CBSE Class 10 Mathematics Theory (Std) Question Paper 2020 Set 30-2-2

SET – 2
Series : JBB/2
 .
Code No. 30/2/2
 .
   -  - 
Roll No.   
Candidates must write the Code on
the title page of the answer-book.

 NOTE
(I)       -   (I) Please check that this question
 15   paper contains 15 printed pages.
(II) -         (II) Code number given on the right
   -  -  hand side of the question paper
should be written on the title page
 
of the answer-book by the candidate.
(III)      -  40  (III) Please check that this question
  paper contains 40 questions.
(IV)         (IV) Please write down the Serial
,       Number of the question in the
answer-book before attempting
it.
(V)  -     15   (V) 15 minute time has been allotted to
     -    read this question paper. The
question paper will be distributed
 10.15     10.15  
at 10.15 a.m. From 10.15 a.m. to
10.30     -   10.30 a.m., the students will read
      -  the question paper only and will not
     write any answer on the answer-
book during this period.

 ()
MATHEMATICS (STANDARD)
{ZYm©[aV g‘¶ : 3 KÊQ>o A{YH$V‘ A§H$ : 80
Time allowed : 3 hours Maximum Marks : 80

.30/2/2. 104B 1 P.T.O.

  :
           
(i) -        – , ,    
 -   40        
(ii) -    1  20  20          
(iii) -    21  26  6          
(iv) -    27  34  8          
(v) -    35  40  6          
(vi) -          -     , - 
   , -     , -      
               
(vii)  , ,            
(viii)        

 – 
  1 – 10        1       
1. k         x + 2y = 3, 5x + ky + 7 = 0  ,  :
14 2
(a) – (b) (c) 5 (d) 10
3 5

2.  x2 – 3x – m (m + 3)    :
(a) m, m + 3 (b) –m, m + 3 (c) m, – (m + 3) (d) –m, –(m + 3)

3.         a  b      
q  r    a = bq + r  
(a) 0 < r < b (b) 0 < r < b
(c) 0 < r < b (d) 0 < r < b

4.  196  -        
(a) 3 (b) 4 (c) 5 (d) 2
.30/2/2. 2

General Instructions :
Read the following instructions very carefully and strictly follow them :
(i) This question paper comprises four sections – A, B, C and D.
This question paper carries 40 questions. All questions are compulsory.
(ii) Section A – Question no. 1 to 20 comprises of 20 questions of one mark
each.
(iii) Section B – Question no. 21 to 26 comprises of 6 questions of two
marks each.
(iv) Section C – Question no. 27 to 34 comprises of 8 questions of three
marks each.
(v) Section D – Question no. 35 to 40 comprises of 6 questions of four
marks each.
(vi) There is no overall choice in the question paper. However, an internal
choice has been provided in 2 questions of one mark, 2 questions of two
marks, 3 questions of three marks and 3 questions of four marks. You
have to attempt only one of the choices in such questions.
(vii) In addition to this, separate instructions are given with each section
and question, wherever necessary.
(viii) Use of calculators is not permitted.

Section – A
Question numbers 1 to 10 are multiple choice questions of 1 mark each.
Select the correct option.

1. The value of k for which the system of linear equations x + 2y = 3,
5x + ky + 7 = 0 is inconsistent is
14 2
(a) – (b) (c) 5 (d) 10
3 5

2. The zeroes of the polynomial x2 – 3x – m (m + 3) are
(a) m, m + 3 (b) –m, m + 3 (c) m, –(m + 3) (d) –m, –(m + 3)

3. Euclid’s division Lemma states that for two positive integers a and b,
there exists unique integer q and r satisfying a = bq + r, and
(a) 0 < r < b (b) 0 < r < b
(c) 0 < r < b (d) 0 < r < b

4. The sum of exponents of prime factors in the prime-factorisation of 196 is
(a) 3 (b) 4 (c) 5 (d) 2

.30/2/2. 3 P.T.O.

