# Class 10 - Sample Question Paper (Mathematics) II – SA-I

```Class 10 - Sample Question Paper (Mathematics) II – SA-I
Time allowed: 3 hours Maximum marks: 80
General Instructions:
(i)
All questions are compulsory.
(ii)
The question paper consists of 34 questions divided into four sections – A, B, C
and D.
(iii) Section A contains 10 questions of 1 mark each, which are multiple choice type
questions, section B contains 8 questions of 2 marks each, section C contains 10
questions of 3 marks each and section D contains 6 questions of 4 marks each.
(iv) There is no overall choice in the paper.
(v)
Use of calculators is not permitted.
Section – A
Question numbers from 1 to 10 are of one mark each.
1. A composite number has at least ________ factors
a) 1
b) 2
c) 3
d) None
2. If the HCF of 96 and 404 is 4 then its LCM is
a) 6969
b) 9696
c) 9966
d) 6699
3. The remainder when
a)
b) 48
c) –
d)
is divided by
is
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4. If a pair of linear equations has unique solution then the lines are
a) Intersecting lines
b) Parallel lines
c) Coincident lines
d) None of these
5. Two right triangles ABC and DEF right angled at B and E respectively are similar. If
then
a)
b)
c)
d)
6. The maximum value of
a) 0
b) 1
c)
d)
7. If
a)
b)
c)
d)
8. The value of
is
then
√
at
is
a) 1
b) 0
c)
d)
9.
a)
b)
c)
d)
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10. If the mean of 4, 5,
a) 5
b) 15
c)
d)
8, p is 5 then p =
Section – B
Question numbers 11 to 18 carry 2 marks each.
11. Without actually performing the long division, state whether the
will have a
terminating decimal expansion or a non-terminating repeating decimal expansion.
12. Find a quadratic polynomial with √
as the sum and product of its zeroes
respectively.
13. The sum of the digits of a two-digit number is 12. The number obtained by
interchanging the two digits exceeds the given number by 18. Find the number.
d PM re med
PQR, prove that
f r
gle ABC
d PQR re pe
vely where Δ ABC ~ Δ
.
15. Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If
AB = 2CD, find the ratio of the areas of triangles AOB and COD.
16. If
and
√
then find A and B.
17. The mean of 10 observations is 15 and the mean of 15 observations is 10. Find the
mean of 25 observations.
18. Write the formula of median for grouped data and explain each term.
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Section – C
Question numbers 19 to 28 carry 3 marks each.
19. U e Eu l d’ d v
lemm to show that the cube of any positive integer is of
the form 9m, 9m + 1 or 9m + 8.
20. Show that
√ is irrational.
21. Verify that 3, –1,
are the zeroes of the cubic polynomial p(x)
, and then verify the relationship between the zeroes and the
coefficients.
22. Solve the following system of linear equations
graphically and find the area of the region bounded by these lines and the x-axis.
23. State and prove Pythagoras theorem.
24. Prove that the area of an equilateral triangle described on one side of a square is
equal to half the area of the equilateral triangle described on one of its diagonals.
25. Find the mode of the given data:
Age
5 – 15
15 – 25
25 – 35
Number of
8
22
32
patients
26. If tan θ
27. If
35 – 45
26
45 – 55
12
Ev lu e
(
then prove that
28. Find the mean of the following data:
Classes
0 – 19
20 – 39
40 – 59
Frequency
5
18
25
60 – 79
16
)
80 – 99
6
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Section – D
Question numbers 29 to 34 carry 4 marks each.
29. If the sum of the squares of zeroes of the polynomial
is
6
findthe
value of k.
30. Solve for x and y
[

]
[

]

;

31. In an equilateral triangle ABC, D is a point on side BC such that BD = BC. Prove
32. Two ships are sailing in the sea on the either side of the light house, the angles
of depression of two ships as observed from the top of the lighthouse are 60°
and 45° respectively. If the distance between the ships is
height of the lighthouse.
33. If e
√
√
, find the
then show that
34. In a talent test conducted by a trust, 1000 students appeared and the marks
scored by them are given in the following distribution table. Draw an ogive and
use it to answer the following :
a) Find the median.
b) How many students scored less than or equal to 45 marks
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