CBSE Class 10th Mathematics-Basic
The CBSE Class 10th Mathematics- The exam paper will be of three hours and a total of 80 marks. the paper will consist of 40 questions all divided into four sections.
A, B, C, and D.
Section A: There will be a total of 20
questions in this section. each question will have one Mark.
Section B: This section comprises 6
questions of 2 marks each.
Section C: In this section, there will be
a total of 8 questions of 5 marks each.
Section D: In this section, there will be
a total of 6 questions of 4 marks each.
There is no overall choice. However internal choices have been
provided in two questions of 1 mark each, two questions of 2 marks each, three
questions of 3 marks each and three questions of 4 marks each. You have to
attempt only one of the alternatives in all such questions.
The use of calculators is not permitted.
SECTION
– A
Q 1- 10 are multiple-choice questions. Select the most appropriate answer from the given options.
1. HCF of 168 and 126 is
(a)21 (b) 42 (c) 14 (d) 18
2. The empirical relationship between the three measures of central tendency is
(a)2 Mean = 3 Median – Mode
(b) 2 Mode = 3 Median – Mean
(c) Mode = 2 Mean –
3 Median
(d) 3 Median = 2
Mode +
Mean
3. In the given figure,
if TP and TQ are tangents
to a
circle with center O, so
that
∠POQ
= 110°, then ∠PTQ is.
(a)110° (b) 90° (c) 80° (d) 70°
4. 325 can be expressed as
a product of its primes as
(a)52×7 (b) 52×13
(c) 5×132 (d) 2×32×52
5. One card is
drawn from a well-shuffled deck of
52
cards. The probability that it is
black queen is.
(a)____ (b) ______ (c) _______ (d) _______
6. The sum of
the zeroes
of the polynomial
2x2-8x
+6
is
(a)- 3 (b) 3 (c) - 4
(d) 4
7. Which of the following is the decimal
expansion of an irrational number.
(a)4.561 (b) 0.12 (c) 5.010010001… (d) 6.03
8. The following figure shows the graph of y = p(x), where p(x) is a
polynomial in variable x. The number of
zeroes of the polynomial p(x)
is
(a)1 (b) 2 (c)3 (d) 4
9. The distance of
the
point P (3, - 4)
from the origin is
(a)7 units (b) 5 units
(c) 4 units
(d) 3 units
10. The midpoint of
the line segment
joining the points (- 5, 7) and (- 1, 3)
is
(a)(-3, 7) (b) (-3, 5)
(c) (-1, 5) (d) (5, -3)
(11 – 15)
Fill in the blanks:
11. The point which divides the line segment joining the points A (0, 5) and B (5, 0)
internally in the ratio 2:3 is _____________.
12. The pair of lines represented by the equations
2x+y+3 = 0 and 4x+ky+6 = 0 will be parallel if
value of k is ______.
OR
If the quadratic equation x2 – 2x + k = 0 has equal roots, then value of
k is ______.
13. The value of sin60
cos 30 + sin30
cos 60
is______.
14. Value of
cos 0°. Cos 30° .cos 45° . cos 60° . cos 90° is ___________.
15. The sides of
two
similar triangles are in the ratio 2:3, then the areas of
these triangles are in the ratio ______________
(16-20) Answer the following.
16. △QPR is a right-angled isosceles triangle, right-angled at
R. Find value
of sin P.
OR
If 15 cot
A = 8, then find the value of
cosec A.
17. If the area of a quadrant of
a circle is 38.5 cm2 then find its diameter (use π = )
18. A dice is
thrown once. Find the probability
of getting
a prime number.
19. In the given fig. If DE ‖ BC Find EC.
20. Find the common difference of
the A.P whose first
term
is 12 and fifth
term
is 0.
SECTION – B
21. If two coins are tossed simultaneously. Find the probability of
getting 2 heads.
22. A lot of 25 bulbs contain 5 defective
ones.
One
bulb is drawn at random
from
the lot. What is the probability that
the bulb is
good.
OR
Two dice are thrown simultaneously at random.
Find the probability of
getting a sum of eight.
23. Prove that the tangents drawn at
the ends of a diameter of a circle are
parallel.
24. Show
thattan48 tan23 tan42 tan67 = 1.
OR
Evaluate cos 48 cos 42 − sin48 sin42
25. Find the
area of a circle whose circumference
is 22cm.
26. Read the following passage and answer
the
questions that follow: A teacher told 10 students to write a polynomial on the blackboard.
Students
wrote.
1. x2 + 2 6. x
– 3
2. 2x + 3 7. x4 + x2 + 1
3. x3+ x2 + 1 8. x2 + 2x + 1
4. x3+ 2x2 + 1 9. 2x3 – x2
5. x2 – 2x
+ 1
10. x4 – 1
(i) How many
students wrote cubic polynomial
(ii) Divide the polynomial (x2 + 2x + 1) by ( x
+ 1).
SECTION C
27. Find the
zeroes of the quadratic polynomial x − 3x − 10 and verify
the
relationship between the zeroes
and coefficient.
28. Draw a circle of radius 4 cm.
From point 7 cm away from its center, construct
the pair of tangents to the circle.
OR
Draw a line segment of
length 8 cm and divide it in the ratio 2:3.
29. The following figure depicts a park
where two opposite sides are parallel and
left
and right ends are
semi-circular
in
shape. It
has a 7m wide track for walking.
30. Prove that ________________ =_______________
OR
Prove that: ___________________ = _____________
31. Prove that
5 -
√3 is irrational, given that √3 is irrational.
OR
An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same
number of columns. What is the maximum number of columns in which
they can march?
32. Prove that the lengths of
tangents are drawn from an external
point
to a the circle is equal.
33. Read the following passage and answer the questions that follow:
In a classroom,
four students Sita, Gita, Rita, and Anita are sitting at A(3,4), B(6,7),
C(9,4),
D(6,1) respectively.
Then
a new student
Anjali joins the class.
(i) The teacher tells Anjali to sit in the middle of
the
four students. Find the
coordinates of the position where she can sit.
(ii) Calculate the distance between Sita
and Anita.
(iii) Which two students are equidistant
from Gita.
34. Solve 2x + 3y = 11 and x
− 2y = −12 algebraically and hence find the value of
‘m’ for
which y = mx + 3.
SECTION D
35. Find two consecutive positive integers sum of whose squares is
365.
36. If
the sum of first
14
terms of an
A.P. is 1050 and its first term is 10, find the 20 th term.
OR
The first
term of an
A.P. is 5, the last
term
is 45 and sum
is
400. Find the number of
terms and the common difference.
37. As observed from the top of a 75m high lighthouse above the sea level,
the
angles of depression of two ships are 30O and 45O respectively If one
ship is exactly behind the other on the same side of the lighthouse and in the same straight line, find the distance between the two ships. (use √3 = 1.732)
38. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that
the other
two
sides are divided in the same ratio.
OR
State and prove the Pythagoras theorem.
39. A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness.
Find the thickness of the wire.
OR
A metallic sphere of radius 4.2 cm is melted and recast into the shape of
a cylinder
of radius
6 cm.
Find the height of
the cylinder.
40. The following distribution gives the daily
income of
50
workers
of
a factory
Convert this distribution to less than the type of cumulative frequency
distribution and
draw its ogive.
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