5.   P (6, 2),   A(6, 5)  B(4, y)      3 : 1  
  ,  y    :
(a) 4 (b) 3 (c) 2 (d) 1
6.       (–3, 5)  x –    (reflection) ,  :
(a) (3, 5) (b) (3, –5) (c) (–3, –5) (d) (–3, 5)
7. x-    P  
  A(–1, 0)  B(5, 0)   ,  :
(a) (2, 0) (b) (0, 2) (c) (3, 0) (d) (2, 2)
8.   a, 3a, 5a, ……  n  
(a) na (b) (2n – 1) a (c) (2n + 1) a (d) 2 na
1 1 – p 1 – 2p
9.   p, p , p
, ……  
   :
1 1
(a) 1 (b) (c) –1 (d) –
p p
10.   x2 – 0.04 = 0    
(a) + 0.2 (b) + 0.02 (c) 0.4 (d) 2
  11 – 15         1   
11.  1   A  
  O1  O2         _________,
_________.

-1
12.  2  MN || BC   AM : MB = 1 : 2 , 
ar( AMN)
= _________.
ar( ABC)

-2
.30/2/2. 4

5. If the point P (6, 2) divides the line segment joining A(6, 5) and B(4, y) in the
ratio 3 : 1, then the value of y is
(a) 4 (b) 3 (c) 2 (d) 1
6. The co-ordinates of the point which is reflection of point (–3, 5) in x-axis
are
(a) (3, 5) (b) (3, –5) (c) (–3, –5) (d) (–3, 5)
7. The point P on x-axis equidistant from the points A(–1, 0) and B(5, 0) is
(a) (2, 0) (b) (0, 2) (c) (3, 0) (d) (2, 2)
8. The nth term of the A.P. a, 3a, 5a, …… is
(a) na (b) (2n – 1) a (c) (2n + 1) a (d) 2na
1 1 – p 1 – 2p
9. The common difference of the A.P. , , , …… is
p p p
1 1
(a) 1 (b) (c) –1 (d) –
p p
10. The roots of the quadratic equation x2 – 0.04 = 0 are
(a) + 0.2 (b) + 0.02 (c) 0.4 (d) 2
In Q. Nos. 11 to 15, fill in the blanks. Each question is of 1 mark :
11. In fig. 1, the angles of depressions from the observing positions O 1 and O2
respectively of the object A are _________, _________.

Fig.-1

12. In fig. 2, MN || BC and AM : MB = 1 : 2, then
ar( AMN)
= _________.
ar( ABC)

Fig.-2

.30/2/2. 5 P.T.O.

13.    3 ,  PB = _________ .

-3
14.  ABC  AB = 6 3 , AC = 12   BC = 6   B   
_________.

    ,     _________  
15. sin 23° cos 67° + cos 23° sin 67°    _________.

  16 – 20       ,    1    
16.  4   10.5 ..            
22
    = 7  

-4

17.   –3, –2, –1, 0, 1, 2, 3     x     x2 < 4 
   

       52       ?
18.                 ?
19.  tan A = cot B ,  (A + B)     
20.  15 – 35  45 – 60      

.30/2/2. 6

13. In given Fig. 3, the length PB = _________ cm.

Fig.-3

14. In ABC, AB = 6 3 cm, AC = 12 cm and BC = 6 cm, then B = _________.
OR
Two triangles are similar if their corresponding sides are _________.

15. The value of sin 23° cos 67° + cos 23° sin 67° is _________.

Q Nos. 16 to 20 are short answer type questions of 1 mark each.

16. In fig. 4 is a sector of circle of radius 10.5 cm. Find the perimeter of the
 22
sector. Take  = 
 7

Fig.-4

17. If a number x is chosen at random from the numbers –3, –2, –1, 0, 1, 2, 3,
then find the probability of x2 < 4.
OR
What is the probability that a randomly taken leap year has 52 Sundays ?

