Cbse class 10 maths sample paper term 2 model 3 - http://cbse.edurite.com/cbse-maths/maths-cbse-class-10.html

1. MATHEMATICS
SAMPLE TEST PAPER (SEMSTER II)
CLASS X
Class:10 Max Mks:80
Time 3hrs No of pages: 3
General Instructions:
Ò All questions are compulsory.
Ò The question paper consists of 34questions divided into four sections - A, B, C and D.
Ò Section - A contains 8 questions of 1 mark each,
Ò Section B is of 12 questions of 2 marks each, Section C is of 8 questions of 3 marks each and
Ò section D is of 6 questions of 4 marks each.
Ò The drawing should be maintained as per the given measurements.
SECTION A
1. If tan ϑ+cot ϑ = 5, then the value of tan2
ϑ+cot2
ϑ is
a) 23 b) 25 c) 27 d) 15
2. π-
15
7 is a
a) a rational number b) an irrational number c)a prime number d) an even number
3. If sin ϑ - cos ϑ = 0 then the value of sin4 ϑ+cos 4ϑ is
a)
1
2 b)
1
4 c)
3
4 d) 1
4. If sec ϑ+tan ϑ= 7 , then sec ϑ- tan ϑ is :
a)
1
7 b) 7 c) 6 d) 49
5. consider the following distribution
The frequency of thee class 30-40 is:
a) 3 b) 4 c) 48 d) 51
6. The height of a tower is 100√3 m. the angle of elevation of its top from a point 100 m away
from its foot is
a)30o
b)45o
c)60o
d)None of these
7. N letter is chosen at random from the letters of the word ‘ASSASSINATION’. Find the
probability that the letter is chosen
a)1/13 b)2/13 c)7/13 d)6/13
8. A cone is cut into 2 parts by the horizontal plane passing through the mid point of its axis, the
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2. ratio of the volumes of the upper part & the cone is
a) 1:2 b) 1:4 c) 1:6 d) 1:8
SECTION B
9. Find the first four terms of the series when first term a = 10 d = 6
10. find the first term of the series when d = 4,a35 = 123
11. Prove that the parallelogram circumscribing a circle is a rhombus.
12. A cubical block of side 9 cm is surmounted by hemisphere . What is the greatest diameter the
hemisphere can have
13. The wicket taken by a bowler in 5 matches are are follows
5 8 10 4 6
14. Prove that the ratio of the ares of two similar triangles is equal to the ratio of the squares of their
corresponding sides.
15. A die is thrown thrice what is the probability of getting a number between 2 and 5
16. If tan(2A)= cot (A-180) where 2A is an acute angel, find the value of A
SECTION C
17. Prove that a10 = a6+4d
18. Draw a circle of radius 5 cm. From a point 6 cm away from its center, construct the pair of
tangents to the circle and measure their angle.
19. Two tangents PA and PB are drawn from an external point P to a circle with center O. Prove that
AOBP is a cyclic quadrilateral.
20.
In the given figure AD ⊥BC and BD =
1
3 CD. Prove that 2AC2
=2AB2
+BC2
21.
solve for x and y
x
a =
y
b ; ax+by = a2
+b2
22. A bag contains lemon flavored candies only , Nanda takes out one candy without looking into
the bag. a)What is the probability of an mango flavored candy b) a lemon flavored candy
23. If the arithmetic mean of the following frequency distribution is 30, find the missing frequency
p:
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3. 24. Prove that (secϑ -tan ϑ)2
=
(1− sinϑ )
(1+ sinϑ )
SECTION D
25. A sum of rs 700 is to be used to give seven cash prizes to students of a school for their overall
academic performance. If each prize is Rs 30 less than its preceding prize, find the value of
each of the prizes.
26. The angle of elevation of top of a building from the foot of the tower is 450
and the angle is
elevation of the top of the tower from the foot of the building is700
. If the tower is 50m high
find the height of the building
27. In the given figure ABC and DBC are two triangles on the same base BC. IfAD intersect BC at
O, show that
(ar △ ABC)
(ar △ DBC ) =
AO
DO
28. A hemispherical tank full of water is emptied at the rate of 7
1
6 liters per second. How much
time will it take to make the tank half empty, if the tank is 5m in radius ? (use π =
22
7 )
29.
If x = r sinA cosC, y= r sinA cosC and Z = r cosA, then prove that x2
+y2
+z2
=r2
30. Draw a more ogive data given below which gives the marks of 100 students.
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