CBSE Class 10 Mathematics Theory (Std) Question Paper 2020 Set 30-2-3

SET – 3
Series : JBB/2
 .
Code No. 30/2/3
 .
   -  - 
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

.30/2/3. 104C 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. x-    P  
  A(–1, 0)  B(5, 0)   ,  :
(a) (2, 0) (b) (0, 2) (c) (3, 0) (d) (2, 2)

2.       (–3, 5)  x –    (reflection) ,  :
(a) (3, 5) (b) (3, –5) (c) (–3, –5) (d) (–3, 5)

3.   P (6, 2),   A(6, 5)  B(4, y)      3 : 1  
  ,  y    :
(a) 4 (b) 3 (c) 2 (d) 1

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

2. 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)

3. 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

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

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

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

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

7. k         x + 2y = 3, 5x + ky + 7 = 0  ,  :
14 2
(a) – (b) (c) 5 (d) 10
3 5

8.   x2 – 0.04 = 0    
(a) + 0.2 (b) + 0.02 (c) 0.4 (d) 2

1 1 – p 1 – 2p
9.   p, p , p
, ……  
   :
1 1
(a) 1 (b) (c) –1 (d) –
p p

10.   a, 3a, 5a, ……  n  
(a) na (b) (2n – 1) a (c) (2n + 1) a (d) 2 na

  11 – 15         1    
11.  1   A  
  O1  O2         _________,
_________.

-1

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

.30/2/3. 4

5. 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

6. 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)

7. 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

8. The roots of the quadratic equation x2 – 0.04 = 0 are
(a) + 0.2 (b) + 0.02 (c) 0.4 (d) 2

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 nth term of the A.P. a, 3a, 5a, …… is
(a) na (b) (2n – 1) a (c) (2n + 1) a (d) 2na

In Q. Nos. 11 to 15, fill in the blanks. Each question carries 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 ABC, AB = 6 3 cm, AC = 12 cm and BC = 6 cm, then B = _________.
OR
Two triangles are similar if their corresponding sides are _________.
.30/2/3. 5 P.T.O.

13.    2 ,  PB = _________ .

-2

14.  3  MN || BC   AM : MB = 1 : 2 , 
ar( AMN)
= _________.
ar( ABC)

-3

15. sin 32° cos 58° + cos 32° sin 58°   _________.

tan 35° cot 78°
+
cot 55° tan 12°
   _________.

  16  20           1    
16.                 ?

17.   –3, –2, –1, 0, 1, 2, 3     x     x2 < 4 
   

       52       ?

18.  sin A + sin2 A = 1    (cos2 A + cos4 A)     
.30/2/3. 6

13. In given Fig. 2, the length PB = _________ cm.

Fig.-2

14. In fig. 3, MN || BC and AM : MB = 1 : 2, then
ar( AMN)
= _________.
ar( ABC)

Fig.-3

15. The value of sin 32° cos 58° + cos 32° sin 58° is _________.
OR
tan 35° cot 78°
The value of + is _________.
cot 55° tan 12°

Q Nos. 16 to 20 are short answer type questions of 1 mark each.
16. A die is thrown once. What is the probability of getting a prime number.

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. If sin A + sin2 A = 1, then find the value of the expression (cos 2 A + cos4 A).

.30/2/3. 7 P.T.O.

19. 6               30  
( = 3.14 )

20.  20 – 50  35 – 60      

 – 
  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.               :
A B C D E A
              (i) A   (ii) D   ?

23.  4     BC     ABC  DBC    AD  BC  O
  ,   
ar ( ABC) AO
=
ar( DBC) DO

-4

 5   AD BC      AB2 + CD2 = BD2 + AC2.

-5
.30/2/3. 8

19. Find the area of the sector of a circle of radius 6 cm whose central angle is
30. (Take  = 3.14)

20. Find the class marks of the classes 20 – 50 and 35 – 60.

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

23. In fig. 4, 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.-4
OR
In fig. 5, if AD BC, then prove that AB2 + CD2 = BD2 + AC2.

Fig.-5
.30/2/3. 9 P.T.O.

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

25.        :
 15 – 20 20 – 25 25 – 30 30 – 35 35 – 40 40 – 45
 3 8 9 10 3 2

26. 14    6              
                  
 
 – 
  27  34     3   

27.      ABC   BC  P         AB 
AC   Q  R    ,    
1
AQ = (BC + CA + AB)
2

28.        22176 2           
` 50        

29.  
  A(3, 4)  B(k, 6)        P (x, y)  
x + y – 10 = 0 ,  k     

 ABC,  A (1, –4)  A        (2, –1)  (0, –1)
,     
30.  6    ABC ~  DEF       ( )    ,
         

-6
.30/2/3. 10

cot2 
24. Prove that 1 + = cosec 
1 + cosec 
OR
Show that tan4 + tan2sec4 – sec2 

25. Find the mode of the following frequency distribution :
Class 15 – 20 20 – 25 25 – 30 30 – 35 35 – 40 40 – 45
Frequency 3 8 9 10 3 2

26. From a solid right circular cylinder of height 14 cm and base radius 6 cm,
a right circular cone of same height and same base radius is removed.
Find the volume of the remaining solid.

Section – C

Q. Nos. 27 to 34 carry 3 marks each.

27. 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

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

29. 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).

30. In Fig. 6, if  ABC ~  DEF and their sides of lengths (in cm) are marked
along them, then find the lengths of sides of each triangle.

Fig.-6
.30/2/3. 11 P.T.O.

 y 
31.  2x + y = 23  4x – y = 19 ,  (5y – 2x)    2      
 x 

1 1 11
x     : – = , x  –4, 7
x + 4 x – 7 30

1 1 3
32.   20, 194 , 182 , 174 , ….         ?

  7, 13, 19, …., 247      

33. 6 .   1.5 .      10 ./        30  
            8     
 ?

cos2 (45° + ) + cos2 (45° – )
34.   : tan (60 + ) tan (30° – ) = 1.

 – 
  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

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

.30/2/3. 12

 y 
31. 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

1 1 3
32. Which term of the A.P. 20, 19 , 18 , 17 , …. is the first negative term.
4 2 4
OR
Find the middle term of the A.P. 7, 13, 19, …., 247.

33. Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of
10 km/h. How much area will it irrigate in 30 minutes, if 8 cm standing
water is required ?

34. Show that :
cos2 (45° + ) + cos2 (45° – )
= 1.
tan (60° + ) tan (30° – )

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.
.30/2/3. 13 P.T.O.

36.       20 .              
  45°  60°        

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

38.    5     

39. 3.5          6       P     -
  

  ABC   ,  AB = 6 , BC = 5   B = 60°    
2
    ,    ABC     3   

40.  ,                   
22
 7 cm      3.5 cm         ( = 7 )
__________

.30/2/3. 14

36. From a point on the ground, the angles of elevation of the bottom and the
top of a tower fixed at the top of a 20 m high building are 45° and 60°
respectively. Find the height of the tower.

37. 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 ?

38. Prove that 5 is an irrational number.

39. Draw a circle of radius 3.5 cm. From a point P, 6 cm from its centre, draw
two tangents to the circle.
OR
Construct a  ABC with AB = 6 cm, BC = 5 cm and B = 60°. Now
2
construct another triangle whose sides are times the corresponding sides
3
of  ABC.

40. A solid is in the shape of a hemisphere surmounted by a cone. If the radius
of hemisphere and base radius of cone is 7 cm and height of cone is 3.5 cm,
22
find the volume of the solid. (Take  = )
7
__________

.30/2/3. 15 P.T.O.

.30/2/3. 16