18. A die is thrown once. What is the probability of getting a prime number.

19. If tan A = cot B, then find the value of (A + B).

20. Find the class marks of the classes 15 – 35 and 45 – 60.

.30/2/2. 7 P.T.O.

-
  21 – 26     2   
21.     10              
         
2x + 3, 3x2 + 7x + 2, 4x3 + 3x2 + 2, x2 + 3x + 7, 7x + 7, 5x3 – 7x + 2,
5 1 1
2x2 + 3 – , 5x – , ax3 + bx2 + cx + d, x + .
x 2 x
     :
(i)        ?
(ii)        ?

22.        :
   0 – 4 4 – 8 8 – 12 12 – 16 16 – 20 20 – 24 24 – 28
( )
 5 7 9 17 12 10 6

23.  5     BC     ABC  DBC    AD  BC  O
  ,   
ar ( ABC) AO
=
ar( DBC) DO

-5

 6   AD BC      AB2 + CD2 = BD2 + AC2.

-6

.30/2/2. 8

Section – B
Q. Nos. 21 to 26 carry 2 marks each.
21. A teacher asked 10 of his students to write a polynomial in one variable
on a paper and then to handover the paper. The following were the
answers given by the students :
2x + 3, 3x2 + 7x + 2, 4x3 + 3x2 + 2, x3 + 3x + 7, 7x + 7, 5x3 – 7x + 2,
5 1 1
2x2 + 3 – , 5x – , ax3 + bx2 + cx + d, x + .
x 2 x
Answer the following questions :
(i) How many of the above ten, are not polynomials ?
(ii) How many of the above ten, are quadratic polynomials ?

22. Compute the mode for the following frequency distribution :
Size of items 0 – 4 4 – 8 8 – 12 12 – 16 16 – 20 20 – 24 24 – 28
(in cm)
Frequency 5 7 9 17 12 10 6

23. In fig. 5, ABC and DBC are two triangles on the same base BC. If AD
intersects BC at O, show that
ar ( ABC) AO
=
ar( DBC) DO

Fig.-5
OR
In fig. 6, if AD BC, then prove that AB2 + CD2 = BD2 + AC2.

Fig.-6

.30/2/2. 9 P.T.O.

cot2 
24.    1 + = cosec 
1 + cosec 

  tan4 + tan2sec4 – sec2

25.                :
A A B C C C
             (i) A   (ii) C   ?

26.  ,                 
          ,     
      

 – 
  27  34     3   

27.  7    ABC ~  DEF       ( )    ,
         

-7
28.      ABC   BC  P         AB 
AC   Q  R    ,    
1
AQ = (BC + CA + AB)
2
29.        22176 2           
` 50        

 y 
30.  2x + y = 23  4x – y = 19 ,  (5y – 2x)    2      
 x 

1 1 11
x     : – = , x  –4, 7
x + 4 x – 7 30
.30/2/2. 10

cot2 
24. Prove that 1 + = cosec 
1 + cosec 
OR
Show that tan  + tan2sec4 – sec2
4

25. A child has a die whose six faces show the letters as shown below :
A A B C C C
The die is thrown once. What is the probability of getting (i) A, (ii) C ?

26. A solid is in the shape of a cone mounted on a hemisphere of same base
radius. If the curved surface areas of the hemispherical part and the
conical part are equal, then find the ratio of the radius and the height of
the conical part.

Section – C

Q Nos. 27 to 34 carry 3 marks each.

27. In Fig. 7, if  ABC ~  DEF and their sides of lengths (in cm) are marked
along them, then find the lengths of sides of each triangle.

Fig.-7

28. If a circle touches the side BC of a triangle ABC at P and extended sides AB
and AC at Q and R, respectively, prove that
1
AQ = (BC + CA + AB)
2

29. The area of a circular play ground is 22176 cm2. Find the cost of fencing
this ground at the rate of ` 50 per metre.

 y 
30. If 2x + y = 23 and 4x – y = 19, find the value of (5y – 2x) and   2  .
 x 
OR
1 1 11
Solve for x : – = , x # –4, 7.
x+4 x+7 30

.30/2/2. 11 P.T.O.

