CBSE TEST PAPER – 2010
Class – X
Subject - Mathematics
Marks: 80 Time: 3hrs
Section - A (10x1=10)
1. Sate the Euclid’s division lemma.
2. The graph of y= f(x) is given below. Find f(x).
Y
X’ -4 -1 2 X
Y’
3. On dividing x2 + 7x + 3 by a polynomial g(x) the quotient and remainder were
x+5 and -7 respectively. Find g(x).
4. What is the nature of roots of the quadratic equation x + 1 = 3?
x
5. In the adjoining figure OACB is a quadrant of a circle with centre O and radius
7cm. If OD = 4cm, find the area of the shaded region
O
D
DD B
C
A
A
6. In ∆ABC, AB = 6 √3, AC= 12cm and BC= 6cm. Find the angle B.
7. Write down the empirical relationship between the three measures of central
tendency.
8. One card is drawn from a well-shuffled deck of 52 cards.
Calculate the proobability that the cards will not be an ace
9. Two tangents TP and TQ are drawn to circle with centre O from an external
point T, and ∟ PTQ = 600, find ∟ OPQ.
10. Find the probability of getting 53 Tuesdays in a leap year.
Section B (5x2=10)
11. How many two-digit numbers are divisible by 7.
12. Evaluate sin700 + tan10 tan40 tan50 tan80
cos 20 2 cos 430 cosec 470
13. In the figure, ABCD is a trapezium in which AB || DC and 2AB = 3CD. Find
the ratio of the areas of ∆AOB and ∆COD.
CCC
D
A
B
O
14. Find the ratio in which the line segment joining the points (6 , 4) and (1 , -7) is
divided by x-axis.
15. Cards numbered 3,4,5,6 ………, 17 are put in a box and mixed thoroughly.
A card is drawn at random from the box. Find the probability that the card
drawn bears
(i) A number divisible by 3 or 5
(ii) A number divisible by 3 and 5.
Section C (10x3=30)
16. Find the zeros of the quadratic polynomial x2 + 7x + 10 and verify the
relationship between the zeros and the coefficients.(OR)
Find all the zeroes of x4 – 5x3 + 3x2 + 15x -18, if two of its zeroes are √ 3 and
-√3.
17. Prove that 7√ 5 is irrational.
(Or)
Explain why 7 x11 x 13 + 13 and 7 x 6 x 5 x 4 x3 x 2 x 1 + 5 are composite
numbers.
18. For which value of k will the following pair of linear equations have no
solution?
3x + y = 1 ; (x-1) 2k – 1(x + y) = 1 – ky.
(Or)
Solve : 6x + 3y = 6xy
2x + 4y = 5xy.
19. Determine the A.P whose 5th term is 15 and the sum of its 3rd and 8th terms
is 34.
(Or)
Find the sum of all three digit numbers which leave the remainder 2 when
divided by 7.
20. Prove that cosA – sinA + 1 = cosecA + cotA
cosA + sinA – 1
21. The line joining the points (2, 1) & (5, -8) is trisected at the points P & Q. If the
point P lies on the line 2x – y +k = 0, Find the value of k.
22. If the points p(x, y) is equidistant from the points A(5, 1) and B(-1, 5),
prove that x = 2.
y 3
(OR)
Show that the points (-3, 2) (1, -2) & (9, -10) can never be the vertices of a
triangle.
23. Draw a pair of tangents to a circle of radius 5cm which are inclines to each
other at an angle of 600.
24. In an equivalateral triangle, prove that three times the square of one side is
equal to four times the square of one of its altitudes.
25. Find the area of the designed region in fig given below between the two
quadrants of radius 7cm each.
Section D (5x6=30)
26. The cost of 5 oranges and 3 apples is Rs 25 and the cost of 3 oranges and 4
Apples is Rs 26 , find the cost of an orange and an apple graphically.
27. In a triangle, if the square on one side is equal to the sum of the squares on
the other two sides, prove that the angle, opposite to the first side is a right
angle. Use the above theorem and prove the following.
In a ∆ABC, AD ┴ BC and BD = 3CD. Prove that 2AB2 = 2AC2 + BC2
(Or)
In an equilateral triangle ABC, D is a point on side BC such that BD = 1 BC.
Prove that 9AD2 = 7AB2. 3
28. A man is standing on the deck of a ship, which is 8cm above of the water
level. He observes the angle of the elevation of the top of the
hill as 60º and the angle of depression of the base of the hill as 30º.
Calculate the height of the hill from the water level.
(Or)
The angle of elevation of the top of a tower from a point A on the ground is
30º. On moving a distance of 20m towards the foot of the tower to a point B,
the angle of elevation increases to 60º. Find the height of the tower.
29. A farmer connects a pipe of internal diameter 20cm from a canal into a
cylindrical tank in her field, which is 10m in diameter and 2m deep. if water
flows through the pipe at the rate of 3km/hr, in how much time will the tank to
be filled?
30. The median of the following data is 28.5.Find the missing frequencies x and
y, if the total frequency is 60
Class interval | Frequency |
0-10 | 5 |
10-20 | X |
20-30 | 20 |
30-40 | 15 |
40-50 | Y |
50-60 | 5 |
(Or)
Verify the relation Mode = 3median – 2 mean from the following data
C.I | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | Total |
Frequency | 5 | 8 | 20 | 15 | 7 | 5 | 60 |
QUESTION NUMBER | ANSWERS |
1 | a = bq+r |
2 | X3+3x2-6x-8 |
3 | X+2 |
4 | Real and distinct |
5 | 24.5 cm2 |
6 | B=90˚ |
7 | Mode=3median-2 mean |
8 | 12/13 |
9 | 30˚ |
10 | 2/7 |
11 | 13 |
12 | 2 |
13 | 9:4 |
14 | 4:7 |
15 | 7/15, 1/15 |
16 | -5,-2 sum=-7 =-b/a product = 10=c/a |
17 |
|
18 | K=2 x=1, y= 2 |
19 | -1,3,7…. ;67404 |
20 |
|
21 | P(4,-5) k= -13 |
22 | AB+BC=CA=12√2 or Area=0 |
23 |
|
24 |
|
25 | 77-49=28cm2 |
26 | (2,5) |
27 |
|
28 | 32m , 10√3m |
29 | 100 mts |
30 | x =8 ,y =7 |
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