° . Calculate
(i) The actual length of AB in Km. (ii) the area of the lot in square
kilometers. (4)
3. (i) Calculate the mean , median and mode of the following numbers : 12, 11,
10. 11, 12, 13, 14, 13, 15, 13. (3)
(ii) If 
, prove that 
. (3)
, prove that . (3) (iii) If cos A= 
and cos B =
, evaluate (i) cosec2 A (ii) cot A + cot B. (4)
and cos B =, evaluate (i) cosec2 A (ii) cot A + cot B. (4)4. (i) Solve the following inequation and graph the solution on the number line:
2x-5 £ 5x + 4 < 11, xÎ R. (3)
(ii) The price of a T.V set inclusive of sales tax of 9% is Rs. 40,221. Find the
marked price. (3)
(iii) Komal deposited Rs. 1,500 per month in a bank for 8 months under the
recurring Deposit Scheme .What will be the maturity value of her deposits ,
if the rate of interest is 12% per annum and interest is calculated at the
end of every month. (4)
SECTION B ( 40 MARKS )
Answer any four questions.
5. (a) A,B and T are three points on a circle . The tangent at T meets BA
produced at P. Given that Ð ATB = 32° and that the Ð APT = 78° , calculate
the angle subtended by BT at the centre of the circle. (3)
(b) Write down the equation of the line whose gradient is 4/3 and which
passes through P, where P divides the line segment joining A ( -2, -3) and B
(5,4) , in the ratio 2:5. (4)
(c) An electric shaver is listed at Rs. 1500 with a discount of 20% . What
additional discount % must be offered to a customer to bring the actual
selling price to Rs. 1080 . (3)
6. (a) Construct a triangle ABC, in which AC= 7cm, BC= 8cm, AB= 6cm. (i) Mark
D, the mid point of BC. (ii) Construct the circle which touches AB at A , and
passes through D. (3)
(b) A man invests Rs. 7500 on buying shares of face value of Rs. 100 each at
a premium of 50% in a company . If he earns Rs. 550 at the end of the year
as dividend, find (i) the number of shares he has in the company. (ii) what is
dividend percentage per share . (4)
(c) Show that 
(3)
(3) 7. (a) Use graph paper for this question. Plot the points A(8,2) and B(6,4) .
These two points are the vertices of a figure which is symmetrical about x=6
and y= 2. Complete the figure on the graph . write down the geometrical
name of the figure. (3)
(b) From a window A, 15m above the ground , the angle of elevation of the top
C of a tower is x° , where tan x = 5/2 and the angle of depression of the foot
D of the tower is y° , where tan y = ¼ . Calculate the height CD of the tower
in meters. (4)
C
B 
D
D ( c) Solve y - 
=2 (3)
=2 (3) 8. (a) The perimeter of a rectangular plot is 180m and its area 1800 m2 . If the
length is x m, express the breadth in terms of x . Hence , form an equation in
x. Solve the equation and find the length and the breadth of the rectangle. (3)
(b) Draw the graphs of 3y=12-2x and 2x-3y=4. Write down the co-ordinates of
the point of intersection. Take 2cm = 1 unit on both the axes. (3)
(c ) The I.Q of 50 people was recorded as follows:
I.Q 80-90 90-100 100-110 110-120 120-130 130-140
No. of people 6 9 16 13 4 2
Draw a histogram for the above data and estimate the mod. (4)
9. (a) A circular garden has a circumference of 440m . It is surrounded by a
circular path which has been built at the cost of Rs. 63,756 at the rate of Rs.
6 per sq m. Find (i) the area of the path (ii) the radius of the outer circle. (3)
(b) A manufacturer produces a good which cost him Rs.500. He sells it to a
Wholesaler at a price of Rs.500 and wholesaler sells it to retailer at a price
of Rs.600. The retailer sells it to the customer at a price of Rs.800. If the
sales tax charged is 5%. Find the tax charged under VAT by :
(i) manufacturer, (ii) wholesaler and (iii) retailer. Find the tax paid by the
customer (4)
(c) The centre of a circle is (x + 2, y – 1).Find x and y if end points of diameter
are (2, - 2) and (8, - 2). Hence find the radius. (3)
10.(a) If 2 sin A – 1 = 0, show that : sin 3A = 3 sin A – 4 sin3 A. (3)
(b) The total amount collected for the picnic by certain number of students is Rs. 19,200. If there were 10 more students , the amount each student had to pay would have been reduced by Rs. 160. find the total number of students attending picnic. (3)
(c) A bag contains 5 red , 4 black and 7 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is
(i) black (ii) black or white , (iii) not red. (4)
11. (a) Mr. Aggarwal had a Saving Bank Account in a bank. His passbook had the following entries :
| Date 2009 | Particulars | Withdrawals (in Rs.) | Deposits (in Rs.) | Balance (in Rs.) |
| Jan. 21 | By cash | − | 500 | 500.00 |
| Mar. 18 | To cheque | 100.00 | − | 400.00 |
| May 22 | By cheque | − | 1,500.00 | 1,900.00 |
| July 28 | To cash | 200.00 | − | 1,700.00 |
| Sept. 03 | By cash | − | 1,300.00 | 3,000.00 |
He closes the account on 30th Oct. 2009 Calculate the amount he received if the rate of interest is 6% p.a. (3)
(b) The perpendicular AD on the base BC of 
ABC intersects BC in D such that BD = 3 CD. Prove that 2 AB2 = 2 AC2 + BC2 (3)
ABC intersects BC in D such that BD = 3 CD. Prove that 2 AB2 = 2 AC2 + BC2 (3)(c) Alok invests Rs. 12800 for three years at the rate of 10% per annum compound interest. Find :
(i) The sum due to alok at the end of the first year.
(ii) The interest he earns for the second year.
(iii) The total amount due to him at the end of the third year. (4)
(ii) The interest he earns for the second year.
(iii) The total amount due to him at the end of the third year. (4)
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