31.  
  A(3, 4)  B(k, 6)        P (x, y)  
x + y – 10 = 0 ,  k     

 ABC,  A (1, –4)  A        (2, –1)  (0, –1)
,     

32.       m    n     n    m ,  
    (m + n)    – (m + n)  

     11     ,    30  

33.      600 ..          3  
          ,        10
../  ,        

1
34.  1 + sin2  = 3 sin  cos ,     tan  = 1  2.
 – 
  35  40     4   

35.      18     19 – 21   f    f   
  11 – 13 13 – 15 15 – 17 17 – 19 19 – 21 21 – 23 23 – 25

 3 6 9 13 f 5 4


     100          :
 40 – 45 45 – 50 50 – 55 55 – 60 60 – 65 65 – 70

   4 6 16 20 30 24

   “   ”         
.30/2/2. 12

31. If the mid-point of the line segment joining the points A(3, 4) and
B(k, 6) is P (x, y) and x + y – 10 = 0, find the value of k.
OR
Find the area of triangle ABC with A (1, –4) and the mid-points of sides
through A being (2, –1) and (0, –1).

32. If in an A.P., the sum of first m terms is n and the sum of its first n terms is
m, then prove that the sum of its first (m + n) terms is –(m + n).
OR
Find the sum of all 11 terms of an A.P. whose middle term is 30.

33. A fast train takes 3 hours less than a slow train for a journey of 600 km. If
the speed of the slow train is 10 km/h less than that of the fast train, find
the speed of each train.

1
34. If 1 + sin2  = 3 sin  cos , prove that tan  = 1 or .
2

Section – D
Q. Nos. 35 to 40 carry 4 marks each.

35. The mean of the following frequency distribution is 18. The frequency f in
the class interval 19 – 21 is missing. Determine f.
Class interval 11 – 13 13 – 15 15 – 17 17 – 19 19 – 21 21 – 23 23 – 25
Frequency 3 6 9 13 f 5 4
OR
The following table gives production yield per hectare of wheat of 100
farms of a village :
Production yield 40 – 45 45 – 50 50 – 55 55 – 60 60 – 65 65 – 70
No. of farms 4 6 16 20 30 24

Change the distribution to a ‘more than’ type distribution and draw its
ogive.

.30/2/2. 13 P.T.O.

36.  8         PQ = 24 , PR = 7   O 
   

-8

                20 .
6 .     24 .  

37.    5     

38.       - (swimming pool)  12         
    4          9      
            -    ?

39. 4              60     

  ABC      3 , 4   5      
4
      ABC     5   

40.              30°        
     60°     50 .         
__________

.30/2/2. 14

36. Find the area of the shaded region in fig. 8, if PQ = 24 cm, PR = 7 cm and
O is the centre of the circle.

Fig.-8

OR
Find the curved surface area of the frustum of a cone, the diameters of
whose circular ends are 20 m and 6 m and its height is 24 m.

37. Prove that 5 is an irrational number.

38. It can take 12 hours to fill a swimming pool using two pipes. If the pipe of
larger diameter is used for four hours and the pipe of smaller diameter for
9 hours, only half of the pool can be filled. How long would it take for each
pipe to fill the pool separately ?

39. Draw two tangents to a circle of radius 4 cm, which are inclined to each
other at an angle of 60.
OR
Construct a triangle ABC with sides 3 cm, 4 cm and 5 cm. Now, construct
4
another triangle whose sides are times the corresponding sides of
5
 ABC.

40. The angle of elevation of the top of a building from the foot of a tower is
30° and the angle of elevation of the top of a tower from the foot of the
building is 60°. If the tower is 50 m high, then find the height of the
building.
__________

.30/2/2. 15 P.T.O.

.30/2/2. 16